tag:blogger.com,1999:blog-64116243665391303372024-02-19T09:12:40.704-08:00Michael Bench-Capon's BlogMichael Bench-Caponhttp://www.blogger.com/profile/13715068990919309271noreply@blogger.comBlogger130125tag:blogger.com,1999:blog-6411624366539130337.post-13118230317588535632023-12-20T12:50:00.000-08:002023-12-20T12:50:10.474-08:00Santa Baby<p><span style="font-family: verdana;"><span face="Calibri, sans-serif" style="font-size: 12pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; line-height: 1.8; vertical-align: baseline; white-space-collapse: preserve;">Christmas is almost upon us, and as is customary its musical outriders have now been harrying the airwaves for weeks. Among the most lyrically perplexing of these is ‘Santa Baby’, the classic version of which was sung by Eartha Kitt, although it has been covered many times by artists including Taylor Swift, Wolf Alice and (with a significant reworking of the lyrics) Michael Bublé. Ostensibly the song is a love song addressed to Santa, in which someone who has been a faithful partner to him over the past year demands a series of extravagant gifts and then eventually at least the promise of marriage, with the implication that if he doesn’t stump up then their fidelity can no longer be counted upon. It’s possible that it’s not really addressed to Santa, and this is just a seasonal metaphor in line with the demand for gifts in exchange for good behaviour. Either way, what kind of relationship is this? One of the demands is for </span><span face="Calibri, sans-serif" style="font-size: 12pt; font-style: italic; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;">the deed to a platinum mine</span><span face="Calibri, sans-serif" style="font-size: 12pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;">! Surely the surface reading is not the whole story.</span></span></p><span id="docs-internal-guid-ac1992f8-7fff-96f9-4598-8f1a4baa3219" style="font-family: verdana;"><br /><p dir="ltr" style="line-height: 1.8; margin-bottom: 0pt; margin-top: 0pt;"><span face="Calibri, sans-serif" style="font-size: 12pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;">The interpretive key to the true meaning is in the title. Who is this “Santa baby”? It’s a Christmas song, and so a natural answer presents itself: </span><span face="Calibri, sans-serif" style="font-size: 12pt; font-style: italic; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;">the santa baby is the baby Jesus</span><span face="Calibri, sans-serif" style="font-size: 12pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;">. “Santa” means “holy”, and the Christ child is famously referred to as a “holy infant” in the classic carol ‘Silent Night’; once it is pointed out the connection becomes unignorable. With this interpretation in hand, other lines begin to make more sense. The demand for marriage is a clear reference to the old idea of the Church as the Bride of Christ. “I believe in you” is self-explanatory. “Sign your X on the line” is a reference to Christ’s ultimate gift to humankind on the Cross, “been an angel all year” is not especially deep but offers additional confirmation of the song’s theological meaning for anyone still hesitant. “Think of all the fun I've missed/</span></p><p dir="ltr" style="line-height: 1.8; margin-bottom: 0pt; margin-top: 0pt;"><span face="Calibri, sans-serif" style="font-size: 12pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;">Think of all the fellas that I haven't kissed” can be taken literally as a reference to the faithful believer adhering to the church’s teachings regarding sexual ethics but I think a more fruitful interpretation of this line is as a metaphor for all the graven images the singer hasn’t made unto themselves and before which they haven’t been bowing down. In any case, the song is a plea to Jesus from a faithful believer, asking for their reward. To feel hard done by in this way may not be the most noble sentiment but it is a perennially relatable one, having clear resonances with the book of Job.</span></p><br /><p dir="ltr" style="line-height: 1.8; margin-bottom: 0pt; margin-top: 0pt;"><span face="Calibri, sans-serif" style="font-size: 12pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;">Equipped with our new understanding of the original, let’s turn to Michael Bublé’s controversial reimagining of the song. The most common complaint against it is that he mostly addresses Santa as “Santa buddy” or “Santa pally” rather than “Santa baby”, which gives the impression that he’s worried that if he, a man, addressed Santa, also a man, as “baby” that would make him seem gay. We expect better than that kind of homophobic cowardice from a song recorded in 2011. Since the song is superficially a love song to Santa and widely read as such, I think this feature of the song was clearly foreseeable and probably intentional, and the standard critique of it is valid. But Bublé is clearly also aware of the true meaning of the song and in his reworking of the lyrics he develops it into the radical theological message that we’ll now explore.</span></p><br /><p dir="ltr" style="line-height: 1.8; margin-bottom: 0pt; margin-top: 0pt;"><span face="Calibri, sans-serif" style="font-size: 12pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;">Baby, buddy, pally, Poppy. Do you see where he's going with this? Well, Santa baby is the baby Jesus, as we’ve already established. It doesn’t take any great insight to realize that Santa Poppy is God the Father. This leaves Santa buddy (and its synonym Santa pally) referring to the Holy Spirit. And with this simple reasoning we unlock Bublé’s message: </span><span face="Calibri, sans-serif" style="font-size: 12pt; font-style: italic; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;">the proper relationship between humans and the Holy Spirit is one of friendship</span><span face="Calibri, sans-serif" style="font-size: 12pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;">. Norman Greenbaum’s classic contribution to theological pop music “Spirit in the Sky” also says “I’ve got a friend in Jesus”, but it’s a throwaway line that can easily be read as saying that Jesus is on his side, whereas the fact that Bublé really is talking about friendship is hammered home repeatedly throughout the song, including him switching to “pally” for the benefit of the inattentive listeners in the back.</span></p><br /><p dir="ltr" style="line-height: 1.8; margin-bottom: 0pt; margin-top: 0pt;"><span face="Calibri, sans-serif" style="font-size: 12pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;">But can one truly be friends with God? It would certainly not be a friendship of equals, and the unequal nature of that friendship is of course laid bare in the song. But even allowing for great inequalities, the relationship of total dependence between God the Father and creation seems to make friendship impossible, and while Jesus had mortal friends during his time on Earth, the inequality is similarly great now that he sits in glory at the right hand of the Father. But the Holy Spirit’s role has always been more mysterious than that of the other two persons, and its proceeding from the Father and the Son gives it a (perhaps undue) sense of being somehow least among equals. Perhaps this is someone we can truly be friends with. </span></p><br /><p dir="ltr" style="line-height: 1.8; margin-bottom: 0pt; margin-top: 0pt;"><span face="Calibri, sans-serif" style="font-size: 12pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;">It won’t be easy, but Bublé never said it would be easy. And the potential payoff is high. What’s the payoff? Bublé gives us a further clue with the gifts he mentions in the song. There are seven of them, corresponding to the seven gifts of the spirit:</span></p><br /><p dir="ltr" style="line-height: 1.8; margin-bottom: 0pt; margin-top: 0pt;"><span face="Calibri, sans-serif" style="font-size: 12pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;">Gifts for Bublé</span><span face="Calibri, sans-serif" style="font-size: 12pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;"><span class="Apple-tab-span" style="text-wrap: nowrap;"> </span></span><span face="Calibri, sans-serif" style="font-size: 12pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;"><span class="Apple-tab-span" style="text-wrap: nowrap;"> </span></span><span face="Calibri, sans-serif" style="font-size: 12pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;"><span class="Apple-tab-span" style="text-wrap: nowrap;"> </span></span><span face="Calibri, sans-serif" style="font-size: 12pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;"><span class="Apple-tab-span" style="text-wrap: nowrap;"> </span></span><span face="Calibri, sans-serif" style="font-size: 12pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;">Gifts of the Spirit</span></p><br /><p dir="ltr" style="line-height: 1.8; margin-bottom: 0pt; margin-top: 0pt;"><span face="Calibri, sans-serif" style="font-size: 12pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;">Rolex</span><span face="Calibri, sans-serif" style="font-size: 12pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;"><span class="Apple-tab-span" style="text-wrap: nowrap;"> </span></span><span face="Calibri, sans-serif" style="font-size: 12pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;"><span class="Apple-tab-span" style="text-wrap: nowrap;"> </span></span><span face="Calibri, sans-serif" style="font-size: 12pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;"><span class="Apple-tab-span" style="text-wrap: nowrap;"> </span></span><span face="Calibri, sans-serif" style="font-size: 12pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;"><span class="Apple-tab-span" style="text-wrap: nowrap;"> </span></span><span face="Calibri, sans-serif" style="font-size: 12pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;"><span class="Apple-tab-span" style="text-wrap: nowrap;"> </span></span><span face="Calibri, sans-serif" style="font-size: 12pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;">Wisdom</span></p><p dir="ltr" style="line-height: 1.8; margin-bottom: 0pt; margin-top: 0pt;"><span face="Calibri, sans-serif" style="font-size: 12pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;">’65 convertible, steel blue</span><span face="Calibri, sans-serif" style="font-size: 12pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;"><span class="Apple-tab-span" style="text-wrap: nowrap;"> </span></span><span face="Calibri, sans-serif" style="font-size: 12pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;"><span class="Apple-tab-span" style="text-wrap: nowrap;"> </span></span><span face="Calibri, sans-serif" style="font-size: 12pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;">Understanding</span></p><p dir="ltr" style="line-height: 1.8; margin-bottom: 0pt; margin-top: 0pt;"><span face="Calibri, sans-serif" style="font-size: 12pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;">Yacht</span><span face="Calibri, sans-serif" style="font-size: 12pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;"><span class="Apple-tab-span" style="text-wrap: nowrap;"> </span></span><span face="Calibri, sans-serif" style="font-size: 12pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;"><span class="Apple-tab-span" style="text-wrap: nowrap;"> </span></span><span face="Calibri, sans-serif" style="font-size: 12pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;"><span class="Apple-tab-span" style="text-wrap: nowrap;"> </span></span><span face="Calibri, sans-serif" style="font-size: 12pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;"><span class="Apple-tab-span" style="text-wrap: nowrap;"> </span></span><span face="Calibri, sans-serif" style="font-size: 12pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;"><span class="Apple-tab-span" style="text-wrap: nowrap;"> </span></span><span face="Calibri, sans-serif" style="font-size: 12pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;">Counsel</span></p><p dir="ltr" style="line-height: 1.8; margin-bottom: 0pt; margin-top: 0pt;"><span face="Calibri, sans-serif" style="font-size: 12pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;">Deed to a platinum mine</span><span face="Calibri, sans-serif" style="font-size: 12pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;"><span class="Apple-tab-span" style="text-wrap: nowrap;"> </span></span><span face="Calibri, sans-serif" style="font-size: 12pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;"><span class="Apple-tab-span" style="text-wrap: nowrap;"> </span></span><span face="Calibri, sans-serif" style="font-size: 12pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;">Fortitude</span></p><p dir="ltr" style="line-height: 1.8; margin-bottom: 0pt; margin-top: 0pt;"><span face="Calibri, sans-serif" style="font-size: 12pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;">Canucks tickets</span><span face="Calibri, sans-serif" style="font-size: 12pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;"><span class="Apple-tab-span" style="text-wrap: nowrap;"> </span></span><span face="Calibri, sans-serif" style="font-size: 12pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;"><span class="Apple-tab-span" style="text-wrap: nowrap;"> </span></span><span face="Calibri, sans-serif" style="font-size: 12pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;"><span class="Apple-tab-span" style="text-wrap: nowrap;"> <span> </span><span> </span></span></span><span face="Calibri, sans-serif" style="font-size: 12pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;">Knowledge</span></p><p dir="ltr" style="line-height: 1.8; margin-bottom: 0pt; margin-top: 0pt;"><span face="Calibri, sans-serif" style="font-size: 12pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;">Mercedes decorations</span><span face="Calibri, sans-serif" style="font-size: 12pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;"><span class="Apple-tab-span" style="text-wrap: nowrap;"> </span></span><span face="Calibri, sans-serif" style="font-size: 12pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;"><span class="Apple-tab-span" style="text-wrap: nowrap;"> <span> </span><span> </span></span></span><span face="Calibri, sans-serif" style="font-size: 12pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;">Piety</span></p><p dir="ltr" style="line-height: 1.8; margin-bottom: 0pt; margin-top: 0pt;"><span face="Calibri, sans-serif" style="font-size: 12pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;">Cold hard cash</span><span face="Calibri, sans-serif" style="font-size: 12pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;"><span class="Apple-tab-span" style="text-wrap: nowrap;"> </span></span><span face="Calibri, sans-serif" style="font-size: 12pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;"><span class="Apple-tab-span" style="text-wrap: nowrap;"> </span></span><span face="Calibri, sans-serif" style="font-size: 12pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;"><span class="Apple-tab-span" style="text-wrap: nowrap;"> </span></span><span face="Calibri, sans-serif" style="font-size: 12pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;"><span class="Apple-tab-span" style="text-wrap: nowrap;"> </span></span><span face="Calibri, sans-serif" style="font-size: 12pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;">Fear of the Lord</span></p><br /><p dir="ltr" style="line-height: 1.8; margin-bottom: 0pt; margin-top: 0pt;"><span face="Calibri, sans-serif" style="font-size: 12pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;">I’ve listed Bublé’s gifts in the order they appear in the song and the gifts of the Spirit in their traditional order, but the mapping from one list to the other is other is straightforward and I leave it as an edifying exercise for the reader.</span></p><br /><span id="docs-internal-guid-bb983be9-7fff-0b16-5dc5-8c0d35c870e4"><p dir="ltr" style="line-height: 1.8; margin-bottom: 0pt; margin-top: 0pt;"><span style="font-size: 12pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;">So there we have it: Bublé’s contention is that the Holy Spirit is or at least can and should be truly and literally our friend, and it is in its capacity as our friend that it gives us its gifts. What can we give it in return, poor as we are? Fortunately, since the Holy Spirit is God, it is entirely self-sufficient and has no need of anything we might give it, or indeed of anything else. But we can give it something anyway, and Bublé’s suggestion can’t really be topped. This Christmas, for the Holy Spirit and indeed for all your friends, just be an </span><span style="font-size: 12pt; font-style: italic; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;">awful good guy</span><span style="font-size: 12pt; font-variant-alternates: normal; font-variant-east-asian: normal; font-variant-numeric: normal; font-variant-position: normal; vertical-align: baseline; white-space-collapse: preserve;">.</span></p></span></span>Michael Bench-Caponhttp://www.blogger.com/profile/13715068990919309271noreply@blogger.com0tag:blogger.com,1999:blog-6411624366539130337.post-42458692130802238032021-06-08T07:10:00.006-07:002022-11-04T05:55:04.357-07:00Is Logic Normative?<!DOCTYPE html>
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<p>Last year I read <a href="https://www.tandfonline.com/doi/abs/10.1080/0020174X.2017.1372305" title="(Journal access required)" target="_blank">a paper by Gillian Russell</a> with the self-explanatory title "Logic Isn't Normative" (Russell 2020). I already had some views about the normativity of logic, and found the paper a bit of a challenge for them, because the picture Russell presents of the relationship between logic and normativity is quite similar to how I see things, even though I think logic is normative and she thinks it isn’t. It seems to me that although our positions are in some ways quite close, there are things we disagree on that would prevent me from framing my position her way, as a view according to which logic isn't normative. I thought it'd be instructive, at least for me, to have a think about why.</p>
<p>Russell’s view, as I understand it, is roughly as follows. The subject matter of logic itself is descriptive.<a href="#note1" title=" I’ll mostly be talking as if there was a straightforward normative/descriptive distinction, and Russell’s argument is framed more or less in those terms, but I think a lot of what she says and what I’m saying would probably still make sense even if there wasn’t a straightforward distinction to be had."><sup>1</sup></a> Logic studies which arguments are and aren’t truth-preserving, and this isn’t in itself a normative matter. If we’re taking the constituents of arguments to be sentences, then whether arguments are truth-preserving or not will depend on what sentences mean, the conditions under which they would and wouldn’t be true given what they mean, and which conditions are and aren’t jointly possible. (We'll look at the idea of truth preservation over things other than jointly possible conditions later.) This is all plausibly non-normative (although see note 1). If we take the constituents of arguments to be something else, say propositions, then the story’s a little different but it’s all still descriptive. (There’s some discussion about what the constituents of arguments are in Russell (2008).) These descriptive facts can then be combined with normative bridge principles from outside logic like <i>you should only believe things that are true</i> and <i>you should only reject things that are not true</i>, resulting in norms like <i>if X ⊨ C then you shouldn’t believe all of X and reject C</i>. The fact that you get the norms out at the end doesn’t make logic normative, because you could combine those bridge principles with any claim P and get the norm “you shouldn’t reject P”. So logic combines with the extralogical bridge principles to give you norms, but that doesn’t make it normative, since the normativity all comes from the bridge principles and not from the claims about truth-preservation, and only the latter are the subject matter of logic.</p>
<p>Now, even though I think logic is normative, this view isn’t so different from mine. (Indeed I expect that to some extent her views expressed elsewhere have probably influenced mine on this issue.) I think that there are the non-normative laws that Russell identifies as logical laws, and normative bridge principles that combine with them to give general principles about the relationship between logical consequence relations and how we should think. The difference between my view and Russell’s is that I think the resulting principles, which are normative, are logical laws. To an extent this may seem to be just bookkeeping, but I think it matters. Russell’s view suggests that when people disagree over what the right logic is, either they’re disagreeing over something descriptive, or their disagreement can at least be traced to a disagreement over something descriptive. The bridge principles are seen as either obvious or at least uncontested, so the descriptive stuff is where the action is. I don’t think that’s right; I think there’s plenty of action on the normative side, and that when people are arguing over what the right logic is, their disagreement is often irreducibly normative. First I’ll talk about three objections to Russell’s position that she discusses and one she mentions briefly; then I’ll talk about two potential cases of logical disagreement that I think strengthen the objection she calls the <i>argument from demarcation</i>, and finally I’ll talk a bit about what I think people are arguing over when they argue over what the right logic is.</p>
<h3>Three Arguments For The Normativity Of Logic</h3>
<p>Russell considers three arguments for the normativity of logic, and argues that they don’t establish anything inconsistent with the picture she’s putting forward, according to which logic itself is descriptive and all the normativity comes from extralogical bridge principles. She calls the three arguments the <i>argument from normative consequences</i>, <i>the argument from error</i>, and the <i>argument from demarcation</i>.</p>
<p><b>The argument from normative consequences</b> says that logic must be normative because it has normative consequences and you can’t derive ought from is. The Humean premise that you can’t derive ought from is can of course be questioned, but even if we grant it there’s nothing here to undermine Russell’s position. What we think about logic does affect how we ought to think, but maybe that’s only because of the bridge principles. There’s no principle making it impossible to derive normative conclusions from a combination of descriptive and normative premises, and that’s what Russell thinks is going on.</p>
<p><b>The argument from error</b> says that the laws of logic must be normative laws and not descriptive laws because people violate them. The laws of physics are descriptive, and we can’t break them. But people do believe inconsistent things and make fallacious inferences, and isn’t that breaking the laws of logic? Not according to Russell. On her view, breaking a logical law would be doing something like wearing a red hat without wearing a hat. (She doesn’t use this example.) You can’t break that kind of law, which indicates that they are descriptive, not normative. It seems to me that the question of whether someone with inconsistent beliefs is violating a logical law or not is very similar to the question of whether norms like <i>you shouldn’t have inconsistent beliefs</i> are logical laws or not, and so I agree with Russell that the argument from error isn’t going to get her opponents anywhere. At best it begs the question.</p>
<p><b>The argument from demarcation</b> is the one that I think is most interesting and poses the biggest threat to Russell’s position. She quotes John MacFarlane:
<blockquote>Logic is often said to provide norms for thought or reasoning. Indeed, this idea is central to the way in which logic has been demarcated as a discipline, and without it, it is hard to see how we would distinguish logic from the disciplines that crowd it on all sides: psychology, metaphysics, mathematics, and semantics. (MacFarlane 2004:1)</blockquote>
Now, as I understand it Russell’s view about where logical laws come from takes them more or less to be reducible without remainder to semantics and metaphysics plus the mathematics involved. (There may be some psychology in there too, perhaps in the semantics.) This means you can see logic as an interdisciplinary thing rather than an autonomous discipline, and it doesn’t need normativity to demarcate a sharp boundary because it doesn’t have one.
</p>
<p>For all that’s there in the MacFarlane quote (which is of course not all that’s there in his paper) we could leave it at that, but she rightly doesn’t leave it at that. There’s another worry, which is basically this: <i>when we argue over what the right logic is, what are we arguing about?</i> I suppose my view is that this is the central question in the philosophy of logic. Defenders of classical and intuitionistic logic don’t disagree over which conclusions follow from which sets of premises in classical logic or in intuitionistic logic; those are basically pure mathematical questions and when it comes to investigating them we’re all on the same side. The defenders of different logics disagree over which conclusions follow from which sets of premises <i>full stop</i>.</p>
<p>Russell’s response to this is that while it’s true that the defenders of different logics are not disagreeing about pure maths, that doesn’t mean what they are disagreeing about isn’t purely descriptive. The semantics/metaphysics mashup that is the study of truth-preservation for arguments is descriptive, and that’s what Russell thinks the defenders of different logics are arguing over. Do arguments from (P→Q)→P to P always preserve truth? Classical logicians say yes; intuitionistic logicians say no. According to Russell that’s their disagreement, and descriptive semantics and metaphysics can settle the question. And since this schema is like a version of Peirce’s law and adding it to intuitionistic logic gives you classical logic, settling it would settle all their other disagreements too. (We'll talk more about intuitionistic logic and whether it's really about truth-preservation later.)</p>
<h3>A Fourth Way To Argue For The Normativity Of Logic</h3>
<p>All three of these arguments have a flavour of indirectness to them; they don’t tell us why or how logic is normative, but just argue that somehow it must be, because otherwise it couldn’t have normative consequences, or we couldn’t break logical laws, or we’d have nothing to distinguish logical questions from mathematical questions. An alternative route would be to argue for a distinctively logical normative reality. Russell (2020: note 15) touches on this possibility when discussing a reviewer’s comment that logic might be normative because truth itself is normative. She accepts the conditional but demurs on the antecedent: she doesn’t think truth is normative (although there are norms involving it, just as there are norms involving many descriptive concepts).</p>
<p>What might this kind of view of truth or logic as normative look like? I’ll make two suggestions. One is a pragmatic theory of truth, where what’s true just is in some sense whatever’s good to believe. Here’s a passage from William James which contains an idea along those lines, although I don’t know enough about James’s views on truth to properly contextualize it:
<blockquote>'What would be better for us to believe'! This sounds very like a definition of truth. It comes very near to saying 'what we ought to believe': and in that definition none of you would find any oddity. Ought we ever not to believe what it is better for us to believe? And can we then keep the notion of what is better for us, and what is true for us, permanently apart?" (James 1907, Lecture VI §16)</blockquote>
<p>A second possibility is suggested by the Aristotelian line that you have to believe the law of non-contradiction if you want to say anything at all.<a href="#note2" title="The argument comes in Metaphysics IV 4, and I understand there's a large literature on it, which I regret to report I have not read much of aside from Dutilh Novaes (2019). I'm not a fan of the law of non-contradiction myself and my hope is that what's correct in Aristotle's argument can be explained in terms of a conflict between accepting and rejecting the same proposition, rather than between accepting both a proposition and its negation. (My view, following e.g. Smiley (1996) is that rejecting a proposition and accepting its negation aren't the same thing.)"><sup>2</sup></a> If his argument works (and I won't attempt to explain how it is supposed to work) then that arguably gives a reason for believing the law of non-contradiction directly, rather than with reference to its truth. Presumably this could also be contested as not entailing that logic itself is normative — so far all Aristotle’s argument does is give a reason for believing something — but both Aristotle’s argument and the pragmatist suggestion offer ways of embedding normativity deeper into the subject matter of logic than it is on Russell’s picture. But we won’t pursue these ways of way of arguing for the normativity of logic further here, and instead we’ll go back to the argument from demarcation.</p>
<h3>Irreducibly Normative Disagreement</h3>
<p>Consider the argument form called <i>explosion</i> (aka <i>ex falso quodlibet</i> or <i>ex contradictione quodilibet</i>), where you derive an arbitrary conclusion from contradictory premises. For example: Australia is big, and Australia is not big, therefore the sky is green. It’s classically (and intuitionistically) valid, and logics where it fails are called <i>paraconsistent</i>. There are two main objections to it that you hear from people who think the right logic is paraconsistent.</p>
<p>One objection is from people who are <i>dialetheists</i>, which means they think that contradictions can be true. Regular readers may recall that <a href="http://michaelbenchcapon.blogspot.com/2019/11/dialetheism-duchamp-and-deloreans.html" title="Blogpost: Dialetheism, Duchamp, And Deloreans" target="_blank">I think dialetheism is probably true</a>. Dialetheists can object to explosion on the grounds that it doesn’t preserve truth. If contradictions can be true (without everything else also being true), then some arguments with contradictory premises can have all true premises without having a true conclusion. This fits into Russell’s model just fine: the disagreement over whether the right logic is paraconsistent stems from a disagreement over whether explosion preserves truth, which here turns on the entirely non-normative matter (bracketing the suggestion that truth is itself normative) of whether contradictions can be true.</p>
<p>Another objection to explosion is about <i>relevance</i>. Even if contradictions can’t be true, and so explosion (vacuously) preserves truth across all possible situations, maybe it still isn’t logically valid because the conclusion might have nothing to do with the premises. This is one of the main motivating thoughts behind <i>relevant logic</i> (also known as <i>relevance logic</i>). Not all fans of relevant logic are dialetheists, although some are. My own view is that the complaint about dialetheism and the complaint about relevance have basically nothing to do with each other, but even if you don’t think that, you don’t have have to be a dialetheist to want your logic to be relevant.</p>
<p>As I see it, the relevantist objection to explosion is a counterexample to Russell’s positive view about what the subject matter of logic is. Here we have a disagreement over what the right logic is which isn’t a disagreement about truth-preservation. This doesn’t yet establish that the disagreement is about something normative, although I think that in fact it probably is and will say more about why later. But how might Russell respond to this potential counterexample?</p>
<p>One possible response is just to maintain that logic is about truth-preservation, and so if the relevantists and non-relevantists agree about which arguments preserve truth then they agree about logic and their disagreement must be about something else. Of course, nothing prevents us from saying this, and indeed nothing prevents us from defining the word ‘logic’ so that what we say is true. But as I understand Russell’s position it’s more ambitious and interesting than that. It’s not meant to be just a recipe for taking a particular side in a verbal dispute. As I understand her position it’s meant to be more like a diagnosis: what all those people arguing over the right logic are arguing about boils down to a disagreement over something descriptive, specifically something about truth-preservation.</p>
<p>Hartry Field (2015) says something related to this that I feel I ought to mention but don’t properly understand. Here he is:
<blockquote>While it is correct that there are logicians for whom truth-preservation is far from the sole goal, this isn’t of great importance for my purposes. That’s because my interest is with <i>what people who disagree in logic are disagreeing about</i>; and if proponents of one logic want that logic to meet additional goals that proponents of another logic aren’t trying to meet, and reject inferences that the other logic accepts only because of the difference of goals, then the apparent disagreement in logic seems merely verbal. (Field 2015: 35, his emphasis)</blockquote>
I think that to see relevantists and non-relevantists as only having different goals isn’t quite right. It’s not just that relevantists want both truth-preservation and relevance while their opponents only want truth-preservation. At least sometimes, I think they’re both targeting the same notion of logical consequence but disagree over whether validating irrelevant arguments is a sign that something has gone wrong. If all you wanted was truth-preservation and relevance you might be happy with a kind of <i>filter logic</i><a href="#note3" title="Filter logics, so called because you get the consequence relation by taking the consequence relation of an irrelevant logic and applying a relevance filter of some kind to it, are mentioned in Priest (2008:173–4). Aside from as a curiosity or just to illustrate a bad approach to securing relevance, I don't really know what they're for. It possible they're not for anything else, but I expect they do have some independent interest, although as I say I don't know what it is."><sup>3</sup></a>, the most flatfooted of which would be classical logic minus any sequents with no variables appearing in both the premises and the conclusion. That logic would be non-transitive, since it would validate (Q&¬Q) ⊨ (Q&¬Q)∨(R&¬R) and (Q&¬Q)∨(R&¬R) ⊨ (R&¬R) but not (Q&¬Q) ⊨ (R&¬R). But relevantists usually aren’t happy with this, because they want an integrated account of logical consequence that is both truth-preserving and relevant. You can still see this as a difference of goals if you like, but even then it seems wrong to me to describe it as a mere verbal dispute. If verbal at all, it’s something along the lines of what Carrie Jenkins (2014) calls a <i>serious verbal dispute</i>; but even without committing to the possibility of there being such things we can note that differences of goals are things we can have serious arguments about. What confuses me even further about Field’s position is that he ends up arguing that we should understand even the arguments about logic that he’s discussing as arguments about how we should regulate our degrees of belief, and not as arguments about truth-preservation. His paper is complex and I think I’m probably missing something, but I just wanted to note that if he’s saying what he sounded to me like he was saying, then that’s a point of disagreement between us.</p>
<p>Supposing we don’t want to say that the disagreement between relevantists and non-relevantists is a (non-serious) verbal dispute turning on two different uses of the term “logic”, another possible response is to diagnose the relevance objection to explosion as not being about truth-preservation but still being descriptive. Maybe logic is about relevance and truth-preservation, or some kind of composite of the two, and the disagreement is over whether explosion meets that (descriptive) condition. Now this option might be available if we all saw relevance the way David Lewis did. Lewis (1988) argues that explosion is relevant after all: asserting a contradiction is equivalent to asserting everything, so a contradiction in the premises asserts whatever the conclusion is, and so it is relevant to the conclusion. The disagreement between Lewis and the relevantists could be thought of as a descriptive disagreement over whether explosion is relevant or not. The problem with this diagnosis is that it would put a lot of non-relevantists on the wrong side. Plenty of people, at least as I understand it, think that explosion is not a relevant inference but it is still part of the correct logic because the correct logic need not be relevant. They agree with the relevantists on the descriptive point but disagree about whether explosion is valid, so their disagreement must be about something else. In the next section we’ll reconsider whether the disagreement over relevance can be made out as being about truth-preservation after all, but for now it doesn’t seem possible to diagnose the dispute over explosion between relevantists and most of their opponents who aren’t David Lewis as being over the descriptive matter of whether explosion is relevant. There is general agreement that it isn’t relevant, even where there is disagreement over whether it’s valid.</p>
<h3>Model Theory</h3>
<p>So, what exactly is truth-preservation? The basic idea is that arguments preserve truth iff whenever the premises are all true the conclusion is true. This could be understood in terms of possibility: it’s not possible for the premises to be true and the conclusion not. That could be metaphysical possibility, or it could be logical possibility, or perhaps it could be some other kind of possibility. It seems to me that for Russell’s purposes it’d be better not to say logical possibility, because of the risk of circularity. If we explain logical possibility in terms of truth-preservation (since that’s what logic is about) and then explain what we mean by truth-preservation by appealing to logical possibility, it seems there’s a circle. It’s a bit like the problem Quine talked about in ‘Two Dogmas Of Empiricism’ (Quine 1951) of all the proposed accounts of analyticity appealing to some notion or other that’s similarly unexplained; but leaving aside what Quine says there, it seems to me there would be a circle in our case, and not in a good way. So we might be better off going with metaphysical possibility than with logical possibility. That way people who disagree over e.g. the law of non-contradiction can be disagreeing over whether all of its instances are metaphysically necessary. People who argue over that law often do disagree about whether all of its instances are metaphysically necessary, and might be happy to agree for the record that this is what they’re arguing about, at least sometimes. But since the relevance objection to explosion is sometimes being posed by people who think that contradictions are not metaphysically possible, truth-preservation over metaphysically possible worlds can’t be what they’re arguing about. The same goes if we understand truth-preservation as just relating to the actual world, in which case they’d be arguing over whether any contradictions are true. The non-dialetheist relevantists agree with the classicists that no contradictions are true, so that’s not what they’re arguing about either. Now, if you think actual-world truth-preservation is a ridiculous thing for logic to be about, you can have some fun ridiculing Quine:
<blockquote> ...the business of formal logic is describable as that of finding statement forms which are <i>logical</i>, in the sense of containing no constants beyond the logical vocabulary, and (extensionally) <i>valid</i>, in the sense that all statements exemplifying the form in question are true. Statements exemplifying such forms may be called <i>logically true</i>. (Quine 1953: 436, his emphasis)</blockquote>
We should note that Quine isn’t saying that everything true is logically true; he’s saying that every instance of a schema that contains no non-logical constants and all of whose instances are true is logically true. The paper is a review of a book by PF Strawson (1952), and he attributes Strawson the same view but with the instances having to be analytic rather than merely true. This makes sense in the context of Strawson and Quine’s differing views over the tenability of the notion of analyticity, and Quine’s avoidance of necessity here is also in keeping with his views about that. Quine’s position does mean putting some weight on a distinction between logical and non-logical vocabulary, but it’s worth noting that fans and detractors of the law of non-contradiction can have their argument over whether all its instances are true without needing to use such a distinction. We only really need such a distinction if we’re trying to distinguish logical truths from non-logical truths.</p>
<p>(As an aside, I really do recommend reading Quine’s review if you’re interested in Quine and have a sort of middling knowledge of his ideas; he says what he thinks about a lot of different things in a fairly casual way, and it’s also the place where the slogan “philosophy of science is philosophy enough” appears in print.) </p>
<p>Getting back to our main thread, the argument between non-relevantists and non-dialetheist relevantists seems like it can’t be about either truth-preservation at the actual world or truth-preservation across all metaphysically possible worlds, because the parties to the disagreement don’t disagree about those things. What other truth-preservation-based options are there? Well, a good place to look is at the model theories for the proposed logics. With relevant logic it’s sometimes a bit tricky how exactly truth-preservation figures in the definition of logical consequence, but to keep things simple let’s look at <i>first degree entailment</i>, or <i>FDE</i>, which is the extensional base for a lot of relevant logics. Suppose the relevantist and the classicist are arguing over what the One True Logic is for sentences with no conditionals or modal operators: just sentence letters, negation, conjunction and disjunction. (The example should work equally well with or without allowing quantifiers.) They might both agree that metaphysical possibility is represented by classical models, and that classical logic describes truth-preservation across metaphysically possible worlds. Nonetheless, the relevantist thinks that the (extensional fragment of the) One True Logic corresponds to truth-preservation across FDE models, in which sentences can be true, false, both, or neither, and the classicist thinks it corresponds to the classical models. Classical logic validates explosion and FDE doesn’t.
</p>
<p>To describe their disagreement as being about truth-preservation we want some neutral description of the class of things they think the One True Logic corresponds to truth-preservation over, and then they can disagree over whether that class of things corresponds to the class of FDE models or the class of classical models. What might that class of things be? It can’t be metaphysically possible worlds, as we’ve seen. I think the most promising option is probably something along the lines of <i>information states</i>. (Sometimes people actually do talk about FDE as modelling information states; I didn’t just make it up.) It’s characteristic of information states that they can be incomplete, and on the FDE picture they can also be inconsistent, even if the world itself can’t.<a href="#note4" title="The apparent fact that information states can be incomplete makes it a bit unsatisfactory to portray the classicist as defending a view about truth-preservation over information states. We might portray the disagreement between fans of FDE and the three-valued logic K3 as being about information states, and K3 still validates explosion, but we’re still left asking where that leaves the classicist. We can get some of the way by saying that information states include classical tautologies for free. You might also wonder why the only admissible information states are prime, in that they must include at least one of P and Q whenever they include P∨Q: can’t someone have the information that P∨Q without having either the information that P or that Q? It’s a fair point, although it can be levelled at the FDE models as much as the classical ones. If both sides expand the class of information states to include any set of sentences closed under their favoured logic, that should give alternative model theories for the same consequence relations, but including non-prime information states. The classicist will also get the information state containing all sentences — FDE had it already — but that doesn’t change the consequence relation either and if they want they can exclude it by fiat. Allowing non-prime models may end up giving the classicist a model theory for classical logic that they can credibly defend as being the appropriate class of information states, although it’s possible there’s a straightforward objection to it that I’ve overlooked. Of course the option including the non-prime models does at least seem to use the logics themselves to define the classes of admissible information states, and this relates to an issue we’ll talk a bit about below."><sup>4</sup></a></p>
<p>For these purposes, an information state isn’t supposed to just be any old set of sentences. The classicist obviously thinks that’s too broad, but so does the relevantist. If an FDE model says P is true then it also has to say P∨Q is true, for example. Now, it’s plausible enough that if you already have the information that P is true, then in a sense it wouldn’t be new information to learn that P∨Q is also true. In a sense it might be new information, since you might have the information that P but not have inferred that P∨Q. But it still seems there’s a sense in which it wouldn’t be new information, and that’s roughly the sense that delimits the notion of an information state that the classicist and relevantist are arguing over, if they're arguing over information states at all.
</p>
<p>If we want to use this as part of an argument that logic isn’t normative, we need to think a bit more about what this sense of an information state is, because the sense in question might itself be normative. Basically, we might be dealing with a notion of an information state that’s <i>good</i> in some way. Maybe it’s good in that it contains all the information that might be rationally permissible for someone in a given situation to use, or just in that it’s closed under rationally permissible inference, where this is understood independently of the model theory, perhaps in terms of proof rules. (The information states may also need to be <i>prime</i>; although see note 3 above.) But these notions involving rational permissibility are normative. If we want a descriptive notion, the most promising place to look seems to me to be psychology. Maybe people have some operations that they perform to round out their information states, and logic is about truth-preservation over information states closed under those operations. That seems to make sense, and it seems plausibly non-normative, but it’s psychologism, and psychologism isn’t in fashion. Some people will tell you Frege refuted it. I wouldn’t go that far and expect it’ll get rehabilitated sooner or later; I read a New York Times review by James Ryerson (2018) that made it sound like Irad Kimhi (2018) has been trying to rehabilitate psychologism in some form, although possibly quite a different form from the one I gestured at a moment ago. (I haven’t read Kimhi’s book myself and get the impression I might not fully understand what he was up to in it if I did, if only because I’m pretty clueless about Hegel.) Nonetheless, my understanding is that psychologism isn’t back in fashion yet and I think that psychologism is where we’ve ended up if we want to diagnose the relevance objection to explosion as being both descriptive and about truth-preservation.</p>
<h3>Old Fashioned Intuitionism</h3>
<p>In her discussion of the demarcation argument, Russell says something about intuitionistic logic that suggests she might think there actually are at least some disputes about what the right logic is that aren’t descriptive disputes about truth-preservation. I’ll quote the whole paragraph so that if I missed some important context you don’t end up missing it too:
<blockquote>But there is also a stronger, more worrying, version of the demarcation argument. It asks what the results of logical inquiry are actually telling us. What do E-sentences like <i>¬¬P ⊨ P</i> mean? What makes them true or false? The answer, as it often does, seems clear at first: it means <i>P</i> is a logical consequence of <i>¬¬P</i>. There are no interpretations on which <i>P</i> is true and <i>¬¬P</i> is not [sic; I think this should be "no interpretations on which <i>¬¬P</i> is true and <i>P</i> is not" - MBC]. But now we find that intuitionists and classical logicians disagree about whether this is so. The classical logician says that <i>¬¬P ⊨ P</i> is true. Asked to support this claim she may offer a short model-theoretic argument: on any interpretation on which <i>¬¬P</i> is true, <i>P</i> is true as well and this is all that is required for logical consequence. The intuitionist disagrees. They say that <i>¬¬P ⊨ P</i> is false and (<b>let’s assume that they are a modern sort of intuitionist, happy to characterise their view in terms of truth-preservation across interpretations in Kripke-models</b>) denies the classical logician’s claim about interpretations. They say that there are Kripke models and interpretations on such models on which <i>¬¬P</i> is true but <i>P</i> is false. (The classical logician denies that these are interpretations – i.e. denies that these are genuine counterexamples to DNE.) (Russell 2020: 377–8, emphasis mine)</blockquote>
Let’s grant that Russell’s account of the disagreement between intuitionists and classicists as being a descriptive disagreement about truth-preservation is correct for modern sorts of intuitionist. What about the other sort of inutitionist? Would the disagreement between them and the classicists be a counterexample to Russell’s view?</p>
<p>Maybe the old-fashioned intuitionist can say the same kind of thing about ¬¬P ⊨ P that our non-dialetheist relevantist says about P, ¬P ⊨ Q: it isn’t metaphysically possible for the premises to be true and the conclusion false, but it takes more than that for an inference to be valid, and this inference doesn’t meet the other criteria. The logic that captures all the criteria for validity is intuitionistic logic, and this can be mathematically defined by its proof theory, or with Heyting algebras, or with Kripke frames. The fact that the Kripke frame definition is extensionally correct doesn’t point to any particular interpretation of the frames as possible states of the world. Perhaps we can think of them as information states while maintaining that what counts as an information state is itself normative, just as we could with relevant logic. As evidence that the intuitionists are serious that they really don’t think it’s possible for ¬¬P to be true and P not be true, they can even point to the fact that ¬(¬¬P & ¬P) is a theorem of intuitionistic logic.</p>
<p>I think that if you can find an old-fashioned intuitionist then they may well have every right to say this sort of thing. Even so, there are at least two ways for Russell to argue that even if old-fashioned intuitionism is technically a counterexample to her account of logical disagreement, it isn’t a very good one. One option is to point out that old-fashioned intuitionism is old-fashioned for a reason, and while they may have been arguing with the classicists over something normative, it’s not something we consider worth arguing over anymore. Of course there’s nothing to stop someone raising their hand in the Q&A after someone defends a logical schema on grounds of truth-preservation, and saying “I don’t care if all instances of this schema preserve truth; you still shouldn’t be making these inferences, and in my book that means it’s not valid!” Perhaps a debate will ensue; perhaps it will get shut down. It is in any case possible to have these debates; the question is whether they are worth having, and whether the debates logicians deem worth having are of this kind. Perhaps old-fashioned intuitionism is old-fashioned because logicians in their wisdom decided that this was not something worth arguing over.</p>
<p>Another option arguably doesn’t even concede that old-fashioned intuitionism is a counterexample. Sometimes philosophers have debates and don’t fully understand what they’re debating about. That’s why they write papers with titles like “What we disagree about when we disagree about ontology” (Dorr 2009), and why I can wind up thinking that “when we argue over what the right logic is, what are we arguing about?” is the central question in the philosophy of logic. It’s why we so often take seriously the possibility that the participants in a debate may be talking past each other, and it’s why Peter van Inwagen can write papers explaining that he doesn’t understand something and he doesn’t think anyone else does either (e.g. van Inwagen (1981)). In this light, maybe what’s old-fashioned about old-fashioned intuitionism isn’t that they weren’t arguing about truth-preservation; it’s that they were working before Kripke had helped them figure out that they were. Of course an intuitionist could refuse to get with the programme (if indeed this is the programme), but then they’d be dealt with as in the previous paragraph, getting told by the wider community of logicians that they don’t have to go home but they can’t stay here.</p>
<p>Now I don’t think this kind of response is available in the case of non-dialetheist relevantism, simply because the relevantist so plainly wants more out of a notion of validity than necessary truth-preservation. Anderson et al (1975 & 1992) was called <i>Entailment: The Logic of Relevance and Necessity</i> because it was about the programme in logic that tries to capture a notion of entailment that is both relevant and necessarily truth-preserving. Maybe a time will come when information states get thoroughly psychologized and we’ll be able to understand relevance non-normatively and in terms of truth-preservation, and then those old-fashioned relevantists that remain may be told to go home too. But we’re not there yet, and if psychologism’s poor reputation is earned, we should hope that we never will be.</p>
<h3>Logical Pluralism</h3>
<p>I’ve said a lot about why I don’t think logic is just a descriptive subject concerned with truth-preservation, and it’s coming from the perspective of my positive view about what we disagree about when we disagree about logic, but I’ve kind of danced around that positive view so far and now I’ll be a bit more explicit about how it goes.</p>
<p>Suppose we have a claim about logical consequence, just considered as such and not further interpreted as being about normativity, necessity, truth-preservation or anything else. Just a claim about, as they say, what follows from what. Claims like that are thought to have implications of various kinds, principally for how we should reason and for metaphysical possibility but perhaps for other things too. With a bit of imagination you could probably find all sorts of places to plug a logical consequence relation into a philosophical theory.</p>
<p>I think that this picture leaves logical consequence itself a bit mysterious, and so I’d prefer to argue over the supposed implications directly. If you want to argue over whether contradictions are metaphysically possible, just go ahead and argue over it. If you want to argue over which inferences people should be making, then argue over that. We don’t need to displace these debates to the question of what the right logic is <i>tout court</i>. And in particular, we don’t always have to give the same logic as our answer. The non-dialetheist relevantists are already doing this, giving a different answer to the questions of whether it’s metaphysically possible for explosion’s premises to be true and its conclusion not and whether it’s rationally permissible to infer explosion’s conclusion from its premises.
</p>
<p>We also don’t just have two questions, one metaphysical and one normative. At least on the normative side, there are many questions to ask. MacFarlane (2004: 7) has a long list of possible bridge principles getting us from logically valid sequents to norms on thought. Some examples:</p>
<ul>
<li>If A, B ⊨ C, then . . .<ul>
<li>Co+: If you believe A and you believe B, you ought to believe C</li>
<li>Bp+: if you may believe A and believe B, you may believe C</li>
<li>Wr+: you have reason to see to it that if you believe A and you believe B, you believe C</li>
</ul></li>
</ul>
<p>MacFarlane adds that these can also all be replaced by versions beginning “If you know that A, B ⊨ C, then…”. For each of those bridge principles we can take a logic and ask whether the corresponding rule always holds for it. Maybe in practice a logic that works with one bridge principle will usually work with the others, or at least the others we’re interested in, but the point is that they’re all meaningful questions, and we might expect that more than one of the questions is interesting. And perhaps MacFarlane’s list, long as it is, doesn’t exhaust all the possibilities. Indeed, I don’t think it does. Here are two other avenues. First, the rules in MacFarlane’s list are all based on material conditionals, (the conditionals here are to be understood materially) but there are other conditionals to be had and these might give different rules. Second, Kwasi Wiredu (1973) makes a distinction between deducibility and inferability, and a related distinction between <i>hypothetical</i> arguments that bring out the consequences of something we may not believe, as in a conditional proof or a reductio ad absurdum, and <i>categorical</i> arguments where we accept some premises and draw a conclusion from them. He argues that some logical schemas are good for one of these notions and not for the other. The distinctions don’t appear in any obvious way in MacFarlane’s list, so that gives us some more questions to explore.</p>
<p>Something to note is that if you want to ask these questions without a robust notion of logical consequence itself, you’ll want to have some independent understanding of metaphysical necessity, or good inference, or whatever it is the question is about. And in fact I do think that it’s good to have notions of those things that aren’t confined to what could be explained by something resembling logical consequence; for example I think metaphysical necessity is also useful for explaining the difference between a physical law and a mere regularity, and perhaps we should have a notion of good inference that applies to both deductive and non-deductive inferences. I don’t expect everyone to agree with me about this, and I see how if a robust notion of logical consequence really could explain both the metaphysical side and the normative side then that would be an attractive thing to have. But we don’t have to decide this now. We debate the first order issues, we put forward accounts of what the debates are really about and debate those too, and we don’t need to prejudge the question of whether the debates are all really about the same thing.</p>
<p>I should spell something out because people have sometimes been unhappy about it when I’ve talked about it before. The different questions we can ask about logical schemas like “are all their instances true?”, “are all their instances metaphysically necessary?” and “is it always permissible to accept the conclusion when it’s permissible to accept all the premises?” are <i>not</i> supposed to give candidate necessary and sufficient conditions for notions of logical truth or validity. When we ask if any instances of “Fn&¬Fn” are true we’re asking exactly the same question about that schema as we can ask about the schema “n is a cat”. In practice the schemas we ask about will often contain no paradigmatically non-logical vocabulary simply because the questions will otherwise tend not to be both interesting and amenable to the methods logicians use. But there’s no need for a demarcation between the logical and the non-logical, or between the questions of this form that are and aren’t legitimate. This relieves the theoretical burden of attempting to give candidate necessary and sufficient conditions for logical truth or validity (since we can have a lot of the debates we want to have without doing so), but it also has the practical benefit of legitimating logics of things like belief, knowledge, obligation, obviousness or whatever that seem to use concepts that aren’t clearly logical but do seem to have a logic in a way that the concept of a cat perhaps does not. Rather than taking a logic as a whole and asking if it’s the One True Logic, we can look at an individual schema, a collection of schemas or even the schemas defining a whole logic and ask whether those schemas satisfy a particular condition. Other (perhaps less interesting) schemas will probably satisfy the condition too, and that’s fine: the inquiry is open-ended.</p>
<p>These days there’s a fair bit of logical pluralism about, considered as a broad category of views united by the idea that there may be more than one correct logic. The picture I’ve described above is the version of logical pluralism I like. Now, considered from a distance it seems like on this picture there’s a whole array of different questions which might have different logics as the answers to them, and different combinations of positions one might adopt. I have thought quite a lot about some of the questions, but I do sometimes worry that a lot of them will end up collapsing into each other, leaving a lot less fun to be had and leaving a lot of logics sitting in the textbooks unused. But even if we end up landing on one true logic with all the metaphysical and normative implications you might expect, it still seems to me that we should start out with the approach I’ve described, and I still hold out hope of ending up somewhere interesting.</p>
<h3>The Organon</h3>
<p>So I’ve proposed that we break down the question of what the right logic is into a bunch of different questions, some normative and some descriptive. (The normative side seems to have a lot more, but the descriptive side has material and necessary truth-preservation, and there’s no telling what questions psychologists may come up with.) There are well formed questions of both kinds, and even when you hold the answers to the descriptive questions fixed, the answers to the normative questions don’t become obvious or trivial. But I think that even if we accept all this, there’s a worry that the normative questions might be somehow second-rate.</p>
<p>Think about what the people investigating the descriptive side get to do. For the semantics aspect they get to engage with linguistics, psychology, maybe computer science; for the metaphysics they might get to engage with physics, and both camps get to to do the pure maths side of things. The descriptive camp's findings thus stand to have an air of impressiveness to them. The normative side seems to risk being rather less impressive, offering recommendations and expressing preferences. Instead of proofs and experiments and citations of science journals, we have handwaving, table-thumping, and appeals to the great importance of believing the true and nothing but the true. It might seem like a serious scholar would prefer to stick to the hard-nosed descriptive stuff and let people use that information how they will.</p>
<p>I don’t think this is something we should panic about, but we don’t have to write it off as a concern altogether either. The first thing to note is that even if philosophers haven’t got much business arguing for one or other logic as the answer to a normative question, they still need to develop the logics for people to choose from. If the non-dialetheist relevantists are any indication, the logics motivated by normativity rather than (mere) truth-preservation may also be rather more complicated. This means that the philosophers will need to think about the normative questions so that they know what kinds of options people are going to want. Even if the normative questions are not the target of the research, they can still motivate the research. However, in practice we can expect that this thinking about what kind of normative options people might want will sometimes be elaborate enough that the normative questions do become the target of at least some of the research.</p>
<p>This doesn’t strike me as a problem, but that may be because I’m on the other side anyway. I think the normative questions are serious philosophical questions in their own right and it is the business of philosophers to investigate them. In short, it’s epistemology. Back in the day people used to use the term ‘logic’ to cover a lot of what we’d now think of as epistemology, and Aristotle’s so-called logical works include the Posterior Analytics as well as the Prior Analytics (plus the Categories, Topics, Sophistical Refutations and On Interpretation, and sometimes the Rhetoric and the Poetics). This isn’t for nothing, since in many ways the normative side of logic is about the justification of beliefs (typically by inferences from other beliefs), and that makes it epistemology. In the MacFarlane quote earlier he said that logic was crowded on all sides by psychology, metaphysics, mathematics, and semantics, and I wouldn’t be sorry to see it crowded on a fifth side by epistemology if it meant the normative logical questions were getting taken seriously.</p>
<p>One last thing I thought I’d mention is about a debate between Aristotelians and Stoics a long time ago. Stoics divided philosophy into ethics, physics (which included a lot of what we’d now call science but also some of what we’d still call philosophy), and logic (which included a lot of epistemology). The Aristotelians didn’t think of logic (and epistemology) as a separate branch like that; they thought of it as a tool used by the other branches. They accordingly called Aristotle’s logical works the <i>Organon</i>, which means ‘tool’. That’s my understanding of how it went, anyway. I don’t really know the history and the similarity between what happened then and what I’ve been talking about here may be superficial, but I’ll continue. (Regular readers may recall me talking about this dispute over the status of logic <a href="https://michaelbenchcapon.blogspot.com/2017/09/they-do-things-differently-there.html" title="Blogpost: They Do Things Differently There" target="_blank">before</a>.) Suppose that the normative questions really are either straightforward given the answers to the descriptive questions or somehow not amenable to philosophical argument. Then we’re left with logic as Russell conceives it, a descriptive discipline involving maths, linguistics, probably psychology, but perhaps not a great deal of philosophy as such, at least as we currently think of it. (There’s admittedly probably some metaphysics in there.) This corresponds to the Aristotelian position: on this model logic is news philosophers can use, but it’s not really philosophy proper. If we like Quinean naturalized epistemology, we might even want to view the rest of epistemology the same way, recapturing the Aristotelian vision of the relationship between logic/epistemology and the rest of philosophy. On the picture I favour, the normative questions aren’t straightforward, are amenable to philosophical argument, and aren’t reducible to descriptive questions about something else. That puts me on the side with the Stoics.</p>
<p>As I say, I may have the history wrong and the parallel may be superficial in any case. But even if it wasn’t the debate the Stoics and Aristotelians were having, I think there’s still a debate to be had. Is logic normative? I think it is, at least sometimes, and when it is, it blends into epistemology. But if the interesting part of epistemology isn’t normative, then the interesting part of logic probably isn’t normative either.</p>
<h3>Notes</h3>
<p id="note1">[1] I’ll mostly be talking as if there was a straightforward normative/descriptive distinction, and Russell’s argument is framed more or less in those terms, but I think a lot of what she says and what I’m saying would probably still make sense even if there wasn’t a straightforward distinction to be had.</p>
<p id="note2">[2] The argument comes in Metaphysics IV 4, and I understand there's a large literature on it, which I regret to report I have not read, aside from Dutilh Novaes (2019). I'm not a fan of the law of non-contradiction and my hope is that what's correct in Aristotle's argument can be explained in terms of a conflict between accepting and rejecting the same proposition, rather than between accepting both a proposition and its negation. (My view, following e.g. Smiley (1996) is that rejecting a proposition and accepting its negation aren't the same thing.)</p>
<p id="note3">[3] Filter logics, so called because you get the consequence relation by taking the consequence relation of an irrelevant logic and applying a relevance filter of some kind to it, are mentioned in Priest (2008:173–4). Aside from as a curiosity or just to illustrate a bad approach to securing relevance, I don't really know what they're for. It possible they're not for anything else, but I expect they do have some independent interest, although as I say I don't know what it is.</p>
<p id="note4">[4] The apparent fact that information states can be incomplete makes it a bit unsatisfactory to portray the classicist as defending a view about truth-preservation over information states. We might portray the disagreement between fans of FDE and the three-valued logic K3 as being about information states, and K3 still validates explosion, but we’re still left asking where that leaves the classicist. We can get some of the way by saying that information states include classical tautologies for free. You might also wonder why the only admissible information states are <i>prime</i>, in that they must include at least one of P and Q whenever they include P∨Q: can’t someone have the information that P∨Q without having either the information that P or that Q? It’s a fair point, although it can be levelled at the FDE models as much as the classical ones. If both sides expand the class of information states to include any set of sentences closed under their favoured logic, that should give alternative model theories for the same consequence relations, but including non-prime information states. The classicist will also get the information state containing all sentences — FDE had it already — but that doesn’t change the consequence relation either and if they want they can exclude it by fiat. Allowing non-prime models may end up giving the classicist a model theory for classical logic that they can credibly defend as being the appropriate class of information states, although it’s possible there’s a straightforward objection to it that I’ve overlooked. Of course the option including the non-prime models does at least seem to use the logics themselves to define the classes of admissible information states, and this relates to an issue we’ll talk a bit about below.</p>
<h3>References</h3>
<ul>
<li>Anderson, Alan R. & Belnap, Nuel D. (1975). <i>Entailment: The Logic of Relevance and Neccessity</i>, Vol. I.</i> Princeton University Press.</li>
<li>Anderson, Alan Ross ; Belnap, Nuel D. & Dunn, J. Michael (1992). <i>Entailment: The Logic of Relevance and Necessity</i>, Vol. II. Princeton University Press.</li>
<li>Dorr, Cian (2005). What we disagree about when we disagree about ontology. In Mark Eli Kalderon (ed.), <i>Fictionalism in Metaphysics</i>. Oxford University Press. pp. 234--86.</li>
<li>Dultilh Novaes, Catarina (2019). Aristotle’s Defense of the Principle of Non-contradiction: A Performative Analysis. In D. Gabbay, L. Magnani, W. Park, and A.V. Pietarinen (eds.), <i>Natural Arguments: A Tribute to John Woods</i>. London, College Publications.</li>
<li>Field, Hartry (2015). What Is Logical Validity? In Colin R. Caret & Ole T. Hjortland (eds.), <i>Foundations of Logical Consequence</i>. Oxford University Press.</li>
<li>James, William (1907). <i>Pragmatism: A New Name for Some Old Ways of Thinking</i>. Duke University Press.</li>
<li>Jenkins, C. S. I. (2014). Serious Verbal Disputes: Ontology, Metaontology, and Analyticity. <i>Journal of Philosophy</i> 111 (9/10):454-469</li>
<li>Kimhi, Irad (2018). <i>Thinking and Being</i>. Harvard University Press.</li>
<li>Lewis, David (1988). Relevant implication. <i>Theoria</i> 54 (3):161-174.</li>
<li>MacFarlane, John. (2004). In What Sense (If Any) Is Logic Normative for Thought?. Draft https://johnmacfarlane.net/normativity_of_logic.pdf</li>
<li>Priest, Graham (2008). <i>An Introduction to Non-Classical Logic: From If to Is</i>. Cambridge University Press.</li>
<li>Quine, Willard V. O. (1951). Two Dogmas of Empiricism. <i>Philosophical Review</i> 60 (1):20–43.</li>
<li>Quine, W. V. (1953). Mr. Strawson on logical theory. <i>Mind</i> 62 (248):433-451.</li>
<li>Russell, Gillian (2008). One true logic? <i>Journal of Philosophical Logic</i> 37 (6):593 - 611.</li>
<li>Russell, Gillian (forthcoming). Logic isn’t normative. <i>Inquiry</i>: An Interdisciplinary Journal of Philosophy 1:1-18.</li>
<li>Ryerson, James (2018). Unpublished and Untenured, a Philosopher Inspired a Cult Following. <i>New York Times</i>, 26 September 2018. https://www.nytimes.com/2018/09/26/books/review/irad-kimhi-thinking-and-being.html</li>
<li>Smiley, Timothy (1996). Rejection. <i>Analysis</i> 56 (1):1–9.</li>
<li>Strawson, P. F. (1952). <i>Introduction to Logical Theory</i>. Routledge.</li>
<li>van Inwagen, Peter (1981). Why I Don't Understand Substitutional Quantification. <i>Philosophical Studies</i> 39 (3):281-285.</li>
<li>Wiredu, J. E. (1973). Deducibility and inferability. <i>Mind</i> 82 (325):31-55.</li>
</ul>
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</html>Michael Bench-Caponhttp://www.blogger.com/profile/13715068990919309271noreply@blogger.com3tag:blogger.com,1999:blog-6411624366539130337.post-23350683441822651182019-11-16T04:24:00.000-08:002020-01-08T13:49:41.996-08:00Dialetheism, Duchamp, And DeLoreans<!DOCTYPE html>
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<p>A while ago I read <a href="https://aeon.co/essays/how-can-duchamp-s-fountain-be-both-art-and-not-art" title="Aeon: How Can Duchamp's Fountain Be Both Art And Not Art" target="_blank">a piece in <i>Aeon</i> by Damon Young and Graham Priest</a>, which argued that Marcel Duchamp's <i>Fountain</i><a href="#note1" title="There's some evidence that Duchamp wasn't the artist behind Fountain, and that it was by one of his female friends. The leading contenders are apparently Louise Norton and Baroness Elsa von Freytag-Loringhoven. I'm not competent to assess the strength of the evidence, and I'll talk as if Duchamp was the artist because that's what Young and Priest do. But bear in mind that it may have actually been by someone else."><sup>1</sup></a> both is and isn't art. Before I read it, I had an idea where they might be going with it and was prepared to be unimpressed. I've got a lot of respect for Graham Priest (I hadn't heard of Damon Young) so I read it anyway, but I was expecting it to be a case of everything looking like a nail when all you've got is a hammer. (Or at least, when you have a hammer you're particularly pleased with.) I'm happy to report that I was wrong, and I suppose I owe them an apology. Sorry. In fact I found the thing so interesting that it's shifted the way I think about dialetheism a bit, or at least crystallized some of my thinking about it.</p>
<h3>Three Truth Values In The Fountain</h3>
<p>Priest is famously a dialetheist, in that he thinks that some statements are true even though their negations are also true. An example is "this statement is not true". Priest thinks this statement is both true and not true. I'm less confident than he is; I guess I'm probably about 60% sure that it's both true and not true<a href="#note2" title="60% is pretty impressionistic, and it isn't based on an explicit calculation. I do find dialethic solutions to the liar paradox the most satisfying, but I don't find them completely satisfying; for example they don't do too well with Curry's paradox. (I don't really think anybody does.) I also don't think the issues are well enough understood yet that anybody should be all that sure about the answer, although prior to knowing what our answers are one might expect him to be entitled to be more confident in his answer than I am in mine, because he's got more information than I have. One other worry I have is that I only prefer the dialethic solutions because I find Priest's writing easier going than Hartry Field's (Field [2008] is probably the main one on this), and so I've read and understood more of it, but if you start worrying about that sort of thing you might end up never being 60% sure of anything."><sup>2</sup></a>. Now, once you've decided that contradictions can be true, it gives you a new option for solving other philosophical problems. Often philosophical problems arise because there's a group of statements that all seem compelling, but they're jointly inconsistent. For most of us, this means we have to give one of them up. Dialetheists can accept them all. This is what I was expecting from Young and Priest's <i>Aeon</i> piece. I thought they were going to say that there were compelling reasons to think <i>Fountain</i> is art, and compelling reasons to think it isn't, and then encourage us to embrace the contradiction here as we already should be doing elsewhere.</p>
<p>That's not what they did, though. Instead, they said that its not being art is <i>the very thing that makes it art</i>. Here's one way they explain it:</p>
<blockquote><i>Fountain</i> can carry the message that it is not art only because it is not art - because its very entry into the artworld is defined by its rejection of art. Had it simply been art in an unproblematic sense - if, for example, Duchamp had chosen to paint an oil painting of a urinal - it could not have carried this message. This contrasts with the sign that is what it is because it has a message inscribed on it. So consider René Magritte's 1928-9 painting of a pipe. This literally bears the message '<i>Ceci n'est pas une pipe.</i>' The very words carry a message. By contrast, <i>Fountain</i> bears no explicit message. It conveys its message by being what it is. It is not art, and that is how it conveys its message. That is precisely why it is art. Put another way: contradiction is essential to <i>Fountain</i> as art. And if it didn't embody a contradiction, it wouldn't be half as interesting; we wouldn't still be talking about it.</blockquote>
<p>It's just a urinal, so it's not art, but presenting a piece of non-art as Duchamp did lets it convey a message in such a way as to make it count as art. (Even though the message is that it isn't art.) The key thing is that the message only works because it's not art. So if it isn't art then it is art, but this can't prevent it from not being art because if it did then there wouldn't be anything making it art anymore. (You can disagree with their intrerpretation of <i>Fountain</i> itself, but admitting it's an available interpretation should be enough to make the general point about dialetheism.) This back-and-forth dynamic parallels what you get with the liar sentence. If it's not true then it is true, but that can't prevent it from not being true, because then it wouldn't have anything making it true, so it wouldn't be true anymore. And then it would be true, and so on.</p>
<p>This isn't what I was expecting. They haven't just said that there are arguments on both sides and as dialetheists they have the option of accepting both sides; they've given an analysis of <i>Fountain</i>'s status that parallels the dynamic with the liar paradox, and it seems reasonable for them to resolve both issues the same way. I think we can all agree that this is much better, and so I was right to pleasantly surprised.</p>
<h3>Contradictions, Contradictions Everywhere</h3>
<p>Now, one thing that dialetheists sometimes worry about is what stops contradictions being true all over the place. If contradictions can be true, why aren't more of them true? If its being the case that I'm eating cornflakes doesn't prevent it from being the case that I'm not eating cornflakes, what <i>does</i> prevent it? I think this is a very difficult question, and often when I think about it I think that maybe I shouldn't be a 60%-committed dialetheist at all. But dialetheists do have things they say about the issue. In his book <i>Spandrels of Truth</i>, which I'm afraid I haven't read much of, JC Beall argues that dialetheias only show up when we're talking about truth. Dialetheias are a consequence of enriching our language with the kind of truth predicate Beall thinks we should use, and the rest of the language avoids them.<a href="#note3" title="I'm not sure whether Beall thinks of the language itself as generating the dialetheias, or whether he thinks of the dialethic propositions as being out there already and adding the truth predicate just enables the language to express them. Or perhaps it's a third option I haven't considered. I don't think it matters a great deal for what we're talking about here, and in any case both options seem like possibilities you might want to consider, depending on whether you think of truth as primarily applying to sentences or to propositions."><sup>3</sup></a> This gives a nice answer to the question of why there aren't dialetheias everywhere. We'll call someone with a view like that a <i>truth dialetheist</i>.</p>
<p>Unfortunately, the kind of dialetheia Priest and Young talk about suggests the phenomenon is more widespread than that. Perhaps with some purported dialetheias you can argue that they're covertly about truth. I can see someone doing that with Russell's paradox (does the set of all sets that don't contain themselves contain itself?) but with the <i>Fountain</i> case it seems a bit of a stretch. There are other cases dialetheists sometimes argue for too that occasionally seem plausible to me, for example inconsistencies in law, or games, or perhaps ethics. The ones that seem most plausible to me are the ones where a rule applies because it doesn't apply. Young and Priest draw attention to this factor themselves:</p>
<blockquote>It might seem that the paradox of the urinal is a cultural oddity: something that could happen only in the strange world of contemporary art; but, actually, it fits a much larger pattern of something being the case because it is not the case: <i>p</i> because it is not the case that <i>p</i>.</blockquote>
<p></p>
<p>So if you're someone like me, and you quite like the idea of dialetheias that fit this pattern but don't like any others, you've got an option for limiting them besides truth dialetheism. Dialetheias arise when something is a certain way because it isn't that way. To me this seems more satisfying, because if this kind of dynamic doesn't have to generate dialetheias, why does it generate them in the case of semantic paradoxes? There are undoubtedly ways to respond to that challenge, but let's suppose we go for the idea that dialetheias arise whenever something is the case because it isn't, but otherwise they don't arise. We'll call that view <i>explanation dialetheism</i>. This doesn't limit dialetheias as much as truth dialetheism, but it's still supposed to limit them a lot. But can it really do that? Will anything be safe?</p>
<h3>Persistent Macroscopic Physical Dialetheias</h3>
<p>Here's something Young and Priest say about the law of non-contradiction before explaining how <i>Fountain</i> manages to break it:</p>
<blockquote>[T]he principle of non-contradiction seems so firmly based in common sense. If an animal is a cat, it can't simultaneously not be a cat. It is either Thursday or not Thursday: it can't be both Thursday and not Thursday on the same day, here and now. But beware, as Ludwig Wittgenstein said, of an inadequate diet of examples!</blockquote>
<p>Now, Priest at least is holding back a bit on the esoteric dope here, because he's said things elsewhere that suggest he may think things can simultaneously be cats and not cats, and that it can be both Thursday and not Thursday. He's expressed sympathy (Priest 2006: chs 11-12) with the idea of dialetheias obtaining at the instant of change, so maybe as the clock strikes midnight it's both Thursday and not, and maybe if things become or stop being cats, around the beginning or end of a cat's life, there are things that are both cats and non-cats. But these situations don't last for very long. You don't go to the pet store and come back with something that both is and isn't a cat, and you don't schedule a meeting on Thursday and then wonder whether or not to go on the grounds that it both is and isn't Thursday. (Although people do set deadlines at 23:59 instead of midnight, presumably to avoid this confusion.)</p>
<p>Aside from instants of change, another place to look for physical dialetheias is in quantum mechanics. When things get very small they also get very weird, and dialetheists would be missing a trick if they didn't at least check to see if embracing contradictions can help us interpret quantum mechanics. Priest himself (2006: 180-1) makes this connection, though he does say his speculation is 'perhaps rather fanciful'.</p>
<p>We do still have some common-sense attachment to the law of non-contradiction, though. Maybe we can accept that physical dialetheias obtain for a moment here and there, or at the quantum level, but we don't expect them to hang around for a long time among middle-sized objects. We don't expect <i>persistent macroscopic physical dialetheias</i>. So, if dialetheias are confined to situations where things are a certain way because they're not that way, should we expect PMPDs? I think the answer is that it depends. Let's think about two more paradoxes: the <i>Pinocchio paradox</i> and the <i>grandfather paradox</i>.</p>
<p>The Pinocchio paradox [Eldridge-Smith and Eldridge-Smith 2010] arises because of Pinocchio's nose's disposition to grow when and only when he lies. If he says "my nose will be growing", then his nose should grow iff it doesn't. This fits into the explanation model of dialetheias: the nose will grow because it doesn't, but its growing would prevent it from growing, and so on. This puts pressure on us to make the semantic world and the physical world play by the same rules, because when you're Pinocchio there's a law-like connection between them. I don't really think someone like Beall should be too worried by it, though. And indeed Beall himself wasn't [2011], but his explanation seemed to me to muddy the waters a bit by talking about fiction, so I'll explain in my own way how I think dialetheists should respond to the Pinocchio paradox.</p>
<p>If physical dialetheias are impossible and semantic dialetheias are possible, then it just won't be possible for someone's nose to have the exceptionless disposition to grow when they say something false and not grow when they say something true. We don't worry that it's not possible for someone's nose to have an exceptionless disposition to grow when they're wearing a red sock and not grow when they're wearing a blue sock, on the grounds that there would have to be an exception when they were wearing one of each. The Pinocchio paradox is the same. At least, I think it's the same. Of course, if PMPDs are possible, then Pinocchio's nose could both grow and not grow, and the Pinocchio disposition need not be impossible after all. But the possibility of the disposition turns on the possibility of physical dialetheias, so to say that the Pinocchio paradox problematically commits semantic dialetheists to the possibility of physical dialetheias is question-begging. (It's also possible that you don't need the Pinocchio paradox itself; you could just ask whether Pinocchio's nose grows or not when he says 'this sentence is not true'.)</p>
<p>What about the grandfather paradox? I think that one's actually a lot harder. The grandfather paradox is the old chestnut where a time-traveller goes back and kills their grandfather. This means the time-traveller never gets born, so they never kill their grandfather, so their grandfather lives and they are born after all, and so on. This seems to fit the explanation model of what generates dialetheias perfectly. You're born because you weren't born; your grandfather lives because he doesn't live, and so on.</p>
<p>One resolution is to say that this isn't possible, and if time travel was possible then it would be possible, and so time travel isn't possible either. I don't find that very satisfying, because it doesn't seem like a good enough <i>reason</i> for time travel to be impossible. I fear that if I tried articulating the feeling further I might say something foolish, but perhaps you feel the same way.</p>
<p>A second resolution is to say that time travel is possible, but killing your grandfather before the relevant parent is conceived is not possible. This response says that there are various ways the world might be, and some of them are like those really carefully written sci-fi stories where all the time travel fits together properly, but none of them involve contradictions.</p>
<p>A third resolution is to say that you can go back and kill your grandfather, and this will generate a PMPD that spreads out throughout the universe from the point at which you arrive in the past onwards. We've established that the laws of physics permit killing, and so if they also permit time travel then the laws of logic will just have to deal with it.</p>
<p>What should the dialetheist say here? I think it's a lot harder to deal with this than with the Pinocchio paradox, because the grandfather paradox only uses dispositions that - we're assuming for the sake of argument - we have independent reason to think are possible. Now, I can imagine that some people who think time travel is fine as long as it doesn't generate paradoxes will say that I'm confused. And it's true, I am a bit confused. But I don't think I'm confused about the thing I think they'll think I'm confused about. David Lewis [1976] wrote what has kind of become the classic paper defending the "only non-paradoxical time travel" view, which I called the second resolution. That paper supplies the materials to accuse me of being confused about different contexts for evaluating possibility. When we say the time traveller can kill their grandfather we're holding fixed facts about their dispositions, and when we say they can't we're holding fixed historical facts about how they got there in the first place, and having those dispositions is compatible with having that history. What's incompatible with having that history is <i>manifesting</i> the disposition at that time.</p>
<p>I don't know. It's hard arguing with David Lewis, and I don't really expect to persuade anyone that he's wrong here. So instead I'll try shift the parameters of the debate a bit. They're already shifted somewhat by the fact we're viewing dialetheism as a live option, which Lewis never properly did<a href="#note4" title="Lewis declined to write an article for a collection on the law of non-contradiction [Beall, Priest and Armour-Garb 2004], and two letters from him to the editors are included in the collection instead [Lewis 2004]. He basically made the same move GE Moore used to make about various hairy metaphysical and sceptical theses: the law of non-contradiction is much more certain than anything you might try to base a refutation of it on."><sup>4</sup></a>. But there's something else going on here. Lewis, in a way, thought that <i>basic physical facts don't really have metaphysical explanations</i>. For Lewis, the universes (he thought there were lots) are just patchworks of local facts. Some look law-governed the way ours seems to; most are a complete mess. But there's no deep metaphysical sense in which one billiard ball hitting another makes the second shoot off to the pocket. One thing happens, another thing happens, we notice patterns and we give explanations in terms of the patterns. But there's no metaphysical explanation there. The proposition that grass is green is true <i>because</i> grass is green. That's real explanation, not just pattern recognition. But causal explanation is just pattern recognition. If the explanation dialetheist adopts this metaphysically lightweight account of causal explanations, they don't have pressure on them to resolve the grandfather paradox the same way they resolve the liar paradox. On this view the world isn't a machine; it's a jigsaw<a href="#note5" title="I owe the idea of jigsaw explanations to Alastair Wilson [2017: n.13], who mentioned the idea in the context of the many-worlds interpretation of quantum mechanics: 'It is also to possible to interpret EQM so that Everett worlds are causally isolated from one another, regarding the dynamical connections between worlds as giving rise to non-causal explanations. (Perhaps phenomena in each Everett world are explained non-causally by phenomena in nearby worlds, in the same sort of way that the shape of a jigsaw piece is explained by the shapes of the surrounding pieces.)' I'm not sure whether what he has in mind is the same thing I've got in mind, but that's where I got the metaphor from anyway."><sup>5</sup></a>. There are only so many ways of fitting pieces together, and time-travellers preventing their own births is not one of those ways.</p>
<p>So that's one way for the explanation dialetheist to avoid PMPDs. They can say that basic physical propositions can't be explained by their not being true, on the grounds that they're not really explained at all. But what if you're not a Lewisian/Humean? What if the world <i>is</i> a machine? Well, I think that in that case you've got problems. Cards on the table, I find the machine view of the universe much more appealing than the jigsaw view. And since I also think dialetheism is an appealing solution to the liar paradox but I'm pretty wary of PMPDs, I guess I've got problems. It's an odd combination of views, though. You're probably fine.</p>
<h3>Notes</h3>
<p id="note1">[1] There's <a href="https://en.wikipedia.org/wiki/Fountain_(Duchamp)#Origin" target="_blank" title="Wikipedia: Fountain (Duchamp) - Origin">some evidence</a> that Duchamp wasn't the artist behind <i>Fountain</i>, and that it was by one of his female friends. The leading contenders are apparently Louise Norton and Baroness Elsa von Freytag-Loringhoven. I'm not competent to assess the strength of the evidence, and I'll talk as if Duchamp was the artist because that's what Young and Priest do. But bear in mind that it may have actually been by someone else.</p>
<p id="note2">[2] 60% is pretty impressionistic, and it isn't based on an explicit calculation. I do find dialethic solutions to the liar paradox the most satisfying, but I don't find them completely satisfying; for example they don't do too well with Curry's paradox. (I don't really think anybody does.) I also don't think the issues are well enough understood yet that anybody should be all that sure about the answer, although prior to knowing what our answers are one might expect him to be entitled to be more confident in his answer than I am in mine, because he's got more information than I have. One other worry I have is that I only prefer the dialethic solutions because I find Priest's writing easier going than Hartry Field's (Field [2008] is probably the main one on this), and so I've read and understood more of it, but if you start worrying about that sort of thing you might end up never being 60% sure of anything.</p>
<p id="note3">[3] I'm not sure whether Beall thinks of the language itself as generating the dialetheias, or whether he thinks of the dialethic propositions as being out there already and adding the truth predicate just enables the language to express them. Or perhaps it's a third option I haven't considered. I don't think it matters a great deal for what we're talking about here, and in any case both options seem like possibilities you might want to consider, depending on whether you think of truth as primarily applying to sentences or to propositions.</p>
<p id="note4">[4] Lewis declined to write an article for a collection on the law of non-contradiction [Beall, Priest and Armour-Garb 2004], and two letters from him to the editors are included in the collection instead [Lewis 2004]. He basically made the same move GE Moore used to make about hairy metaphysical and sceptical theses: the law of non-contradiction is much more certain than anything you might try to base a refutation of it on.</p>
<p id="note5">[5] I owe the idea of jigsaw explanations to Alastair Wilson [2017: n.13], who mentioned the idea in the context of the many-worlds interpretation of quantum mechanics:</p>
<blockquote>It is also to possible to interpret EQM so that Everett worlds are causally isolated from one another, regarding the dynamical connections between worlds as giving rise to non-causal explanations. (Perhaps phenomena in each Everett world are explained non-causally by phenomena in nearby worlds, in the same sort of way that the shape of a jigsaw piece is explained by the shapes of the surrounding pieces.)</blockquote>
<p>I'm not sure whether what he has in mind is the same thing I've got in mind, but that's where I got the metaphor from anyway.</p>
<h3>References</h3>
<ul>
<li>Beall, JC 2009: <i>Spandrels of Truth</i> (Oxford University Press)</li>
<li>Beall, JC. 2011: 'Dialetheists against Pinocchio', <i>Analysis</i> 71(4): 689-91</li>
<li>Eldridge-Smith, P. and Eldridge Smith, V. 2010: 'The Pinocchio paradox', <i>Analysis</i> 70(2): 212-215</li>
<li>Field, H. H. 2008: <i>Saving Truth From Paradox</i> (Oxford University Press)</li>
<li>Lewis, D. 1976: 'The Paradoxes of Time Travel', <i>American Philosophical Quarterly</i> 13(2): 145-152</li>
<li>Lewis, D. 2004: 'Letters to Priest and Beall', pp176-7 in Priest, Beall and Armour-Garb [2004]</li>
<li>Priest, G., 2006: <i>In Contradiction: A Study of the Transconsistent</i>, 2nd ed., (Oxford University Press)</li>
<li>Priest, G., Beall, JC and Armour-Garb, B. 2004: <i>The Law of Non-Contradiction: New Philosophical Eassays</i> (Oxford University Press)</li>
<li>Wilson, A. 2017: 'The Quantum Doomsday Argument', <i>British Journal for the Philosophy of Science</i> 68(2): 597-615</li>
<li>Young, D. and Priest, G. 'It is and it isn't', <i>Aeon</i>, 22/9/16, https://aeon.co/essays/how-can-duchamp-s-fountain-be-both-art-and-not-art, accessed 31/5/18</li>
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</html>Michael Bench-Caponhttp://www.blogger.com/profile/13715068990919309271noreply@blogger.com1tag:blogger.com,1999:blog-6411624366539130337.post-45756238220457754732019-01-25T04:23:00.000-08:002019-01-26T14:13:33.812-08:00My Hair Is Remarkably Long<!DOCTYPE html>
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<p>I've written a new poem about my hair. It's called 'My Hair Is Remarkably Long'. I hope you like it. Here it is.</p>
<p>I can wrap it around myself thrice when it's cold<br>
It's the texture of silk and the colour of gold<br>
I've been growing it since I was seven months old<br>
My hair is remarkably long</p>
<p>Yes it's long, and it's strong, and it's fragrant and fair<br>
If I sold it then I'd be a millionaire<br>
But I love it, it's mine, and I don't want to share<br>
My hair is remarkably long</p>
<p>For a terrible moment I thought it was lost<br>
(It had trailed in some gum that a litterbug tossed)<br>
But the gum was removed at exorbitant cost<br>
So my hair's still remarkably long</p>
<p>I will grow it until I'm one hundred and three<br>
Till Antarctica melts and we're back in the sea<br>
Until even Rapunzel is balder than me...</p>
<p>But it's already remarkably long!</p>
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</html>Michael Bench-Caponhttp://www.blogger.com/profile/13715068990919309271noreply@blogger.com2tag:blogger.com,1999:blog-6411624366539130337.post-67684106929783606212018-12-22T09:41:00.000-08:002019-02-04T03:36:13.451-08:00Rationalism And Science <html>
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<p>I've been thinking a bit about rationalism, empiricism and science, and I tried writing some notes to organize my thoughts about it. It's all pretty half-baked and unsatisfactory, but I've turned it in into something I can put here anyway, in case it's the kind of thing anyone likes to read.</p>
<h3>Rationalism vs Empiricism</h3>
<ul>
<li>Roughly: empiricists think knowledge only comes from experience, while rationalists think pure reason has an important role.</li>
<li>Rationalists tend to think experience has some role too, although they might think that the kind of knowledge that involves experience isn't so good, or perhaps isn't knowledge strictly speaking at all.</li>
<li>Empiricists sometimes think it's OK to get mathematical and/or logical knowledge from pure reason. Maybe you can get some knowledge of analytic truths that way too, although under the influence of Quine (and Morton White, usually via Quine) they might not think there are any properly analytic truths.</li>
<li>If you want to firm up this second source of knowledge as part of your position, you can appeal to <i>Hume's Fork</i>. Hume's Fork is the idea summed up in this quote from the end of his <a href="https://www.gutenberg.org/files/9662/9662-h/9662-h.htm" target="_blank" title="Gutenberg.org edition"><i>Enquiry Concerning Human Understanding</i></a> (emphasis in original):
<blockquote>"If we take in our hand any volume; of divinity or school metaphysics, for instance; let us ask, <i>Does it contain any abstract reasoning concerning quantity or number?</i> No. <i>Does it contain any experimental reasoning concerning matter of fact and existence?</i> No. Commit it then to the flames: for it can contain nothing but sophistry and illusion."</blockquote>
It takes some interpreting to get this passage to be arguing for exactly the empiricism-plus-maths-and-logic position, but it's in the ballpark. If you do adopt this package, you might even be able to get away with calling yourself a logical empiricist, like Rudolf Carnap. Carnap is very in at the moment, and is also generally considered to have been a great guy.</li>
</ul>
<h3>Descartes And Leibniz</h3>
<ul>
<li>They were scientists and mathematicians, but they were also metaphysicians.</li>
<li>As philosophers, we tend to look more at their metaphysics than their science, unless we're specialists. The science is more obsolete than the metaphysics (although perhaps not more wrong), science isn't really taught via 300-year-old texts even when it isn't obsolete, and we're not studying science anyway. And we're probably even less interested in reading their maths than in reading their science.</li>
</ul>
<h3>The Appeal Of Empiricism</h3>
<ul>
<li>When you're reading their metaphysics, sometimes they will invoke principles of pure reason to derive their metaphysical conclusions. For example, Leibniz invokes such useful gizmos as the <i>Principle of Sufficient Reason</i> and the <i>Identity of Indiscernibles</i>. Descartes says things like <i>there must be at least as much reality in an efficient and total cause as in the effect of that cause</i> (from Desmond M Clarke's 1998/2000 translation of Descartes' third <i>Meditation</i>). And Spinoza, the other member of the Big Three rationalists, takes this kind of thing to a whole new level with an axiomatic presentation of his grand metaphysical system in the <i>Ethics</i>. You have to wonder what justifies their principles, and sometimes it can seem like they're just making up premises on the fly to get themselves out of an argumentative tight spot. I suppose this is particularly the case with Descartes, who makes things even worse by appealing to the <i>light of nature</i>, or the <i>natural light of reason</i>, and we often read Descartes when we're young and impressionable. Perhaps harping on about the natural light of reason makes a good impression on some young philosophy students, but it didn't make a good impression on me.</li>
<li>The metaphysical conclusions that they derive aren't even especially attractive to a lot of us. The existence of God, the non-physical soul, pre-established harmony and so on. We feel like we could easily get by without them, and then we wouldn't have to accept the premises, or the embarrassing Light Of Nature methodology by which they arrived at them.</li>
<li>Science, on the other hand, is an <i>empirical</i> discipline. We're quite sure of that. So while we might not know exactly what goes on across campus in the science departments, we don't really worry that anything of importance will be lost to science if we become empiricists. So we can keep science much as it is, while taking a suitably unenthusiastic attitude towards metaphysics, saying that metaphysical theses are either unknowable, or probably wrong, or Not Even Wrong.</li>
<li>We can still do a little bit of metaphysics, criticizing theses for conflicting with our best science, or for being internally incoherent. And we can also sometimes have a go at offering an empiricist critique of some of the things scientists get up to, when we take them to be straying into metaphysics. The interpretation of quantum mechanics is a good source of material there, although it is often difficult for philosophers to understand the relevant science well enough to get taken seriously. (And even if they do understand the science, getting taken seriously still isn't a given.)</li>
</ul>
<h3>Pure Reason In Science?</h3>
<ul>
<li>All this seems like a very nice package, but there's a fly in the ointment, which is that scientific methodology may actually include an awful lot of rationalism. Sure, it's an empirical discipline, in that scientists gather data and do experiments and so on. But they also spend a lot of time filling whiteboards with equations, and they're even known to have flashes of inspiration in the shower, as if their problem has been suddenly illuminated by the light of nature. (Archimedes' alleged eureka moment in the bathtub is <i>not</i> a good example of this, since his flash of inspiration was about his displacement principle, and one has experiences relevant to that in a bathtub. But it does happen to scientists working on things besides bathtubs too.) </li>
<li>Empiricists do have resources to push back on this line of thought. They're still allowed to use pure reason for maths, and for logical inferences. Perhaps that's what's going on with the whiteboards and the flashes of inspiration, and so under closer examination it will turn out that scientists aren't doing anything outside the empiricist's rules. </li>
<li>Now, the closer examination of actual scientific practice is something that has been done an awful lot by other people, under the auspices of history and/or philosophy of science. I blush to confess that I do not have much familiarity with any of this literature. If you do, then please do correct me if I'm wrong, because I'm going to make a naive pessimistic case that under closer examination what we'll find is that science is in fact a bit of a Cartesian free-for-all.</li>
</ul>
<h3>The Problems Of Induction</h3>
<ul>
<li>Induction, roughly, is when you take some observations, find a general rule that fits the observations, and then apply that rule to make predictions about new observations. If it didn't work, then it'd be hard to see how science could work. But there are two reasons why it is hard to see how induction could possibly work.</li>
<li>The classic <i>problem of induction</i> is the problem of justifying the idea that old patterns can be expected to persist at all. We set up the dilemma as follows. (It'll be based on AJ Ayer's presentation of the problem in chapter two of <i>Language, Truth and Logic</i>, although Ayer himself thinks the problem's very hopelessness makes it a pseudo-problem as traditionally conceived.) Either inductive reasoning is justified deductively or inductively. An inductive justification would point to how old patterns have persisted after being identified before, and this is itself a pattern we can expect to persist into the future. But this reasoning seems circular. The deductive justification is in bad shape too, on the grounds that there just isn't any logical inconsistency in patterns being broken. A coin landing heads twenty times in a row is consistent with its landing heads the twenty-first time, as an inductive reasoner would presumably predict, but it's also consistent with its landing tails the twenty-first time, providing a counterexample to any attempted deductive justification of induction.</li>
<li>The <i>new riddle of induction</i>, which we have Nelson Goodman to thank for, is still a problem even if you can solve the classic problem of induction. This time the problem is no longer showing that patterns will persist, but deciding which patterns we should expect to persist. There are lots of patterns consistent with any dataset, and we will get different predictions depending on which patterns we identify. Of course, there are some patterns that humans identify more readily than others. But justifying this as anything more than a cognitive bias, while still working within the empiricist's rules, is difficult.</li>
<li>Rationalists, as we've learned, can appeal to the light of nature to get themselves out of just this kind of tight spot. Can't justify induction inductively or deductively? Just appeal to the light of nature! Not sure which pattern is more likely to persist? Let the light of nature show you the way.</li>
<li>This is of course a bit flippant. Rationalists do have resources to invoke premises when an empiricist would be in a tight spot, but they can't do this arbitrarily, at least not by their own lights. Are the resources you need to deal with induction the kind of resources rationalists would appeal to?</li>
<li>I think they are, or could well be. To get a handle on why, consider Plato's theory of forms. One of the problems the forms are supposed to solve is how we can have knowledge of general things, even though we only experience particular things. Plato's idea is that knowledge of general things is knowledge of transcendent forms, which are somehow reflected in the particular things, and which we apprehend with the intellect rather than with the senses. Mathematical knowledge is knowledge of forms, but scientific knowledge is knowledge of forms too. Aristotle didn't think that forms were transcendent, but (as I understand it) he still thought that scientific knowledge was knowledge about forms, or essences if that's different, and that in any case these are apprehended by the intellect. The exact mechanism by which the intellect apprehends the forms is hard to pin down - Plato suggested we remember them from directly experiencing them before we were born - but the idea of scientific knowledge being knowledge of something general apprehended by the intellect has had real staying power, and is the kind of thing rationalists in particular are into.</li>
<li>This gives rationalists a bit of purchase on the problems of induction. For the classic problem, the idea is that we can learn something about events before we observe them, because the same forms show up in those events as the ones we have already observed. For the new riddle, the idea is usually that not all rules are equal because some correspond simply to forms, and some don't. Not every gerrymandered property you might think of corresponds to a form, and the ones that don't aren't as likely to fit in robust generalizations.</li>
<li>You can try to rerun the arguments against the rationalist if you like. How do we know that forms will carry on behaving the same way we're used to? How do we know which properties correspond to forms? Well, because we examine them with our intellects and discover which forms there are and that they behave uniformly. How do we pull that off? Good question! But it seems we do pull it off, since science works. Denying that it could possibly work flies in the face of the evidence, and denying that it could work this way risks begging the question against the rationalist.</li>
<li>So, we've got an argument that science has a problem that rationalists have the resources to solve and empiricists don't. For that, we didn't need to look at the actual practice of science at all. But now things get a little trickier. I'm going to make two suggestions, neither of which I have the expertise to properly back up.
<ul>
<li>First, a large part of what Descartes and Leibniz liked about being rationalists was that it gave them the resources as scientists to respond to just this kind of problem.</li>
<li>Second, not much has changed. Scientists are still leaning heavily on roughly the same rationalist methodology that Descartes was into, and being wildly successful with it too.</li>
</ul></li>
</ul>
<h3>How Descartes And Leibniz Did Science</h3>
<ul>
<li>In the seventeenth century it was possible to feel really good about the prospects for science. The progress they were making made understandable a level of optimism that may only have been equalled before or since by physicists in the late 1920s. They really felt like they would soon have it all figured out, and that when they did the answers would be simple, beautiful, and powerful.</li>
<li>Descartes and Leibniz also took it more or less as a methodological axiom that the world was nicely ordered along principles that could be understood and discovered by humans. This is an idea that goes back at least to Plato's <i>Timaeus</i>, and on some accounts goes all the way back to Thales and is what sets philosophers like him apart from the storytellers like Homer and Hesiod who came before him. The Stoics were big on the idea, it persisted in some form throughout the middle ages, and in the seventeenth century it was as popular as ever. It's an appealing idea, and people working with the idea keep making discoveries and building cool stuff, while sceptics just bring everybody down. When asked to justify this methodological axiom, neither Descartes nor Leibniz was above talking about God. Both of them thought that God in his goodness had given us rational faculties which when used properly would be able to get us significant scientific knowledge of the world. Leibniz in particular also thought that God's perfection meant that he would make the world excellent - the best of all possible worlds, as they say - and that we could work out what would count as excellent, and use this to guide our theorizing both in science and metaphysics.</li>
<li>So, how do you do science with this attitude? Well, prompted by observations and guided by the light of nature, you come up with a beautiful, simple, powerful theory of how the world works. You make the theory nice and mathematical, and maybe come up with some new maths like calculus (Leibniz) or co-ordinate geometry (Descartes) especially for the purpose. You do experiments to test the theory. If the predictions are borne out, great! If not, maybe there's something wrong with the experiments. Or <i>maybe</i> there's something wrong with the theory. Eventually you come up with something nice that fits the results you're getting. And because the world does in fact conform at least approximately to the kind of principles that seem simple and beautiful to seventeenth-century optimists, the whole thing went swimmingly.</li>
</ul>
<h3>How We Do Science Now</h3>
<ul>
<li>Basically what I want to say is that we do things much the same way. We might not think that's what we're doing, but it is. More or less.</li>
<li>When scientists are explaining how science progresses now, they'll sometimes offer an account based on Karl Popper's ideas. I haven't read Popper, and I expect the scientists often haven't either, because the account isn't really very plausible and it'd be uncharitable to attribute it to Popper himself. Here's how it goes. Scientists look at the data they're already aware of, and they come up with a theory that fits. The important thing about the theory is that it be <i>falsifiable</i>, in that there are experiments they could do or observations they could make that would show that the theory was false. Then they do experiments and/or make observations. If the results are what the theory predicts, the theory is more likely to be true. If the results aren't what the theory predicts, the theory is false and so they go back to the drawing board.</li>
<li>When pressed, people usually admit that this does not really reflect scientists' actual responses to data not fitting their theories. There might be something wrong with the experiment, or maybe the theory does predict it after all but there was something in the initial conditions you weren't aware of. A classic example is the orbit of Uranus: it didn't fit with the predictions people made for it using Newtonian mechanics and gravity, but that's just because they didn't know Neptune existed. Include the gravitational effects of Neptune and Newtonian mechanics and gravity aren't falsified after all. That's how Neptune was discovered, or so I'm told. (The hero of that story is Urbain Le Verrier.) They tried to pull the same trick with a planet inside Mercury, which they called Vulcan, but there it turned out Newtonian mechanics and gravity really were the problem, and Einstein's theory of gravity explains it much better. But there was a long time in between unsuccessfully looking for Vulcan and rejecting Newtonian gravity.</li>
<li>OK, so let's put aside naive falsificationism. How <i>does</i> science work, then? Well, I'd suggest they do pretty much what Descartes did. You have a sense of the kind of data you're trying to fit your theory into, and then you make something up that you're happy with, guided by the light of nature. Your theory will have some blanks in it like the mass of the electron or whatever, and when you find some way of taking measurements to fill in the blanks, you do. Then you cling on to the theory like grim death in the face of both friendly and unfriendly data until finally you come up with something you're not quite as unhappy with. This account adopts some themes people tell you come up in Kuhn and Lakatos - I haven't read them either - and what it agrees with Popper about is that the whole process works much more smoothly if your theory is the kind of thing that data can be friendly or unfriendly to. (That's why it doesn't work so well for metaphysics, I suppose.)</li>
<li>The account is a total caricature, of course. But I'm hoping it's a caricature of the actual practice of science, unlike naive falsificationism, which is a caricature of what some scientists imagine they must be doing because rationalism somehow doesn't seem hard-nosed enough. Now, while it might sound like I'm being a bit mean to scientists, that's not my intention. If the rationalists are right, then this could be exactly what scientists ought to be doing. And whatever they're doing, they seem to be doing it very well.</li>
</ul>
<h3>The Moral Of The Story</h3>
<ul>
<li>Sometimes people give the rationalists a hard time. We do sort of acknowledge that Descartes, Spinoza and Leibniz were great philosophers - I mean, everyone says so, right? - but when we look at their philosophical systems what we see are bad arguments for false conclusions. It's all too easy to attribute this to a bad methodology, saying that the problem is that they were rationalists. Maybe we should ditch the light of nature, stick with empirical methods plus maths and logic, embrace science and be quietist about metaphysics.</li>
<li>What I'm suggesting is that this line of thought has a great big hole in it, which we don't notice because we don't think of the rationalists as scientists. Or perhaps we do think of them as scientists, but don't think of that as relevant to their philosophy. But it is relevant. They were scientists, they were good at it, they did science as rationalists, and we're still doing that today. If you want to assess rationalism at its best, then don't consider it as a method in metaphysics; consider it as a method in science. That's the moral of the story. The question is, is it a <i>true</i> story?</li>
</ul>
<h3>What's Wrong With This Picture?</h3>
<ul>
<li>I mentioned earlier that there's a lot of stuff here that I'm pretty ill-informed about. Maybe you thought I was being disingenuous, but I wasn't. There's a lot to learn here, and I haven't learned it. And if you have, you probably don't need me to tell you that. The evidence is right there on the page.</li>
<li>Nonetheless, this is where I am at the moment with this stuff. From where I'm sitting, it looks like you can't really get anywhere in science as an empiricist, the actual practice of science bears this out, and the rationalists should be given a bit more credit for it. So, what might I be wrong about?</li>
<li>First, I might be wrong about empiricism's platform. Maybe they've got some clever solutions to the issues with induction that I was worrying about. Or maybe they're willing to embrace a greater level of scepticism than I appreciate.</li>
<li>Second, I might have Descartes and Leibniz wrong. I've read a fair bit of both, but there's an enormous amount left that I haven't read, and I do find the scientific practice they envisage all a bit mysterious. That's why I describe it in these scathing terms, before insisting that what I described is the tried and tested scientific method that built the modern world. I think we should have a fairly low prior that a method that sounds like that could build a world that looks like this.</li>
<li>Third, I might have modern science wrong. Who knows what these people get up to? <i>They</i> don't even seem to know. But those historians and philosophers of science I mentioned before probably have some idea, and I could try checking some of that out. I could at least read Kuhn. Everyone reads Kuhn.</li>
<li>Fourth, I might be wrong about something else. I don't know what. But the whole situation is very unsatisfactory, and I think I must be missing something.</li>
</ul>
<h3>Reading List</h3>
<ul>
<li>So, I've got some reading to do! If you've got this far and you think I'm a doofus who should calm down and read X and then everything will become clear, then please point me towards X in the comments. In the meantime, here are some things I could look at.</li>
<li>The logical positivists/empiricists in the first half of the twentieth century were often pretty clued up about science, but they were also pretty thoughtful and self-aware about their empiricism. So perhaps I should read some Schlick or something.</li>
<li>I found a book in a second hand shop the other day by Daniel Garber called <i>Descartes' Metaphysical Physics</i>. I probably won't read it all, because I am a non-serious person, but it looks relevant and I'll probably read some of it.</li>
<li>I could have a look at some of Descartes and Leibniz's more scientific stuff, and see how they talk about what they're doing.</li>
<li>I've only got a pretty sketchy understanding of Plato and Aristotle's understanding of form and how it helps with epistemology, so I should probably read something about that.</li>
<li>Like I say, I could read Kuhn, at least <i>The Structure of Scientific Revolutions.</i> I should probably read something by Lakatos too. Popper is less of a priority.</li>
<li>I saw an NDPR review of a book called <a href="https://ndpr.nd.edu/news/platonism-at-the-origins-of-modernity-studies-on-platonism-and-early-modern-philosophy/" target="_blank"><i>Platonism at the Origins of Modernity: Studies on Platonism and Early Modern Philosophy</i></a>, and it looked like some of the papers in that would be relevant.</li>
<li>Once I've got through that lot I'll probably be down multiple rabbit-holes, so for me to put anything else on the list now would probably be a bad idea. But if you can point me to anything that would sort all this out for me, I'm all ears.</li>
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</html>Michael Bench-Caponhttp://www.blogger.com/profile/13715068990919309271noreply@blogger.com0tag:blogger.com,1999:blog-6411624366539130337.post-70738379573002659552018-10-12T06:33:00.000-07:002018-10-12T06:33:19.499-07:00Gambling With The Metaphysics Oracle<!DOCTYPE html>
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<h3>A Tax On Bullshit</h3>
<p>There's a lot of bullshit around. Wherever you look, people are confidently making predictions, often while being paid to so, and by the time we've been able to test these predictions the people who made them are long gone, sunning themselves on a beach somewhere, spending our money and laughing at us. It's a sorry state of affairs. What can we do about it?</p>
<p>One idea, and it's a good one, is to get people to put their money where their mouths are. Offer people bets on their predictions. If they really believe what they're saying, they shouldn't mind having a little bet on it. If they don't believe it and bet anyway, then at least their bullshit is costing them something. People sometimes call betting on predictions a "tax on bullshit". The person I've heard talking most enthusiastically about this idea is Julia Galef, who I suppose is a pillar of what people refer to as the Rationality Community. Apparently she does it in her everyday life. She's always sounded to me as if she has a fun life, but I think I'm probably too much of an epistemic pessimist to fit in well with the Rationality Community myself.</p>
<p>Regular readers may recall that I sometimes worry about <a href="http://michaelbenchcapon.blogspot.com/2016/03/bullshit-philosophy-and-regulatory.html" title="Bullshit, Philosophy and Regulatory Capture" target="_blank">bullshit in philosophy</a>. A lot of the claims philosophers make aren't really very testable at all, and so you can keep up your bullshit for thousands of years without ever being found out. Of course, if something isn't testable then it's not practical to bet on it. But lately I've been wondering how philosophers, particularly metaphysicians, would react if we somehow could offer them bets on their claims. Peter van Inwagen (1990), for example, doesn't think tables exist. When we think we're in the presence of a table, he thinks we're really just in the presence of some simples arranged tablewise. But if we could go to an Oracle to settle the question, would he put his simples arranged moneywise where his simples arranged mouthwise are?</p>
<h3>Taking The Bet</h3>
<p>The simplest response is for the philosopher to just take the bet, and offer us very favourable odds corresponding to how very sure they are that they're right. Maybe the methods we use for answering metaphysical questions aren't so different in principle from the methods we use for answering any other kind of question, and if we've got what we take to be a good argument then we should be confident in its conclusion. I think that plenty of metaphysicians would have no problem at all taking these bets. They mean what they say quite literally and they are confident that their answers are right.</p>
<h3>Declining The Bet</h3>
<p>A second response is not to take the bet, on the grounds that you don't actually believe the metaphysical positions you've taken. There are at least two ways this could work, one obvious and disreputable and the other less obvious and more respectable. The obvious one is that you're not actually committed to these positions the way you said you were. You were bullshitting, perhaps without properly realizing it, and now you've been found out. The more respectable one is that you are committed to your metaphysical positions, but the mode of commitment you take to be appropriate to metaphysical positions is not belief. It's something else. Helen Beebee (2018) argues for <a href="https://www.aristoteliansociety.org.uk/pdf/beebee.pdf" target="_blank" title="Beebee: Philosophical Skepticism (pdf)">something along these lines</a>, building on Bas van Fraassen's work on the analogous question in the philosophy of science. For Beebee it's largely a response to the phenomenon of expert disagreement in philosophy and concern about the reliability of philosophical methods, while for van Fraassen I understand it's more about the underdetermination of scientific theories by evidence<a href="#Fraassen"><sup>1</sup></a>. For Beebee and van Fraassen, this kind of commitment is less about believing the untestable parts of the theory and more about committing oneself to participating in a particular research programme.</p>
<h3>Rejecting The Setup</h3>
<p>A third response is to reject the bet on the grounds that you reject the authority of the Oracle. How can you reject the authority of an Oracle? The basic idea is that we can't imagine anything the Oracle could say or do to convince us that our position is wrong, but you have to be careful with this sort of dialectical move. You don't want to be the sort of person who responds to the trolley problem<a href="#Trolley1"><sup>2</sup></a> (<a href="https://philpapers.org/archive/FOOTPO-2.pdf" title="Foot: The problem of abortion and the doctrine of the double effect" target="blank">Foot 1967</a>) by saying they'd dive off the trolley and push the workers out of the way, or some other such silliness. This kind of move usually just serves to derail the conversation and prevent us from engaging with the point the thought experiment was trying to make. In the trolley problem you just stipulate that the situation is simple and the outcomes given each action are certain.<a href="#Trolley2"><sup>3</sup></a> In the Oracle thought experiment you similarly stipulate that the Oracle is reliable (or infallible) and trusted by all parties. Nonetheless, I think that sometimes it does tell us something useful if we push back on the setup.</p>
<p>The cleaned up certain-outcomes version of the trolley problem isn't very realistic, but it's still something we can imagine. With at least some metaphysical questions, however, the Oracle thought experiment might give rise to what philosophers call <i>imaginative resistance</i>. This is what happens when what you're being asked to imagine somehow doesn't make sense to you, to the point that you struggle to imagine it. It can happen in various ways, including when a story is blatantly inconsistent, or when the moral facts in a story as stipulated conflict with the moral judgements we're inclined to make ourselves when given the non-moral facts. I want to suggest that this imaginative resistance is an indication that even if we take for granted that the Oracle is reliable and that we trust it, this might not be enough. We might still disagree with it, for reasons other than our not trusting it.</p>
<p>I can think of a couple of kinds of case where this situation might arise. Both embody a kind of Carnapian attitude towards philosophical questions. First, suppose we're asking the Oracle about whether there are tables, and it says that there are. Van Inwagen could respond in a couple of ways:</p>
<ul>
<li>"Fair enough; that's a weird and oddly cluttered world, and there was no way for me to find out that there were tables, but I guess you're the Oracle here."</li>
<li>"Look, if you want to describe the world as having tables in it, that's up to you. I'm going to keep describing it as not having tables. We're both right by the lights of our own description schemes, and choosing between the schemes is a practical matter about which you're not the boss of me."<a href="#vanInwagen"><sup>4</sup></a></li>
</ul>
<p>Second, suppose that we're asking the Oracle what the correct analysis of knowledge is, and it says the correct one is Robert Nozick's (1981) counterfactual truth-tracking analysis. We point out all the bizarre results this commits us to as outlined by Saul Kripke (2011), and the Oracle just shrugs, says that's what the word "know" means, and presents a bunch of linguistic usage data to back up its claim. Again, two responses:</p>
<ul>
<li>"Fair enough; the word 'know' isn't as useful as we thought it was, and we can be forgiven for thinking Nozick was wrong, but it means what it means and we must accept that."</li>
<li>"Look, if that's what the word means, then the word isn't fit for purpose. We need a concept of knowledge we can use for talking about important issues about humans' access to information about the world, and the concept embodied by this linguistic usage data simply can't be used for that."</li>
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<p>These two cases are quite similar. The difference is that in the tables case the philosopher says they weren't wrong about anything: the Oracle and the philosopher have just made different choices, and they are the authorities over their own choices. In the knowledge case the philosopher is shown to be wrong about who knows what, but they push back by saying this just means we need different concepts. The cases kind of shade into each other a bit, but I think the distinction is there, and that the knowledge and tables cases are on different sides of it. Van Inwagen would not be surprised to be shown that we talk as if there are tables. Kripke would be surprised to be shown that we talk as if Nozick's is the correct analysis of the concept expressed by the word "know". That's a difference.</p>
<p>Now, even if you take one of these Carnapian lines, the Oracle could still push back and say that actually you're wrong about whose concepts are better. It might not want to do that in the knowledge case; it might agree that our word "know" attaches to a concept that isn't very useful. But the point is that the Oracle knows everything there is to know, and so it might know something that would make you change your mind. The thought here is along the lines of what <a href="https://www.dropbox.com/s/cfpcezfc6k0ew0d/SeriousVerbalDisputes.pdf" title="Jenkins: Serious Verbal Disputes (pdf)" target="_blank">Carrie Jenkins (2014)</a> argues for and calls <i>Quinapianism</i>: the decisions over which concepts to use to describe the world are up to us the way Carnap thinks, but our views about which concepts are best are revisable in the light of new information the way Quine thinks all our cognitive commitments are. But even if the Oracle's omniscience gives it an advantage over us, what we end up with here is still a philosophical discussion of the more familiar kind. The Oracle makes the case for its recommended set of concepts, but it's still up to us which concepts we end up using.</p>
<h3>So What?</h3>
<p>I've had a bit of fun thinking about this, but does it tell us anything about anything? I think it does. I'm inclined to take philosophical questions at face value, and to have the same commitments with respect to them inside and outside of the philosophy room. If I'm bullshitting, I'm not consciously or deliberately bullshitting. I've got a lot of philosophical commitments, albeit subject to a great deal of uncertainty, and I'm sincere about them. But I think my responses to this thought experiment vary a lot depending on which philosophical question we're talking about. Sometimes I think I'd take the bet. Sometimes considering being offered a bet makes me feel more uncertain. (I guess in these cases either I'm being called on my bullshit or the feeling of added uncertainty is itself unjustified. Perhaps it's rooted in risk aversion.) And sometimes I come over a bit Carnapian and get one or other kind of imaginative resistance. (I'm not sure I ever feel the way Beebee suggests I should feel, but I don't understand her position terribly well, and in any case I've only run the thought experiment on a few questions.)</p>
<p>This variation is interesting to me. When people are talking about the status of philosophical propositions and beliefs, they sometimes make it sound like they think we should go for the same response to everything, or perhaps one response for ethics and another for everything else. But I feel very torn between the different responses for a lot of questions, and I lean quite different ways for different questions even within the same branch of philosophy. So when Beebee, Carnap and the rest are putting forward views on the status of philosophical disputes, an answer that works well for one dispute may not work so well for another. One more thing to worry about, I guess.</p>
<h3>Notes</h3>
<p id="Fraassen">[1] There is a connection here, in that van Fraassen is sceptical about the reliability of scientific methods to verify the parts of theories that go beyond their empirical adequacy, for example by positing unobservable entities. I'm not a good source for van Fraassen though: most of this is coming from Beebee's account of his position.</p>
<p id="Trolley1">[2] The trolley problem is a thought experiment where someone driving a train (or trolley) is going to hit five workers on the tracks, and the only way to avoid killing them is to steer down a side track and kill another, different worker. The original puzzle is explaining why the driver ought to steer and kill one to save five, even though in some other situations it's better to do nothing and let five people die than to act to save them at the cost of killing someone else. Foot gave the example of framing someone to prevent a riot, and another common one is killing someone to use their organs, which I think is due to Judith Jarvis Thomson (1985). Since Thomson's paper there has been a large research programme involving variants on the trolley problem. Some people think it is silly and dismissively call it 'trolleyology'. My own view is that it's unfairly maligned, although I do quite like the word 'trolleyology'.
<p id="Trolley2">[3] Foot does acknowledge that the trolley case isn't especially realistic and that the worker might be able to get out of the way. But she also notes that the relevant aspects of the outcomes often really are more or less certain in the real-life medical situations she's using the trolley problem to illuminate.</p>
<p id="vanInwagen">[4] As I understand him, van Inwagen himself is probably enough of a realist about metaphysics that he should go for the first answer rather than the second. But the availability of the second is what I'm interested in here, and other philosophers do apply a Carnapian approach to questions about composition, including the question of whether there are tables. The main person for this approach is probably Eli Hirsch.</p>
<h3>References</h3>
<ul>
<li>Beebee, Helen (2018). I - <i>The Presidential Address</i>: Philosophical Scepticism and the Aims of Philosophy. <i>Proceedings of the Aristotelian Society</i> 118 (1):1-24.</li>
<li>Foot, Philippa (1967). The problem of abortion and the doctrine of the double effect. <i>Oxford Review</i> 5:5-15.</li>
<li>van Inwagen, Peter (1990). Material Beings. Cornell University Press.</li>
<li>Jenkins, C. S. I. (2014). Serious Verbal Disputes: Ontology, Metaontology, and Analyticity. <i>Journal of Philosophy</i> 111 (9-10):454-469.</li>
<li>Kripke, Saul A. (2011). Nozick on Knowledge. In <i>Philosophical Troubles. Collected Papers Vol I.</i> Oxford University Press.</li>
<li>Nozick, Robert (1981). <i>Philosophical Explanations.</i> Harvard University Press.</li>
<li>Thomson, Judith Jarvis (1985). The Trolley Problem. <i>The Yale Law Journal</i> 94 (6):1395-1415</li>
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</html>Michael Bench-Caponhttp://www.blogger.com/profile/13715068990919309271noreply@blogger.com1tag:blogger.com,1999:blog-6411624366539130337.post-47952426016057515802018-07-26T05:48:00.000-07:002018-07-26T05:48:12.646-07:00Domestique<!DOCTYPE html>
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<p>I've been following the Tour de France this year, and yesterday I wrote a poem about it. It's called 'Domestique'. I hope you like it. Here it is.</p>
<p>I am a humble domestique<br>
I ride the Tour de France<br>
My sponsor's name is on my shirt<br>
And also on my pants</p>
<p>And though I will not win today<br>
I must pretend to try<br>
So when the cameras film it all<br>
They're advertising Sky</p>
<p>It's even worse when riding up<br>
An Alp or Pyrenee<br>
Those are the days I'm someone it's<br>
No fun at all to be</p>
<p>I'm not as strong as Froome, of course<br>
But Froomey needs to chill<br>
So he stays in my slipstream, while<br>
I drag him up the hill</p>
<p>If Froomey's feeling peckish, he<br>
Can have my protein gel<br>
And if his bike breaks down, and he<br>
Needs mine, that's his as well</p>
<p>If such a thing were possible<br>
I'd give my very soul<br>
Maintaining Froomey's comfort<br>
Is my one and only goal</p>
<p>I feel I must explain myself<br>
I feel it makes no sense<br>
That Chris gets all the glory, and<br>
It's all at my expense</p>
<p>To really get inside my head<br>
You have to understand<br>
For three short weeks of agony<br>
They pay me ninety grand</p>
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</html>Michael Bench-Caponhttp://www.blogger.com/profile/13715068990919309271noreply@blogger.com0tag:blogger.com,1999:blog-6411624366539130337.post-4782580749299244792018-06-15T02:35:00.000-07:002018-06-15T02:35:53.580-07:00Harsanyi vs The World<!DOCTYPE html>
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<h3>Utilitarians and Egalitarians</h3>
<p>One of the things impartial consequentialists get to argue with each other over is how much equality matters. If John has one util (utils are units of utility or wellbeing) and Harriet has four, is that better or worse than if they both have two? Or is it just that the first setup is better than the second for Harriet and the second is better than the first for John, and that's all there is to it? I'm inclined towards this last view, but impartial consequentialists - utilitarians and the like - tend to want to say that setups can be better or worse <i>overall</i>, because they want to go on to say that the overall goodness of the setup an action brings about, or will probably bring about, or something like that, determines whether the action was right or wrong. You can't very well say that your action was right for John and wrong for Harriet, and that's all there is to it. Goodness and badness may seem to be plausibly relative to individuals, but it's less plausible to say that about rightness and wrongness.</p>
<p>So, let's suppose you've decided you want to be an impartial consequentialist. You know how good a setup is for each person, and you want to work out how good it is overall. What are your options?</p>
<ul>
<li>You add up everyone's utility. That makes you an <i>aggregating utilitarian</i>.</li>
<li>You can take the mean of everyone's utility. That makes you an <i>averaging utilitarian</i>.</li>
<li>You can say that sometimes a setup with less total/average utility is better because it's more equal. That makes you an <i>egailitarian</i>.</li>
<li>You can say that sometimes a setup with less total/average utility is better because it's less equal. That makes you an <i>elitist</i>, or something - it's not a very popular view and we'll ignore it in what follows.</li>
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<p>For a fixed population, the average will be higher whenever the aggregate is higher and vice versa, so it doesn't matter which kind of utilitarian you are. The population is of course sometimes affected by our actions, but I won't have anything to say about that today. I'm thinking about the difference between being a utilitarian and being an egalitarian. Mostly I'd thought that both were pretty live options, and while there were considerations that might push you one way or the other, ultimately you would have to decide for yourself what kind of impartial consequentialist you were going to be, assuming you were going to be an impartial consequentialist at all. But a few days ago someone on Twitter (@genericfilter - thanks) drew my attention to a paper by John Harsanyi which threatens to settle the question for us, in favour of the utilitarian. That was disquieting for me, since my sympathies are on the other side. But Harsanyi's got a <i>theorem</i>. You can't argue with a theorem, can you? Well, of course you can argue with a theorem: you just argue with its premises. So I'm going to see how an egalitarian might go about arguing with Harsanyi's theorem.</p>
<h3>Harsanyi's Theorem</h3>
<p>I'm actually reliably informed that Harsanyi has two theorems that utilitarians use to support their case, but I'm only talking about one. It's his theorem that says, on a few assumptions that are plausible for people who think von Neumann-Morgenstern decision theory is the boss of them, that the only function of individual utilities that can give you the overall utility is a weighted sum (or average; we're taking the population to be fixed here). Since we're already <i>impartial</i> consequentialists, that leaves us with a straight sum (or average). So the egalitarians lose their debate with the utilitarians, unless they reject one or more of the assumptions.</p>
<p>Now, I think I understood the paper OK. Well enough to talk about it here, but not well enough to explain the details of the theorem to you. Hopefully this doesn't matter. Harsanyi's work may have been new to me but it isn't all that obscure, and you may already be familiar with it. In case you're not, I'll also try to tell you what's relevant to the argument when it comes up, but if you want a proper explanation of the details you'll really have to go elsewhere for them.</p>
<p>Harsanyi proves five theorems. The first three seem kind of like scene-setting, with the real action coming in theorems IV and V. Here they are (Harsanyi 1955: 313-4):</p>
<ul>
<li>Theorem IV: W [the social welfare function] is a homogeneous function of the first order of U<sub>1</sub>, U<sub>2</sub>... U<sub>n</sub> [where these are the utilities of each of the n individuals in the setup].</li>
<li>Theorem V: W is a weighted sum of the individual utilities, of the form W = ∑ a<sub>i</sub>•U<sub>i</sub>, where a<sub>i</sub> stands for the value that W takes when U<sub>i</sub> = 1 and U<sub>j</sub> = 0 for all j ≠ i.</li>
</ul>
<p>Some clarifications before we go on. A <i>homogeneous function of the first order</i> means that if you multiply all the U<sub>i</sub>s by a constant k then that multiplies W by k as well. The utility functions U<sub>i</sub> and the social welfare function W aren't just functions on categorical states of the world; they're functions on probability distributions over such states. He shows in theorem III that you can treat W as a function of the individual utility functions, and you can also treat it as a function on probability distributions over distributions of utility.</p>
<p>Theorem V basically says that the utilitarians are right. Harsanyi doesn't seem to have assumed anything as radical as that, and yet that's what he's proved. It's as if he's pulled a rabbit out of a hat. So the question is: where does the rabbit go into the hat? As I say, theorems I-III seemed like scene-setting, so let's start by looking at theorem IV.</p>
<h3>Diminishing Returns</h3>
<p>You might think, as I did, that egalitarians should be pretty unhappy with theorem IV. To get an idea of why, think about diminishing returns. If you give someone with no money a million pounds, that will make a big difference. Give them another million, and it makes less of a difference. The third million makes less difference again. Now, the utilitarians aren't saying that John having two million and Harriet having nothing is just as good as both having one million. You build that into the utility function, by saying money has a diminishing return of utility. But here's the thing: the returns of giving John or Harriet money should diminish <i>faster</i> from the point of view of the egalitarian social planner than they do from the point of view of the person getting the money. That's because boosting an individual's utility becomes less important to the planner as the person gets better off.</p>
<p>You can get a feel for why by thinking about different people's agendas. John's agenda remains John's agenda, however much of it he achieves. He achieves the first item, and moves down the list to the second. That's just what it is for it to be John's agenda. But the planner's agenda is different. If John's agenda is totally unmet, the planner might prioritize the first thing on John's list. But if John is getting on well with his agenda, the planner can ignore him a bit and start prioritizing the agendas of people who aren't doing so well. John's fine now. And however you take into account the diminishing returns of John's agenda for John, they should diminish faster for the planner.</p>
<p>For me, this idea had a lot of instinctive pull, and I expect it would for other egalitarians. And this idea is the very thing theorem IV contradicts. Theorem IV says that boosting U<sub>John</sub> from 0 to 1 has just as much impact on W as boosting U<sub>John</sub> from 10 to 11, when everyone else's utility is 0. You have to do a little more to generalize it to hold when other people's utilities aren't 0, which is what theorem V does, but this consequence of theorem IV is bad enough. The rabbit is already in the hat at this point. Or so it seems.</p>
<p>It turns out that denying theorem IV, or at least accepting the egalitarian principle that conflicts with it, gives a result which is even worse, or at least to me it seems even worse. It's well established that diminishing returns can manifest themselves as risk aversion. (Though it's possible not all risk aversion can be explained by diminishing returns.) A second million is worth less to you than a first, and this explains why you wouldn't risk the first for a 50% chance of winning a second. Maybe you're already risk-averse enough that you wouldn't do that anyway, but the point is that diminishing returns on a thing X generate risk-averse behaviour with respect to X. So if Harriet's utility has diminishing returns for the planner, this means that the planner will be more risk-averse with Harriet's utility than she is, other things being equal. That result is very odd. What it means is that in two situations where the only difference is whether Harriet takes a certain gamble or not, one will be better for Harriet but the other will be better overall, even though they're both equally good for everyone else. This is a weird result indeed, and Harsanyi makes sure his assumptions rule it out. It seems that it should be possible to be an egalitarian without accepting this weird result.</p>
<h3>The Repugnant Conclusion</h3>
<p>So if we're granting theorem IV, we could look for the rabbit going in somewhere in the proof of theorem V. I couldn't really see anything much to work with there, though, so I thought I'd try a different tack. To get an idea of the new strategy, think about <a href="https://plato.stanford.edu/entries/repugnant-conclusion/" target="_blank" title="Stanford Encyclopedia of Philosophy: The Repugnant Conclusion">Derek Parfit's (1984) <i>repugnant conclusion</i> argument</a> against aggregate utilitarianism (and against lots of other positions). The idea of that argument is to show that aggregate utilitarians are committed to saying that for any setup with lots of people all of whom have great lives, there is a better setup in which everyone's life is only just worth living. (The second setup manages to be better because there are so many more people in it.)</p>
<p>Now, you could try setting up the objection by just taking some postulates that aggregate utilitarians are committed to and then formally proving the result. That's more or less how Harsanyi proceeds with his argument. But what Parfit does has a different flavour. He takes his opponent on a kind of forced march through a series of setups, and the opponent has to agree that each is no worse than the last, and this gets you from the nice world to the repugnant world. Here's a version of how it can go. Start with a world A with lots of happy people. Change it to world B by adding in some people whose lives aren't good but are still worth living. That can't make the world <i>worse</i>, because it's just as good for the initial people and the new people's lives are still better than nothing. Then take a third world C which has the same total utility as B but it's equally distributed. That shouldn't make the world worse either. C is like A but with more people who are less happy. Then you repeat the process until you get the repugnant world R. (If your opponent says R is just as good as A, you construct R' by making everyone a tiny bit better off. R' is still repugnant, and if it's not repugnant enough for you then just continue the process again from R' until you find a world that is.)</p>
<p>What I'm thinking is that if Harsanyi's proofs are valid, which they are, then you should be able to get a similar forced-march argument that embodies the proof, but where you move from a world where lots of people are happy to a repugnant world where one person has all the utility and everyone else has none. This argument should be more amenable to philosophical analysis, and once we've worked out what's wrong with it, we should be able to return to Harsanyi's proof and say where the rabbit goes into the hat. I'm not Parfit, and I haven't come up with anything as good as the repugnant conclusion argument. But I have come up with something.</p>
<h3>Harsanyi Simplified</h3>
<p>What we want to show, without loss of generality, is why one util for John and four for Harriet is better than two utils for each. One and four are placeholders here; what's important is that they'd each go for a 50-50 shot between one and four, rather than a guaranteed two. Here's the forced march:</p>
<ul>
<li>Independent 50-50 shots between one and four for each is better than a guaranteed two for each.</li>
<li>A 50-50 shot between one for John and four for Harriet or four for John and one for Harriet is just as good as independent 50-50 shots between one and four for each.</li>
<li>One for John and four for Harriet is as good as four for John and one for Harriet.</li>
<li>Since these two outcomes are equally good, and a 50-50 shot between them is better than two for each, both are better than two for each.</li>
<li>So one for John and four for Harriet is better than two for each.</li>
</ul>
<p>This doesn't track his theorem exactly, I don't think, but as I understand the important moves, if the egalitarian can explain what's wrong with this argument, then they can explain what's wrong with Harsanyi's. And if they can't, they can't. A couple of things are worth pointing out, before we think about what might be wrong with it.</p>
<p>First, in a way it's more general than Harsanyi's. You don't have to assume that people should be expected utility maximizers. The point of the argument is that whatever risk profiles self-interested people should be most willing to accept for themselves, the corresponding distributions are the best ones for everyone overall.</p>
<p>Second, and very relatedly, it more or less shows that the best setup (at least for a fixed population) is the one that someone self-interested would choose behind the veil of ignorance to be in. Harsanyi was a fan of that idea, I'm told, but that idea drops out of the reasoning behind his theorem. You don't need that idea to prove the theorem.</p>
<p>So, where should the egalitarian resist the argument? To me, given what we saw earlier in the section on diminishing returns, it seems they would have to resist the idea that if a 50-50 shot at outcomes X or Y is better than outcome Z, then at least one of X and Y must be better than Z. (And if X and Y are equally good, both must be better than Z.) This idea is very intuitive, at least considered in the abstract, and if it's wrong then it seems a lot of decision theory won't really be applicable to impartial moral decision-making. It's not just expectation-maximizing that will have to go either, because the move in question is pretty much just dominance reasoning. (If Z is better than X and better than Y, then it's better than a 50-50 shot between X and Y.) When you give up dominance reasoning, I'm not sure how much of decision theory is left.</p>
<p>Longtime readers may remember that I <a href="http://michaelbenchcapon.blogspot.com/2011/01/gambling-with-goodness.html" target="_blank" title="Michael Bench-Capon's Blog: Gambling With Goodness">once said</a> I preferred versions of consequentialism that assessed actions by their actual consequences rather than by their expected consequences. Harsanyi does set things up in a way that's much more friendly to expected-consequences versions, but I don't hold out much hope for resisting Harsanyi's argument along these lines. One problem I have with expected consequences was that it's hard to find a specific probability distribution to use which doesn't undermine the motivation for using expected consequences in the first place. (People will be unsure of the probabilities and of their own credences, just as they're unsure of the consequences of their actions.) But Harsanyi doesn't exploit that at all. Another problem I had, and the one I talked more about in the post, was that expectation consequentialism gives a norm about the proper attitude towards risk, and I don't see that there is a plausible source for such a norm. It's just up to us to take the risks and put up with the consequences. Harsanyi does exploit expectation-maximizing to get the strong utilitarian result, but you just need simple dominance reasoning to get the weaker result that inequalities are justified in a setup if people would choose that setup behind a veil of ignorance (with an equal chance of occupying each position).</p>
<p>All of this, even the weaker result, seems to me to be huge if true. I've long been a fellow traveller of impartial consequentialism, and the main reason I keep using the term 'impartial consequentialism' rather than 'utilitarianism' is that I've got egalitarian sympathies. Readers of my <a href="http://michaelbenchcapon.blogspot.com/2018/05/hipparchias-paradox.html" target="_blank" title="Michael Bench-Capon's Blog: Hipparchia's Paradox">recent posts</a> on <a href="http://michaelbenchcapon.blogspot.com/2018/05/what-we-demand-of-each-other_25.html" target="_blank" title="Michael Bench-Capon's Blog: What We Demand Of Each Other">Hipparchia</a> will have already noticed me losing my enthusiasm for the project. This Harsanyi stuff may force me to give up on it altogther.</p>
<h3>References</h3>
<ul>
<li>Arrhenius, G., Ryberg, J. and Tännsjö, T. 2017: 'The Repugnant Conclusion', <i>The Stanford Encyclopedia of Philosophy</i> (Spring 2017 Edition), Edward N. Zalta (ed.), URL = https://plato.stanford.edu/archives/spr2017/entries/repugnant-conclusion/</li>
<li>Harsanyi, J. 1955: 'Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility', <i>Journal of Political Economy</i> 63(4): 309-321</li>
<li>Parfit, D. 1984: <i>Reasons and Persons</i> (Oxford University Press)</li>
</ul>
</div>
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</html>Michael Bench-Caponhttp://www.blogger.com/profile/13715068990919309271noreply@blogger.com2tag:blogger.com,1999:blog-6411624366539130337.post-54180192844225335942018-05-25T04:47:00.002-07:002018-12-20T12:50:46.934-08:00What We Demand Of Each Other<html>
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<p style="line-height:1.5">In the last post I was thinking about <a href="http://michaelbenchcapon.blogspot.co.uk/2018/05/hipparchias-paradox.html" target="_blank" title="Michael Bench-Capon's Blog: Hipparchia's Paradox">Hipparchia's paradox</a>. Hipparchia was a cynic philosopher who lived in Athens in the 4th and 3rd centuries BCE, and she posed the puzzle of why it wasn't OK for her to hit a guy called Theodorus, even though it would have been OK for him to hit himself and morality is supposed to be universalizable. I did try discussing the puzzle a bit, but what I mostly wanted was for moral philosophers to take the puzzle more seriously, to work out how their moral theories can accommodate it, and to start calling it 'Hipparchia's paradox'. I'm not really the kind of person I was hoping would think about it more, but I've been thinking about it a bit more anyway.</p>
<p style="line-height:1.5">I mentioned that we can try resolving the paradox by saying that people were allowed to waive consideration of negative consequences to themselves in the moral evaluation of their own actions. And I worried that if these moral waivers are a thing, then there might be other kinds of moral waivers, and our final theory might end up looking unrecognizable as consequentialism. Some people will be fine with that, of course, but I've long been a bit of a fellow-traveller of (impartial, agent-neutral) consequentialism, and consequentialists (especially impartial agent-neutral ones) are probably the people Hipparchia's paradox is most of a puzzle for.</p>
<p style="line-height:1.5">So, I've been thinking some more about these waivers, and what I'm thinking is that the reason they feel kind of scary is that they're an example of <i>voluntarism</i><a href="#note1"><sup>1</sup></a>. Voluntarism is the idea that what's right and wrong is fixed in some special way by someone's will. What counts as the will and what counts as the relevantly special way is a bit up for grabs, and some of the disputes over voluntarism will be verbal. But it's not all verbal, and a certain kind of moral philosopher should be scared of voluntarism. A classic version of voluntarism is <i>divine command theory</i>, which is sometimes called <i>theological voluntarism</i>. Divine command theorists say this sort of thing:</p>
<ul style="line-height:1.5">
<li>When something is wrong, it's because it goes against God's will.</li>
<li>When something is wrong, it's because God has decreed that it's wrong.</li>
</ul>
<p style="line-height:1.5">Divine command theory isn't all that popular among moral philosophers nowadays, although it had a pretty good run with them in the middle ages, and it's still alive and well in the moral thinking of some religious people. Its detractors often view it as getting things backwards. Things aren't wrong because they go against God's will; God wants us not to do them because they're wrong. Similarly, when God says something's wrong, that's because it is wrong, not the other way round. This problem is called the <i>Euthyphro problem</i>, after the dialogue Plato wrote about it. The Euthyphro problem isn't just about divine command theory though; it applies in some way to all versions of voluntarism. People don't make things wrong by wanting them not to be done; they want them not to be done because they're wrong, or at least they should. The worry is that anyone adopting a version of voluntarism is taking the wrong side in the Euthyphro problem. That sounds like bad news for the waiver response to Hipparchia's paradox.</p>
<p style="line-height:1.5">Nonetheless, I think it might be worth giving voluntarism another look, at least in the form of these waivers. There are two reasons. First, Hipparchia's paradox does provide a direct argument for waivers. Second, there's a big difference between God being the boss of us and <i>us</i> being the boss of us, or even better, <i>the people our actions have an impact on</i> being the boss of us. Arguments against divine voluntarism may well not carry over to this more worldly form of voluntarism. So now here's the next question: if waivers are a thing, <i>which</i> waivers are a thing? In the previous post I made a list of questions about possible waivers, and I'll repeat that list here, with a bit of commentary explaining why I thought they were worth asking.</p>
<ul style="line-height:1.5">
<li>Can I waive consideration of consequences to myself in the moral evaluation of someone else's actions?</li>
</ul>
<p style="line-height:1.5">The idea there is that if I volunteer to take one for the team, then it isn't wrong for the team to go along with that. Suppose you want to go to a party which will be pretty good, and I want to go to a different party which will be very good, but one of us has to stay home and wait for the plumber to come and fix the toilet. (We'll assume we'd both enjoy staying home equally.) What I'm suggesting is that if I volunteer to stay home, you don't wrong me in going along with this, even though I would probably enjoy my party more than you would enjoy yours. Now, you might disagree with this assessment of the situation. But the point is quite similar to Hipparchia's paradox: just as Theodorus is allowed to hit himself, people are allowed to sacrifice their own interests for others, even if the sacrifice is greater than the benefit. And even if they can't make the sacrifice without the co-operation of the beneficiaries, the beneficiaries don't do anything wrong in co-operating. If the person making the sacrifice says it's OK, then it's OK. (I'm not saying this is right, but this is the thinking behind the question.)</p>
<ul style="line-height:1.5">
<li>Can I waive consideration of some but not all negative consequences to myself?</li>
</ul>
<p style="line-height:1.5">I'm not sure I expressed this one as clearly as I could have, but here's what I'm thinking. Maybe it's OK for me to waive consideration of minor things, but not major things. Or maybe it's OK for me to waive consideration of forgone pleasures, but not of positive harms. I won't go into the details of what sorts of things I might not be morally allowed to do to myself, or other people might be wrong to do to me even with my permission, but there's a reasonably venerable tradition of thinking that there is such a distinction to be made. But if there is, you have to wonder what its basis might be.</p>
<ul style="line-height:1.5">
<li>Can I waive consideration of bad things happening to me even if someone else cares about me and so these would also be negative consequences to them?</li>
</ul>
<p style="line-height:1.5">Nobody is an island, and often if something bad happens to Theodorus, he's not the only person who suffers. If Theodorus hits himself, this might upset his friends, and maybe it's wrong because of that. I think there's a fair bit of pressure from common-sense morality to say that Theodorus hitting himself is nobody's business but his own, and if it bothers his friends then he's entitled to waive that fact from the moral evaluation of his action. There are probably limits to what common-sense morality permits along these lines, and maybe I'm getting common-sense morality wrong. But even if I'm not getting it wrong, I'm not really sure how this dynamic is supposed to work. One possibility is that waiving the harm Theodorus does you by hitting himself is partly constitutive of the very relationship in virtue of which Theodorus hitting himself harms you. While I do think this idea has some superficial appeal, I fear its appeal may be only superficial. But perhaps there's the germ of something workable in there.</p>
<ul style="line-height:1.5">
<li>Can I do this on an action-by-action basis, or at least a person-by-person basis, or do I have to waive it for all people or all actions if I waive it for one?</li>
</ul>
<p style="line-height:1.5">This is an issue about universalizability and fairness. How arbitrary am I allowed to be in dishing out permissions? One possibility is that we have a lot of latitude about what permissions we <i>can</i> give, but a lot less latitude about what permissions we <i>should</i> give. But I expect we also probably have a fair bit of latitude with the ones we should give, because these permissions are bound up with personal relationships, and we don't have personal relationships with everyone. In particular, waivers in personal relationships might often be part of a mutually beneficial reciprocal arrangement. Being morally in the wrong is bad for you, and personal relationships are difficult, and provided you're both trying hard it might be better not to be morally in the wrong every time you mess up. These waivers probably shouldn't have to be blanket waivers: a certain amount of mutual pre-emptive forgiveness doesn't make it impossible for you to to wrong each other.</p>
<ul style="line-height:1.5">
<li>Are there ever situations where someone can waive consideration of a negative consequence to someone other than themselves?</li>
</ul>
<p style="line-height:1.5">Part of the issue here is the nobody-is-an-island problem I discussed a couple of questions ago. But the issue also arises in the case of children, and other people who have someone else responsible for their welfare to an extent. It may also arise with God. I think it's quite possible that there just aren't any exceptions of this kind. You're allowed to take one for the team, but you're not allowed to have your children take one for the team. But here's an example I've been thinking about a bit. Suppose that you and I are doing a high-stakes pub quiz together, and we win a family trip to Disneyland. A reasonably fair thing to do would be for us to auction half of the trip between us and have the higher bidder pay the lower bidder for the lower bidder's half. But suppose I just tell you to go ahead and enjoy yourself. My family are losing out here as well as me, but somehow it still feels like I've done something nice, rather than robbing my family of the equivalent of half a trip to Disneyland. I think I'd probably end up coming down on the side of saying I'm wrong to give you my half of the trip, although perhaps the matter is complicated by the fact that my family weren't on the team, so it's my prize not theirs. But letting you have the trip does still put my family out. I'm really not sure what I think about this. But I think it's likely people <i>do</i> make this kind of collective sacrifice from time to time, and that they feel like they've done a good thing and not a bad thing.</p>
<p style="line-height:1.5">I think that a moral theory that incorporated these kinds of waivers in a big way might have some mileage in it. There are plenty of worries about it, of course. I'll talk about two.</p>
<p style="line-height:1.5">First, how freely does someone have to be giving these permissions? People make decisions with imperfect information and imperfect rationality, and they also make them under conditions of oppression. It's a common criticism of libertarian capitalism that letting people make whatever contracts they want will lead to a lot of inequality of outcome resulting from unequal bargaining positions. Most countries don't want the economically disempowered bargaining away their kidneys, and maybe we don't want people bargaining away the fact that harming them is wrong. I think some libertarian rhetoric makes it sound as if they think that contracts actually do have this wrongness-nullifying effect, but it's possible they don't say this, and if they do then I'm really not optimistic about them being right. You might be able to imagine idealized situations where the waivers look plausible, but the reality of it might look pretty hideous in some cases. And when you're doing ethics, hideousness detracts from plausibility.</p>
<p style="line-height:1.5">My second worry is that constructing a theory of moral waivers might be joining what I think of as <i>the excuses industry</i>. Impartial consequentialism is notoriously demanding, especially in our interconnected world. But I don't think that should be surprising really: we don't expect it to be easy doing the right thing all the time. A long time ago <a href="http://michaelbenchcapon.blogspot.co.uk/2010/10/selfishness-and-squeamishness.html" target="_blank" title="Michael Bench-Capon's Blog: Selfishness And Squeamishness">I wrote about</a> how the supposedly counterintuitive results of impartial consequentialism seemed to me to appeal to either selfishness, squeamishness, or a bit of both. I still feel the pull of that line of thought, and although I'm not really an impartial consequentialist myself, I am as I say a fellow traveller. Some people try to construct theories that don't have these demanding results, but I don't really want to be in the business of constructing theories that are basically elaborate excuses that allow us to <a href="https://global.oup.com/academic/product/living-high-and-letting-die-9780195108590?cc=gb&lang=en&" target="_blank" title="Peter Unger: Living High And Letting Die">live high while other people die</a>. I hope that's not all I'd be doing, and I don't think it's all that other opponents of impartial consequentialism are doing, but I do think it's a trap you have to be careful not to fall into.</p>
<p style="line-height:1.5">With those worries out in the open, I'll sketch the basic outline of the theory I've got in mind. You start with a background of some kind of impartial consequentialism, and then overlay the waivers. Morality might legitimate us making some very heavy demands on each other, but we don't have to actually make these demands. I guess the way it works is these waivers will create a category of supererogatory actions - actions which are good but not obligatory - which impartial consequentialism sometimes struggles to accommodate. If someone's waived a harm it's still better not to cause the harm, but it's not obligatory. I'm imagining the theory as being most distinctive in its treatment of morality within personal relationships. I mentioned earlier that some reciprocal waiving might be a common or even constitutive feature of some relationships. Perhaps it could be extended to involve relationships between people who don't know each other as well or at all, but who are members of the same community. If I was going to think seriously about that then I'd need to learn more about communitarian ethical theories. I'm really not very familiar with how they work, but from what I've heard they sound pretty relevant.</p>
<p style="line-height:1.5">The post a few days ago closed with this argument against consequentialism:</p>
<ul style="line-height:1.5">
<li>Hipparchia's paradox shows that fully agent-neutral consequentialism is absurd.</li>
<li>The only promising arguments for consequentialism are arguments for fully agent-neutral consequentialism.</li>
<li>So there are no good arguments for consequentialism.</li>
</ul>
<p style="line-height:1.5">It's not great, really, and I said so at the time. But let's think about how all this waivers stuff started with Hipparchia's paradox. You could just look at the paradox and say "waivers are in, impartial consequentialism is out", and then merrily start constructing theories with waivers all over the place. I think that would be a mistake. An alternative, which I don't think would be the same kind of mistake, is to look at other candidates for waivers that are somehow similar to the original case. The best case I've got in mind is when a group of people see themselves as somehow on the same side, and so individual team-members' failures aren't moral failures, even though they could have done better and the other members of the team would have been better off. The team has a sufficient unity of purpose that the members view the team as analogous to an individual. Team members don't press moral charges against team members just as Theodorus doesn't press moral charges against himself.</p>
<p style="line-height:1.5">One last thing about waivers is that you might share a lot of the intuitions about the examples but try to incorporate them within a straight impartial consequentialist theory. Maybe people being able to take advantage of the waivers without feeling guilty about it turns out to have the best consequences overall. There's a long tradition of moral philosophers doing this sort of thing. The main trick is to distinguish what it is for an action to be right or wrong with the information we use to decide whether an action is right or wrong. In John Stuart Mill's <i>Utilitarianism</i> he makes this move several times, and in fellow utilitarian RM Hare's Book <i>Moral Thinking: Its Levels, Method, and Point</i> those were the sorts of levels he was talking about. (At least if I remember them right.)</p>
<p style="line-height:1.5">I used to be quite impressed with this move. Now I'm not so sure. The reason I've long been a fellow-traveller of impartial consequentialism without properly signing up is that I'm also a bit of an error theorist. I read JL Mackie's <i>Ethics</i> at an impressionable age, and while I'm a lot more sceptical about philosophical conclusions than I used to be, it's still got some pull for me. But maybe the reason it's got all this pull is because I'm thinking about moral facts in terms of what Henry Sidgwick (I think) called 'the point of view of the universe'. On that topic I read something once about the conflict between deontological and consequentialist ethics that stayed with me. The point was that deontologists shouldn't argue that sometimes there are actions we should do even though things will be worse if we do them. To concede that is to concede too much to the consequentialist: it makes things too easy for them if <i>that's</i> the position they have to attack. The consequentialist needs to earn the claim that there's some meaningful way in which consequences, or the whole world, can be good or bad <i>simpliciter</i> rather than just good or bad from the point of view of a person, or a particular system of rules, or perhaps something else. It's true: the consequentialist needs this claim and the deontologist doesn't. It's non-trivial and the deontologist should make the consequentialist earn it. And I don't think they have earned it. I can't remember where I read this, unfortunately. I'd thought it was in a Philippa Foot paper, but I re-read the two papers I thought it might be in (Foot 1972 and 1995), and while re-reading them was rewarding I couldn't find it in either. I still think it's probably her. If you can tell me where it's from, please do so in the comments. [UPDATE 24/6/18: She makes the point in Foot 1985: 'Utilitarianism and the virtues'.]</p>
<p style="line-height:1.5">Anyway, maybe error theory wouldn't have the same pull for me if I got away from the idea of the point of view of the universe and instead thought about morality as being fundamentally about human relationships, collective decision-making and what have you. The levels move takes the manifest image of morality and explains it in terms of something more systematic at a lower level. But this systematic lower level is where the point of view of the universe is, and that's what threatens to turn me into an error theorist. The manifest image is where the human relationships and collective decision-making are, and maybe those aren't so weird. The dilemma arises because the lower level stuff about how good the universe is can seem more plausibly normative, while the higher level stuff about relationships is more plausibly real.</p>
<p style="line-height:1.5">Of course, as things stand with the theory I've got in mind there's still an impartial consequentialist background with the waivers laid on top. The impartial consequentialist background is as weird as ever, and you can't have a moral theory that's <i>all</i> waivers. But maybe this could be a transitional step on the way to me having a more accurate conception of what moral facts are facts about, and perhaps eventually losing interest in moral error theory altogether. That might be nice.</p>
<p style="line-height:1.5"><b>Notes</b></p>
<p style="line-height:1.5" id="note1">[1] I'm a little unsure about the terminology here. It's pretty established to call divine command theory 'theological voluntarism', and I'm fairly sure I've seen 'voluntarism' used more generally to include non-theological versions like the waiver theory I'm talking about here. But 'voluntarism' also seems to be used to refer to theories according to which the moral properties of an action depend on the will with which the action was performed. (This idea is important in Kant's ethics.) The two ideas could overlap, but it's not obvious that they have to. So if you've got strong views about what 'voluntarism' means and think I'm using it wrong, then I apologize. And when you're discussing this blogpost with your friends, you should be careful how you use the word. But I don't know another word for the thing I'm talking about, and I think I've heard people calling it 'voluntarism', so that's the call I've made.</p>
<p style="line-height:1.5"><b>References</b></p>
<ul style="line-height:1.5">
<li>Foot, P. 1972: 'Morality as a system of hypothetical imperatives', <i>Philosophical Review</i> 81 (3):305-316</li>
<li>Foot, P. 1985: 'Utilitarianism and the virtues', <i>Mind</i> 94 (374):196-209</li>
<li>Foot, P. 1995: 'Does moral subjectivism rest on a mistake?', <i>Oxford Journal of Legal Studies</i> 15 (1):1-14</li>
<li>Hare, R. M. 1981: <i>Moral Thinking: Its Levels, Method, and Point</i> (Oxford University Press)</li>
<li>Mackie, J. L. 1977: <i>Ethics: Inventing Right and Wrong</i> (Penguin Books)</li>
<li>Mill, J. S. 1863/2004: <i>Utilitarianism</i>, Project Gutenberg ebook #11224, http://www.gutenberg.org/files/11224/11224-h/11224-h.htm</li>
<li>Plato c.399-5 BCE/2008: <i>Euthyphro</i>, trans. Benjamin Jowett, Project Gutenberg ebook #1642, http://www.gutenberg.org/files/1642/1642-h/1642-h.htm</li>
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</html>Michael Bench-Caponhttp://www.blogger.com/profile/13715068990919309271noreply@blogger.com0tag:blogger.com,1999:blog-6411624366539130337.post-86959407956224287842018-05-21T03:37:00.000-07:002018-12-20T12:50:23.287-08:00Hipparchia's Paradox<html><head><style type="text/css">@import url('https://themes.googleusercontent.com/fonts/css?kit=fpjTOVmNbO4Lz34iLyptLUXza5VhXqVC6o75Eld_V98');.lst-kix_x99pst76ftbu-0>li:before{content:"\0025cf "}.lst-kix_x99pst76ftbu-1>li:before{content:"\0025cb "}.lst-kix_pgfk3jv1tgwc-2>li:before{content:"\0025a0 "}.lst-kix_x99pst76ftbu-2>li:before{content:"\0025a0 "}.lst-kix_pgfk3jv1tgwc-1>li:before{content:"\0025cb "}.lst-kix_g8c0fv10q2f8-7>li:before{content:"\0025cb "}.lst-kix_pgfk3jv1tgwc-0>li:before{content:"\0025cf "}.lst-kix_g8c0fv10q2f8-8>li:before{content:"\0025a0 "}.lst-kix_g8c0fv10q2f8-2>li:before{content:"\0025a0 "}.lst-kix_g8c0fv10q2f8-4>li:before{content:"\0025cb "}.lst-kix_g8c0fv10q2f8-3>li:before{content:"\0025cf 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<span class="c2 c0">The most famous cynic philosopher was Diogenes of Sinope, who lived in an old wine jar and told Alexander the Great to get out of his light. But he wasn’t the only cynic; there was a whole bunch of them. The second or third most famous cynic was Hipparchia. (The third or second was Crates, Hipparchia’s husband.) Hipparchia doesn’t seem to have written much if anything, as tended to be the way with the cynics, but history has recorded at least one of her arguments, via an anecdote about an exchange she had with some jackass called Theodorus at a party one time. Here’s how Diogenes Laertius (not to be confused with Diogenes the jar-dweller) tells it:</span></div>
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<span class="c0">Theodorus, the notorious atheist, was also present [at Lysimachus’s party], and she posed the following sophism to him. ‘Anything Theodorus is allowed, Hipparchia should be allowed to do also. Now if Theodorus hits himself he commits no crime. Neither does Hipparchia do wrong, then, in hitting Theodorus.’ At a loss to refute the argument, Theodorus tried separating her from the source of her brashness, the Cynic double cloak. Hipparchia, however, showed no signs of a woman’s alarm or timidity. Later he quoted at her lines from </span><span class="c0 c1">The Bacchae</span><span class="c0"> of Euripides: ‘Is this she who abandoned the web and women’s work?’ ‘Yes,’ Hipparchia promptly came back, ‘it is I’. But don’t suppose for a moment that I regret the time I spend improving my mind instead of squatting by a loom.’ [</span><span class="c0 c1">Lives of the Ancient Philosophers</span><span class="c2 c0"> 6: 96-8; pp45-6 in Dobbin]</span></div>
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<span class="c0">I’ve quoted the context as well as just the argument, the alternative being to quote it out of context. </span><span class="c2 c0">I think it’s pretty clear that Hipparchia is the winner of this story, although it’s possible the reality of the situation was pretty unpleasant for everyone concerned. But having acknowledged the context, I’d like to think a bit about the argument in isolation. Here’s the argument laid out neatly:</span></div>
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<li class="c3 c4"><span class="c2 c0">Anything Theodorus is allowed, Hipparchia should be allowed to do also.</span></li>
<li class="c3 c4"><span class="c2 c0">If Theodorus hits himself he commits no crime.</span></li>
<li class="c3 c4"><span class="c2 c0">So neither does Hipparchia do wrong in hitting Theodorus.</span></li>
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<span class="c2 c0">The first premise is about universalizability: morality is supposed to apply equally to everyone. It’s a bit less clear what the theoretical basis of the second premise is. It seems like a part of most people’s common sense morality that if someone wants to hit themselves then that’s their own business, and while it might be inadvisable, it isn’t immoral. Common sense morality changes from place to place, but I guess this is part of it that my society has in common with Hipparchia’s. You could explain the truth of the second premise in various ways, some of which will mean qualifying or restricting it, and I think that how exactly we explain it will affect how the paradox gets resolved. The conclusion is meant to be absurd, showing that something is wrong with either the premises or the inference.</span></div>
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<span class="c0">I think the most obvious way to try to resolve the paradox is to interpret the permission in the second premise as being explained by a general permission for people to hit themselves, rather than a general permission to hit Theodorus. The action that Theodorus is allowed to do is </span><span class="c0 c1">hitting oneself</span><span class="c0">, not </span><span class="c0 c1">hitting Theodorus</span><span class="c0">. Hipparchia is allowed to do the action </span><span class="c0 c1">hitting oneself</span><span class="c2 c0"> too, so universalizability is saved.</span></div>
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<span class="c0">There’s a problem with this, though: Theodorus is also allowed to do </span><span class="c0 c1">hitting Theodorus</span><span class="c0">. He’d better be, because if an action is immoral under some description, then it’s immoral. This means there is something he’s allowed to do and Hipparchia isn’t, and so universalizability isn’t saved. Universalizability isn’t the idea that some of morality applies equally to everyone; it’s the idea that all of morality applies equally to everyone. Now, I don’t mean to be disingenuous. I’m not saying that Hipparchia’s paradox shows that universalizability is bunk; I’m just saying there’s more work to do. I don’t think there can be much doubt that it somehow matters that the description of the action as </span><span class="c0 c1">hitting oneself</span><span class="c2 c0"> applies to Theodorus’s action and not Hipparchia’s. It just doesn’t resolve the paradox completely, and it’s perhaps more of a restatement of the paradox than anything else. Sometimes a restatement of a paradox is more or less all you need, but in this case I don’t think the restatement is enough.</span></div>
<div class="c3 c6">
<span class="c2 c0"></span></div>
<div class="c3">
<span class="c0">Here’s another line of attack. Maybe on any given occasion it really is only OK for Theodorus to hit Theodorus if it’s OK for Hipparchia to hit Theodorus. The difference is that occasions when he hits himself will be those rare occasions when he wants to be hit, whereas occasions when she hits him are likely to be occasions when he doesn’t want to be hit. (And also he won’t hit himself harder than he wants to be hit.) This kind of reasoning is behind some anti-paternalist thinking in political philosophy. The classic anti-paternalist work is </span><span class="c0 c1">On Liberty</span><span class="c2 c0">, which was published under John Stuart Mill’s name but was probably coauthored with Harriet Taylor Mill, if you take its dedication literally. (It’s possible the Mills were the greatest philosophical power couple since Hipparchia and Crates. I can’t think of a greater one in the roughly 2150 years betweeen them, although perhaps you can, and perhaps there’s an obvious one I’m missing. [UPDATE: A friend pointed out I forgot Abelard and Heloise.]) They argued that the state shouldn’t be interfering with you if you’re not doing anyone else any harm. Here they are:</span></div>
<div class="c3 c6">
<span class="c2 c0"></span></div>
<div class="c3 c8">
<span class="c0">The object of this Essay is to assert one very simple principle, as entitled to govern absolutely the dealings of society with the individual in the way of compulsion and control, whether the means used be physical force in the form of legal penalties, or the moral coercion of public opinion. That principle is, that the sole end for which mankind are warranted, individually or collectively, in interfering with the liberty of action of any of their number, is self-protection. That the only purpose for which power can be rightfully exercised over any member of a civilised community, against his will, is to prevent harm to others. His own good, either physical or moral, is not a sufficient warrant. [</span><span class="c0 c1">On Liberty</span><span class="c2 c0">: p17]</span></div>
<div class="c3 c6">
<span class="c2 c0"></span></div>
<div class="c3">
<span class="c0">People disagree over how far you can reconcile this with the consequentialism you find in </span><span class="c0 c1">Utilitarianism</span><span class="c2 c0">, but if you’re trying to reconcile them it usually goes roughly as follows. People will do things that have good consequences for themselves, so if their actions don’t have bad consequences for anyone else then they don’t have bad consequences for anyone. Given consequentialism, that means the actions aren’t bad. That means the state shouldn’t be interfering with them. It’s a bit of a Swiss cheese of an argument, and I think it remains so even if you’re properly doing justice to it, but I also think they were on to something important.</span></div>
<div class="c3 c6">
<span class="c2 c0"></span></div>
<div class="c3">
<span class="c2 c0">A classic example of paternalism is seatbelt laws. Idealizing a bit, the set-up is this: by not wearing a seatbelt you’re not putting anyone at risk but yourself. But by having laws demanding people wear seatbelts, you can save lives. Let’s consider a couple of things a libertarian might have to say about this: </span></div>
<div class="c3 c6">
<span class="c2 c0"></span></div>
<ul class="c7 lst-kix_pgfk3jv1tgwc-0 start">
<li class="c3 c4"><span class="c2 c0">“If I value my life so much and my convenience so little that the small chance that wearing a seatbelt will save my life is worth the inconvenience of wearing one, then I will wear a seatbelt.”</span></li>
<li class="c3 c4"><span class="c2 c0">“The only person who stands to get hurt here is me, and I’m fine with it. Mind your own business.” </span></li>
</ul>
<div class="c3 c6">
<span class="c2 c0"></span></div>
<div class="c3">
<span class="c2 c0">The first is a simple consequentialist argument: we don’t have to worry about people not wearing seatbelts in situations where the expected consequences are negative. (It also takes the relative value of someone’s life and convenience to be the relative value they themselves assign to them, but maybe that’s not so silly at least in the case of most adults.) The second libertarian response is harder to categorize. It can still be made out as consequentialist in a way, but it says that people are allowed to waive consideration of negative consequences to themselves. The first objection, where it applies, flows straightforwardly from a simple consequentialism that says the right thing to do is the thing with the best consequences. The second applies more generally, but it says that sometimes it’s OK to do the thing that doesn’t have the best consequences. If we’re allowing people to waive consideration of consequences to themselves in the moral evaluation of their own actions, this raises questions about what other kinds of waivers are allowed:</span></div>
<div class="c3 c6">
<span class="c2 c0"></span></div>
<ul class="c7 lst-kix_x99pst76ftbu-0 start">
<li class="c3 c4"><span class="c2 c0">Can I waive consideration of consequences to myself in the moral evaluation of someone else’s actions?</span></li>
<li class="c3 c4"><span class="c2 c0">Can I do this on an action-by-action basis, or at least a person-by-person basis, or do I have to waive it for all people or all actions if I waive it for one?</span></li>
<li class="c3 c4"><span class="c2 c0">Can I waive consideration of some but not all negative consequences to myself?</span></li>
<li class="c3 c4"><span class="c2 c0">Can I waive consideration of bad things happening to me even if someone else cares about me and so these would also be negative consequences to them?</span></li>
<li class="c3 c4"><span class="c2 c0">Are there ever situations where someone can waive consideration of a negative consequence to someone other than themselves?</span></li>
</ul>
<div class="c3 c6">
<span class="c2 c0"></span></div>
<div class="c3">
<span class="c2 c0">None of these seem to me like they have obvious answers, with the possible exception of the last one, even if we grant that people can waive consideration of harm to themselves in the moral evaluation of their own actions. I expect some readers will think some of the answers are fairly obvious (and that the last one is obviously obvious), or will at least have views on some of the questions, perhaps based on the literatures which presumably exist on each of them. To be clear, I’m not saying that a consequentialism with a self-sacrifice caveat can’t be made coherent. You could say that an action is permissible iff it either maximizes expected utility or has an expected utility for other people at least as high as the expected utility for other people of some permissible action. That seems to get the right results. The problem I have is that if waivers are a thing, then there are other waivers we might want to include in our theory as well, and after a while our theory might end up not looking much like consequentialism at all.</span></div>
<div class="c3 c6">
<span class="c2 c0"></span></div>
<div class="c3">
<span class="c2 c0">One way to avoid these questions is to deny that people can waive consideration of themselves in the first place. But then Hipparchia’s paradox comes back, at least a little. The problem with this simple consequentialist response to the paradox is that people don’t always do what’s best for them. Unless we supplement the response somehow, it will mean that whenever Theodorus hits himself and it isn’t what’s best for him, he is doing something wrong after all. (At least when he had enough information to work out that it probably wouldn’t be best for him.) Is this what we want to say?</span></div>
<div class="c3 c6">
<span class="c0 c2"></span></div>
<div class="c3">
<span class="c2 c0">I can sort of see how some people might want to bite this bullet. If you’re an agent-neutral consequentialist, then you think that the only information relevant to whether an action is wrong or not is how good its consequences are. Who did the action isn’t relevant. So this kind of consequentialist should say that Theodorus hitting himself really is immoral whenever it’s inadvisable. If someone gets on their high horse with you about how you’re not doing what’s best for yourself, they actually do have the moral high ground. Perhaps this is right. But it’s weird. </span></div>
<div class="c3 c6">
<span class="c2 c0"></span></div>
<div class="c3">
<span class="c2 c0">I don’t really feel like I’ve got very far with this. But my main aim was to present the argument as something worth thinking about, because I do think it’s worth thinking about. I’ll close by presenting another argument, which is also a Swiss cheese of an argument, but which I’m also worried might be on to something.</span></div>
<div class="c3 c6">
<span class="c2 c0"></span></div>
<ul class="c7 lst-kix_c70x3ewyop26-0 start">
<li class="c3 c4"><span class="c2 c0">Hipparchia’s paradox shows that fully agent-neutral consequentialism is absurd.</span></li>
<li class="c3 c4"><span class="c2 c0">The only promising arguments for consequentialism are arguments for fully agent-neutral consequentialism.</span></li>
<li class="c3 c4"><span class="c2 c0">So there are no good arguments for consequentialism.</span></li>
</ul>
<div class="c3 c6">
<span class="c2 c0"></span></div>
<div class="c3 c6">
<span class="c2 c0"></span></div>
<div class="c3">
<span class="c5">References</span></div>
<ul class="c7 lst-kix_ot5k053fd51v-0 start">
<li class="c3 c4"><span class="c0">Dobbin, R. 2012: </span><span class="c0 c1">Anecdotes of the Cynics</span><span class="c2 c0">, selected and translated by Robert Dobbin. Penguin Random House.</span></li>
<li class="c3 c4"><span class="c0">Mill, J. S. 1859/2011: </span><span class="c0 c1">On Liberty</span><span class="c2 c0">, Project Gutenberg ebook #34901, http://www.gutenberg.org/files/34901/34901-h/34901-h.htm</span></li>
<li class="c3 c4"><span class="c0">Mill, J. S. 1863/2004: </span><span class="c0 c1">Utilitarianism</span><span class="c2 c0">, Project Gutenberg ebook #11224, http://www.gutenberg.org/files/11224/11224-h/11224-h.htm</span></li>
</ul>
</body></html>Michael Bench-Caponhttp://www.blogger.com/profile/13715068990919309271noreply@blogger.com0tag:blogger.com,1999:blog-6411624366539130337.post-15709291282512127512018-05-06T13:03:00.001-07:002018-05-10T02:03:18.320-07:00Comparing Size Without (Much) Set Theory<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "cambria"; font-size: 12pt; white-space: pre-wrap;">At the end of <a href="http://michaelbenchcapon.blogspot.co.uk/2018/05/the-continuum-hypothesis-without-set_5.html" target="_blank">my last post</a>, I said that I’d like to know whether it’s possible to make sense of there being more Xs than Ys when there are uncountably many of each, without using set theory. I’m not a proper mathematician, as I expect will become painfully apparent to any proper mathematicians reading this, but I’ve tried to hack something together that might sort of work. It uses plural quantification, which George Boolos (1984) has argued isn’t set theory in disguise. </span><span style="font-family: "cambria"; font-size: 16px; white-space: pre-wrap;">It does use some actual set theory too. </span><span style="font-family: "cambria"; font-size: 12pt; white-space: pre-wrap;">But hopefully it’s a start.</span></div>
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<span style="font-family: "cambria"; font-size: 12pt; white-space: pre-wrap;">Georg Cantor, and apparently David Hume before him, came up with a rule for comparing the sizes of infinite collections. If the Xs and the Ys can be paired off one-one, then there are the same number of each. If the Xs can be paired of one-one with some of the Ys, there are at least as many Ys as Xs. In set theory, you can use this idea to make a nice precise open formula expressing that a set x is at least as big as a set y, in terms of there being another set z that represents this one-one pairing. The usual way is to make it a set of ordered pairs with one member from each of x and y, having previously said what it is for a set to count as an ordered pair.</span></div>
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<span style="font-family: "cambria"; font-size: 12pt; white-space: pre-wrap;">Since this set-theoretic version of “at least as big as” relies on there being a set in the model to represent the correspondence whenever there is such a correspondence, you can sometimes get models that don’t give the results about which sets are bigger than which that you intuitively might think they ought to. That’s how you end up with things like Skolem’s paradox, which is the puzzle of how set theories that say (under their intended interpretations) that there are uncountably large sets can have models with only countably many things in the domain. We can sort of ignore this here, although if you know a lot more than I do about Skolem's paradox it may help to keep it in mind.</span></div>
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<span style="font-family: "cambria"; font-size: 12pt; white-space: pre-wrap;">Suppose I want to do this pairing thing without set theory. One thing I could do is take “at least as many” as primitive, so I’ve got a predicate Xs ⪰ Ys, which takes plural terms on both sides, and is true just when there are at least as many Xs as Ys. That’s not really legitimate for this project though, because the good standing of the concept is exactly what we’re trying to establish. What I’ll suggest is that we use just enough set theory to make comparisons of size, but not all the extra stuff that leads to indeterminacies in which model we're talking about and whether or not the continuum hypothesis is true in it.</span></div>
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<span style="font-family: "cambria"; font-size: 12pt; white-space: pre-wrap;">What do we need to define “Xs ⪰ Ys”? We’ve already got plural quantification, outsourcing the defence of its set-theoretic innocence to Boolos, as is traditional. What I’m suggesting is adding just ordered pairs of things which aren’t themselves ordered pairs, and then saying that there at least as many Xs as Ys whenever there are some ordered pairs representing a one-one correspondence between some of the Xs and all of the Ys. And then you throw away the ordered pairs again, since ordered pairs are fictional and all.</span></div>
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<b style="font-weight: normal;"><br /></b></div>
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<span style="font-family: "cambria"; font-size: 12pt; white-space: pre-wrap;">So, you start off with the model M you’re interested in, and you want to extend it to a model M+ with Xs ⪰ Ys defined in it. To do that, you take another model N which is the same except you add in a bunch of ordered pairs. Whenever there are one or two things in the domain of M, there are the ordered pairs of them in N. None of the ordered pairs are duplicated, and there’s nothing else in N. Then you can define Xs ⪰ Ys as being true in M+ iff it’s true in N that whenever there are some ordered pairs Ps such that nothing is the first of more than one p in Ps, and nothing is the second of more than one p in Ps, and all the firsts of a p in Ps are in Xs, and all the seconds of a p in Ps are in Ys, and all the Ys are the second of some p in Ps.</span></div>
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<b style="font-weight: normal;"><br /></b></div>
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<span style="font-family: "cambria"; font-size: 12pt; white-space: pre-wrap;">I’ve tried to be careful not to introduce any general set-theoretic stuff in the definitions, except for the ordered pairs. The idea is that given a model M of plural logic without ⪰, we can always pin down a unique model N, and then we can define a new model M+ of plural logic with ⪰ in terms of M and N. The M+ models constructed in this way are the admissible models for plural logic with ⪰. The way this definition goes is supposed to be unaffected by what is and isn’t true about the universe of sets out there, if it even is out there, and in particular it’s unaffected by the truth or otherwise of the set-theoretic version of the continuum hypothesis. This means we should be able to express the non-set-theoretic version of the continuum hypothesis that I talked about in the last post, purely in terms of plural logic and without leaving any hostages to set theory.</span></div>
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<b style="font-weight: normal;"><br /></b></div>
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<span style="font-family: "cambria"; font-size: 12pt; white-space: pre-wrap;">A potential source of problems is that the model theory for plural logic, just like the model theory for most things, tends to be given in terms of set theory. Can you avoid that, and just give it in terms of plural logic? I sort of expect you could, perhaps with a little extra stuff but way short of full set theory, although I’m not sure whether this is something anyone has taken it upon themselves to do. The idea would be that instead of saying things like “a model M is an ordered pair <D, V> where D is a set of objects and V is a valuation function”, you say “a model M is defined by some things the Ds, which are its domain, and…”. (This is the point at which it becomes difficult.) If set theory does turn out to be indispensible to the model theory, then there will always be a suspicion that the definitions are hostage to set theory. It’s a little bit like the problem of doing the model theory for non-classical logics in classical logic, or giving a model theory for variable domains modal logic without committing yourself to a possibilist ontology. I don’t really want to get into this debate because in debates like this there’s always a danger you’ll find Tim Williamson on the other side.</span></div>
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<b style="font-weight: normal;"><br /></b></div>
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<span style="font-family: "cambria"; font-size: 12pt; white-space: pre-wrap;">So, I’m not going to present a non-set-theoretic semantics for plural logic, and I’m also not going to defend the set-theoretic innocence of plural logic with a set-theoretic semantics. But when I try to formalize the method for constructing the M+s, I’ll try to mention sets as little as possible. In particular, the ordered pairs in the domain of the intermediate model won’t actually be ordered pairs. But the domains will be sets, and the extensions will be sets of ordered n-tuples of objects and/or sets, the way you’d normally do it if you weren’t worried about set theory. The idea is that if plural logic can be set-theoretically innocent unless the subject matter happens to be sets, then this construction is set-theoretically innocent too. The model theory helps us clarify what we're saying, but you still only have to commit to the entities in the domains.</span></div>
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<b style="font-weight: normal;"><br /></b>
<br />
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<span style="font-family: "cambria"; font-size: 12pt; white-space: pre-wrap;">Here’s the syntax of the language L. It doesn’t have ⪰ in it yet; adding that will make L+.</span></div>
<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
</div>
<ul>
<li><span style="font-family: inherit;">Singular names a, b, c, etc</span></li>
<li><span style="font-family: inherit;">Singular variables x, y, z etc</span></li>
<li><span style="font-family: inherit;">Plural names C, D, E, etc</span></li>
<li><span style="font-family: inherit;">Plural variables X, Y, Z etc</span></li>
<li><span style="font-family: inherit;">Predicates P, Q, R etc, which can be any finite number of places ≥ 1, and which can be singular or plural in each position.</span></li>
<li><span style="font-family: inherit;">A binary “one of” predicate <, singular in the first position and plural in the second.</span></li>
<li><span style="font-family: inherit;">A binary “among” predicate ⊑, plural in both positions.</span></li>
<li><span style="font-family: inherit;">A binary identity predicate =, singular in both positions. (Plural identity can be defined in terms of = and < in the normal way if need be. (Our language L can't express many-one identities, even though regular readers will recall that I think some many-one identities are true.)</span></li>
<li><span style="font-family: inherit;">Atomic wffs composed out of predicates and names or variables in the normal way.</span></li>
<li><span style="font-family: inherit;">Compound wffs composed from wffs and & and ¬ in the normal way, with other connectives defined as normal.</span></li>
<li><span style="font-family: inherit;">Quantifiers ∃ and ∀. </span>∃! is defined as a unique-existence quantifier in the normal way.</li>
<li><span style="font-family: inherit;">If φ is a wff and v is a singular or plural variable, ∃vφ and ∀vφ are wffs.</span></li>
</ul>
<br />
<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "cambria"; font-size: 12pt; white-space: pre-wrap;">Now the semantics:</span></div>
<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
</div>
<ul>
<li><span style="font-family: inherit;">A model M is an ordered pair <D, V> where D is a set of objects and V is a function on members of L.</span></li>
<li><span style="font-family: inherit;">An assignment A is a function from singular variables to members of D and from plural variables to non-empty subsets of D.</span></li>
<li><span style="font-family: inherit;">If t is a singular name, V<span style="font-size: 7.2pt; vertical-align: sub; white-space: pre-wrap;">A</span><span style="font-size: 10pt; vertical-align: baseline; white-space: pre-wrap;">(t) = V(t) ∈ D.</span></span></li>
<li><span style="font-family: inherit;">If t is a singular variable, V<span style="font-size: 7.2pt; vertical-align: sub; white-space: pre-wrap;">A</span><span style="font-size: 10pt; vertical-align: baseline; white-space: pre-wrap;">(t) = A(t) ∈ D.</span></span></li>
<li><span style="font-family: inherit;">If t is a plural name, V<span style="font-size: 7.2pt; vertical-align: sub; white-space: pre-wrap;">A</span><span style="font-size: 10pt; vertical-align: baseline; white-space: pre-wrap;">(t) = V(t) ⊆ D, and must be non-empty</span></span></li>
<li><span style="font-family: inherit;">If t is a plural variable, V<span style="font-size: 7.2pt; vertical-align: sub; white-space: pre-wrap;">A</span><span style="font-size: 10pt; vertical-align: baseline; white-space: pre-wrap;">(t) = A(t) ⊆ D, and must be non-empty</span></span></li>
<li><span style="font-family: inherit;">If P is an n-place predicate, V(P) is a set of n-tuples <o<span style="font-size: 7.2pt; vertical-align: sub; white-space: pre-wrap;">1</span><span style="font-size: 10pt; vertical-align: baseline; white-space: pre-wrap;">, o</span><span style="font-size: 7.2pt; vertical-align: sub; white-space: pre-wrap;">2</span><span style="font-size: 10pt; vertical-align: baseline; white-space: pre-wrap;">, …, o</span><span style="font-size: 7.2pt; vertical-align: sub; white-space: pre-wrap;">n</span><span style="font-size: 10pt; vertical-align: baseline; white-space: pre-wrap;">>, where o</span><span style="font-size: 7.2pt; vertical-align: sub; white-space: pre-wrap;">i</span><span style="font-size: 10pt; vertical-align: baseline; white-space: pre-wrap;"> ∈ D when P is singular in the i</span><span style="font-size: 7.2pt; vertical-align: super; white-space: pre-wrap;">th</span><span style="font-size: 10pt; vertical-align: baseline; white-space: pre-wrap;"> place, while o</span><span style="font-size: 7.2pt; vertical-align: sub; white-space: pre-wrap;">i</span><span style="font-size: 10pt; vertical-align: baseline; white-space: pre-wrap;"> is a non-empty subset of D when P is plural in the i</span><span style="font-size: 7.2pt; vertical-align: super; white-space: pre-wrap;">th</span><span style="font-size: 10pt; vertical-align: baseline; white-space: pre-wrap;"> place.</span></span></li>
<li><span style="font-family: inherit;">V(<) is the set of ordered pairs <x, y> where y is a subset of D and x is in y.</span></li>
<li><span style="font-family: inherit;">V(⊑) is the set of ordered pairs <x, y> where y is a subset of D and x is a subset of y.</span></li>
<li><span style="font-family: inherit;">V(=) is the set of ordered pairs <x, x> where x is in D.</span></li>
<li><span style="font-family: inherit;">If P is an n-place predicate and t<span style="font-size: 7.2pt; vertical-align: sub; white-space: pre-wrap;">1</span><span style="font-size: 10pt; vertical-align: baseline; white-space: pre-wrap;"> … t</span><span style="font-size: 7.2pt; vertical-align: sub; white-space: pre-wrap;">n</span><span style="font-size: 10pt; vertical-align: baseline; white-space: pre-wrap;"> are terms, then V</span><span style="font-size: 7.2pt; vertical-align: sub; white-space: pre-wrap;">A</span><span style="font-size: 10pt; vertical-align: baseline; white-space: pre-wrap;">(Pt</span><span style="font-size: 7.2pt; vertical-align: sub; white-space: pre-wrap;">1</span><span style="font-size: 10pt; vertical-align: baseline; white-space: pre-wrap;">...t</span><span style="font-size: 7.2pt; vertical-align: sub; white-space: pre-wrap;">n</span><span style="font-size: 10pt; vertical-align: baseline; white-space: pre-wrap;">) = T if <V</span><span style="font-size: 7.2pt; vertical-align: sub; white-space: pre-wrap;">A</span><span style="font-size: 10pt; vertical-align: baseline; white-space: pre-wrap;">(t</span><span style="font-size: 7.2pt; vertical-align: sub; white-space: pre-wrap;">1</span><span style="font-size: 10pt; vertical-align: baseline; white-space: pre-wrap;">), …, V</span><span style="font-size: 7.2pt; vertical-align: sub; white-space: pre-wrap;">A</span><span style="font-size: 10pt; vertical-align: baseline; white-space: pre-wrap;">(t</span><span style="font-size: 7.2pt; vertical-align: sub; white-space: pre-wrap;">n</span><span style="font-size: 10pt; vertical-align: baseline; white-space: pre-wrap;">)> ∈ V(P), and V</span><span style="font-size: 7.2pt; vertical-align: sub; white-space: pre-wrap;">A</span><span style="font-size: 10pt; vertical-align: baseline; white-space: pre-wrap;">(Pt</span><span style="font-size: 7.2pt; vertical-align: sub; white-space: pre-wrap;">1</span><span style="font-size: 10pt; vertical-align: baseline; white-space: pre-wrap;">...t</span><span style="font-size: 7.2pt; vertical-align: sub; white-space: pre-wrap;">n</span><span style="font-size: 10pt; vertical-align: baseline; white-space: pre-wrap;">) = F otherwise.</span></span></li>
<li><span style="font-family: inherit;">The values for & and ¬ are assigned truth-functionally in the normal way.</span></li>
<li><span style="font-family: inherit;">V<span style="font-size: 7.2pt; vertical-align: sub; white-space: pre-wrap;">A</span><span style="font-size: 10pt; vertical-align: baseline; white-space: pre-wrap;">(∃vφ) = T iff there is an assignment B which differs from A at most in the value for v, such that V</span><span style="font-size: 7.2pt; vertical-align: sub; white-space: pre-wrap;">B</span><span style="font-size: 10pt; vertical-align: baseline; white-space: pre-wrap;">(φ) = T, and V</span><span style="font-size: 7.2pt; vertical-align: sub; white-space: pre-wrap;">A</span><span style="font-size: 10pt; vertical-align: baseline; white-space: pre-wrap;">(∃vφ) = F otherwise.</span></span></li>
<li><span style="font-family: inherit;">V<span style="font-size: 7.2pt; vertical-align: sub; white-space: pre-wrap;">A</span><span style="font-size: 10pt; vertical-align: baseline; white-space: pre-wrap;">(∀vφ) = T iff all assignments B which differ from A at most in the value for v are such that V</span><span style="font-size: 7.2pt; vertical-align: sub; white-space: pre-wrap;">B</span><span style="font-size: 10pt; vertical-align: baseline; white-space: pre-wrap;">(φ) = T, and V</span><span style="font-size: 7.2pt; vertical-align: sub; white-space: pre-wrap;">A</span><span style="font-size: 10pt; vertical-align: baseline; white-space: pre-wrap;">(∀vφ) = F otherwise.</span></span></li>
<li><span style="font-family: inherit;">M(φ) = T iff V<span style="font-size: 7.2pt; vertical-align: sub; white-space: pre-wrap;">A</span><span style="font-size: 10pt; vertical-align: baseline; white-space: pre-wrap;">(φ) = T for all assignments A, and M(φ) = F otherwise.</span></span></li>
<li><span style="font-family: inherit;">Σ ⊨ φ iff for every model M such that M(ψ) = T for all ψ ∈ Σ, M(φ) = T as well.</span></li>
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<span style="font-family: "cambria"; font-size: 12pt; white-space: pre-wrap;">This is the basic logic. It isn’t supposed to be original. It’s supposed to be unoriginal, because if it was original I’d be in danger of having to defend its set-theoretic innocence myself, instead of outsourcing the job to Boolos. (I'm not sure if Boolos himself is the first person to formalize the model theory along these lines, but other people in the tradition use a set-theoretic model theory and lean on Boolos for the case for ontological innocence. I think they do, anyway. If I'm honest it's a long time since I read Boolos's paper. I think he says something pretty persuasive about how when you eat a bowl of Cheerios you're eating the Cheerios, not a set of Cheerios.) I felt it was important to write it down so you could see just how much set theory is involved, and what it's doing.</span></div>
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<span style="font-family: "cambria"; font-size: 12pt; white-space: pre-wrap;">Now we construct a model M+ = <D, U> from a given model M = <D, V>. We start by constructing a model N = <E, W>.</span></div>
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<li><span style="font-family: inherit;">E = D ∪ G, where G is the set of objects representing ordered pairs of members of D.</span></li>
<li><span style="font-family: inherit;">D and G are disjoint.</span></li>
<li><span style="font-family: inherit;">Introduce two binary predicates P<span style="font-size: 7.2pt; vertical-align: sub; white-space: pre-wrap;">1</span><span style="font-size: 10pt; vertical-align: baseline; white-space: pre-wrap;"> and P</span><span style="font-size: 7.2pt; vertical-align: sub; white-space: pre-wrap;">2</span><span style="font-size: 10pt; vertical-align: baseline; white-space: pre-wrap;"> which are undefined in M. These are singular in both positions. You can think of N as a model of an expanded language L*.</span></span></li>
<li><span style="font-family: inherit;">For every object x in D, there is one object y in G such that <x, y> is in W(P<span style="font-size: 7.2pt; vertical-align: sub; white-space: pre-wrap;">1</span><span style="font-size: 10pt; vertical-align: baseline; white-space: pre-wrap;">) and W(P</span><span style="font-size: 7.2pt; vertical-align: sub; white-space: pre-wrap;">2</span><span style="font-size: 10pt; vertical-align: baseline; white-space: pre-wrap;">).</span></span></li>
<li><span style="font-family: inherit;">For every two objects x and y in D, there is exactly one object z in G such that <x, z> is in W(P<span style="font-size: 7.2pt; vertical-align: sub; white-space: pre-wrap;">1</span><span style="font-size: 10pt; vertical-align: baseline; white-space: pre-wrap;">) and <y, z> is in W(P</span><span style="font-size: 7.2pt; vertical-align: sub; white-space: pre-wrap;">2</span><span style="font-size: 10pt; vertical-align: baseline; white-space: pre-wrap;">).</span></span></li>
<li><span style="font-family: inherit;">Nothing else is in G.</span></li>
<li><span style="font-family: inherit;">For every object x in G, <y, x> is in W(P<span style="font-size: 7.2pt; vertical-align: sub; white-space: pre-wrap;">1</span><span style="font-size: 10pt; vertical-align: baseline; white-space: pre-wrap;">) and <y, z> is in W(P</span><span style="font-size: 7.2pt; vertical-align: sub; white-space: pre-wrap;">2</span><span style="font-size: 10pt; vertical-align: baseline; white-space: pre-wrap;">) for only one y and only one z.</span></span></li>
<li><span style="font-family: inherit;">Nothing else is in W(P<span style="font-size: 7.2pt; vertical-align: sub; white-space: pre-wrap;">1</span><span style="font-size: 10pt; vertical-align: baseline; white-space: pre-wrap;">) or W(P</span><span style="font-size: 7.2pt; vertical-align: sub; white-space: pre-wrap;">2</span><span style="font-size: 10pt; vertical-align: baseline; white-space: pre-wrap;">).</span></span></li>
<li><span style="font-family: inherit;">Let A be an assignment on D, and let B be an assignment on E that extends A.</span></li>
<li><span style="font-family: inherit;">Now we define the extension of ⪰ in M+, that is U(⪰), in terms of the assignments A relative to which W evaluates an open sentence with two free plural variables X and Y as true.</span></li>
<li><span style="font-family: inherit;">Let φ be ∃Z[∀y(y<Y → ∃!z[z<Z & P<span style="font-size: 7.2pt; vertical-align: sub; white-space: pre-wrap;">1</span><span style="font-size: 10pt; vertical-align: baseline; white-space: pre-wrap;">yz]) & ∀z(z<Z → ∃x[x<X & P</span><span style="font-size: 7.2pt; vertical-align: sub; white-space: pre-wrap;">2</span><span style="font-size: 10pt; vertical-align: baseline; white-space: pre-wrap;">xz & ∀w[(w<Z & P</span><span style="font-size: 7.2pt; vertical-align: sub; white-space: pre-wrap;">2</span><span style="font-size: 10pt; vertical-align: baseline; white-space: pre-wrap;">xw) → w = z]])]</span></span></li>
<li><span style="font-family: inherit;">U(⪰) = {<s, t>: W<span style="font-size: 7.2pt; vertical-align: sub; white-space: pre-wrap;">A</span><span style="font-size: 10pt; vertical-align: baseline; white-space: pre-wrap;">(φ) = T for some assignment A such that A(X) = s and A(Y) = t}</span></span></li>
<li><span style="font-family: inherit;">In words, φ is meant to mean “There are some things [stand-ins for ordered pairs] such that every Y is the first of exactly one of them, and each of them has a distinct X as its second.”</span></li>
<li><span style="font-family: inherit;">Now we can say that a model of L+ is admissible iff it is the model M+ for some admissible model M of L.</span></li>
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<span style="font-family: "cambria"; font-size: 12pt; white-space: pre-wrap;">That’s the proposal formalized. There’s a lot of set theory in the formalization, and indeed there’s so much that you could be forgiven for forgetting that I was trying to avoid set theory at all. But I <i>was</i> trying to avoid set theory. There are two things set theory is doing there. One is to construct the models of plural logic. I already said I wasn’t going to try finding a non-set-theoretic model theory for plural logic. The other thing is a very weak set theory that adds something equivalent to ordered pairs to the domains of the intermediate models (N in the construction), but the ordered pairs don't themselves form further ordered pairs. How should we interpret this? I think the most principled way for a fictionalist about sets like me is to interpret those models as representing a fiction. The fiction says that every one or two objects that aren’t themselves ordered pairs form one or two ordered pairs respectively. (So for every non-pair x there’s <x, x> and for every non-pair x and non-pair y there are <x, y> and <y, x>.) When it’s true in the ordered pairs fiction that there are some ordered pairs representing a one-one correspondence between some of the Xs and all the Ys, it’s true in reality that there are at least as many Xs as Ys.</span></div>
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<span style="font-family: "cambria"; font-size: 12pt; white-space: pre-wrap;">The point of using the ordered-pairs fiction instead of the full-ZFC fiction is that the ordered-pairs fiction specifies a single fully determinate model N, given a model M for reality-minus-size-comparison-facts. You then use this to get a model M+ for reality-including-size-comparison-facts. Full ZFC doesn’t specify a single model, and the different models may have different one-one correspondences in them, which will give you different size-comparison facts. The models themselves are set-theoretic objects. I’m not sure how much of a problem that is. I think the kind of answer I’d like to give is along the lines people give for variable domains modal logic: we already understand plural logic, and the use of this model theory is just supposed to precisify which particular thing that we already understand we’re talking about. Someone who thinks you can’t understand plural logic without set theory won’t buy that, and those are the people I’m referring to Boolos.</span></div>
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<span style="font-family: "cambria"; font-size: 12pt; white-space: pre-wrap;">Maybe a promising way around this would be to construct a model theory for plural logic along the same lines as the ordered-pairs fiction itself. There’s a whole lot of ZFC not being used in the model theory, so maybe you could have a much lower-powered fiction which could still do the job but didn’t have the underspecification you get with ZFC. I only have a vague idea of how that might go though, and there could be straightforward reasons why it wouldn’t work.</span></div>
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<span style="font-family: "cambria"; font-size: 12pt; white-space: pre-wrap;">In closing I’d like to make it clear what my ambitions are. I claimed in my last post that we could understand a version of the continuum hypothesis independently of set theory. The continuum hypothesis without sets, or CHWS, is a statement about how many real numbers there are. To make sense of CHWS without using sets, we need to understand how there can be more Xs than Ys when there are uncountably many of each. Normally we do that using sets. I’ve been trying to show how we might do it while avoiding full ZFC and its indeterminacies, using only plural logic and the much lower-powered and more determinate fiction of ordered pairs. I’m trying to show that we can <i>understand</i> CHWS as something with a determinate answer, even if we’re fictionalists about sets. I’m not trying to offer any reason for optimism that we could ever <i>settle</i> CHWS. And if I had to guess, I’d say we probably never will.</span><br />
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<span style="font-family: "cambria";"><span style="white-space: pre-wrap;"><b>**********************</b></span></span><br />
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<ul>
<li>Boolos, George (1984). To be is to be a value of a variable (or to be some values of some variables). <em class="pubName" style="background-color: white; box-sizing: border-box; color: #333333; font-family: inherit;">Journal of Philosophy</em><span style="background-color: white; color: #333333; font-family: inherit;"> 81 (8):430-449.</span></li>
</ul>
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Michael Bench-Caponhttp://www.blogger.com/profile/13715068990919309271noreply@blogger.com0tag:blogger.com,1999:blog-6411624366539130337.post-80979699323229359952018-05-05T07:27:00.000-07:002018-05-10T01:46:01.092-07:00The Continuum Hypothesis Without Set Theory<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span id="docs-internal-guid-166efcfb-3094-5261-8c02-ec2816e4007d"><span style="font-family: "calibri"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">Regular readers may recall that a while ago I posted a </span><a href="http://michaelbenchcapon.blogspot.co.uk/2013/12/fallacious-proof-of-continuum-hypothesis.html" style="text-decoration-line: none;"><span style="color: black; font-family: "calibri"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;"><b>fallacious proof of the continuum hypothesis</b></span></a><span style="font-family: "calibri"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">. They may also recall that a bit more recently I </span><a href="http://michaelbenchcapon.blogspot.co.uk/2016/11/mathematical-and-moral-deference.html" style="text-decoration-line: none;"><span style="color: black; font-family: "calibri"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;"><b>tried unsuccessfully to understand forcing</b></span></a><span style="font-family: "calibri"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">. Forcing is a technique for building models of set theories, which Paul Cohen used to show that the continuum hypothesis doesn’t follow from the ZFC axioms. (The ZFC axioms are the Zermelo-Fraenkel axiomatization of set theory plus the axiom of choice, and I’m told that most normal maths that can be proved at all can in principle be cast in terms of set theory and then its set-theoretic version can be proved from these axioms, if you feel the need to do that.) Anyway, in spite of the evidence that I’m not very good at it, I’ve been thinking about the continuum hypothesis again.</span></span></div>
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<span id="docs-internal-guid-166efcfb-3094-afa3-49cd-35d218f8ec1e"><span style="font-family: "calibri"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">The continuum hypothesis, for those of you who don’t know but are still reading, is the proposition that the number of real numbers is the second smallest infinite number. It’s been proved that the number of integers is the smallest infinite number, that the number of real numbers is bigger, and that there is a second smallest infinite number. Georg Cantor conjectured that the number of real numbers was the second smallest, Kurt G</span><span style="background-color: white; font-family: "calibri"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">ödel proved that the continuum hypothesis was consistent with the ZFC axioms, and Paul Cohen proved that it didn’t follow from them. So we’ve established that the ZFC axioms, even if true, don’t settle the question. And in the time since Cohen finished the independence proof, set theorists have learned a great deal more about which axiom systems do and don’t settle the continuum hypothesis, which models it is and isn’t true in, and the relationships between them. (I don’t understand this work myself: in order to understand it I’d have to understand how forcing works, and I’m sorry to report that I still don’t.)</span></span></div>
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<span id="docs-internal-guid-166efcfb-3095-c9fb-82d3-a07db22c0f6a"><span style="background-color: white; font-family: "calibri"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">Now, some people respond to this situation by saying that the continuum hypothesis (CH from now on) is indeterminate. This might be because they think that the notion of a set corresponding to ZFC doesn’t pin down a particular model, and CH is true in some and not in others. It might be because they think there are multiple set-theoretic universes out there, and CH is true in (or of) some of them but not others. It might be because they think mathematical truth basically amounts to provability, and we know that neither CH nor its negation is provable. Or perhaps they think the indeterminacy comes in somewhere else, for example as fundamental metaphysical indeterminacy.</span></span></div>
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<span style="background-color: white; font-family: "calibri"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;"><br /></span></div>
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<span id="docs-internal-guid-166efcfb-3096-00f0-9802-9461b7d9d47b"><span style="background-color: white; font-family: "calibri"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">Some people are set-theoretic Platonists, who think there’s a real, determinate universe of sets out there, and that even though we don’t know enough about it yet to prove that CH is true or false in it, CH is nonetheless true or false in it. To settle the question we would have to learn things about the set-theoretic universe that don’t follow logically from what we already know about it. How exactly we’d go about learning something like that is a vexed question, but (so the story goes) we have already managed to learn some things about it that don’t follow from nothing, so perhaps we could pull off the trick again. I’ve heard something like this view attributed to </span><span style="font-family: "calibri"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">G</span><span style="background-color: white; font-family: "calibri"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">ödel, though I’m not sure how fair a reflection of his views what I heard was, or how badly I’ve garbled what I heard.</span></span></div>
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<span style="background-color: white; font-family: "calibri"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;"><br /></span></div>
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<span id="docs-internal-guid-166efcfb-3096-5699-41e6-2697fee9a753"><span style="background-color: white; font-family: "calibri"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">I’ve got a certain amount of sympathy with this kind of view in principle, but I don’t agree with it. I think sets are made up, and that makes me a fictionalist about sets. I don’t think that integers and real numbers are made up, and my attitude towards them probably makes me a Platonist about those. I sympathize with the Platonist view about CH in principle because I’d be happy to take this attitude towards mathematical entities I didn’t think were made up. But it’s not my view because I do think sets are made up. In fact, the more I hear about sets, the more made up they sound.</span></span></div>
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<span style="background-color: white; font-family: "calibri"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;"><br /></span></div>
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<span id="docs-internal-guid-166efcfb-3096-a26a-db27-c2b3f4d3b7d8"><span style="background-color: white; font-family: "calibri"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">Sometimes we talk about things being true or false in fictions, and I think that’s a reasonable way to talk. It’s true in the relevant fictions that Miss Marple solves crimes, for example. I think that there are a few fictions relating to set theory, and that we have pretty tight rules for establishing what is and isn’t true in several of these fictions. (Much tighter rules than we have for Miss Marple.) As is the way with fictions, sometimes the rules don’t settle what’s true in the fictions, and maybe sometimes nothing settles it at all. We tend to be more easygoing about indeterminacy in fiction than about indeterminacy in reality, and that’s probably fair. If you give a set-theoretic statement of CH, that will tend to be true in some of these fictions, false in others, and indeterminate in others. So you might think that a fictionalist about CH should think this is all there is to the truth or otherwise of CH.</span></span></div>
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<span style="background-color: white; font-family: "calibri"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;"><br /></span></div>
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<span id="docs-internal-guid-166efcfb-3097-29bd-77c8-e2a29b2cbe73"><span style="background-color: white; font-family: "calibri"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">Well, that’s not what I think. Take another look at what I said CH was, earlier in the post:</span></span></div>
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<i><span style="background-color: white; font-family: "calibri"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">"</span><span style="background-color: white; font-family: "calibri"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">T</span><span style="font-family: "calibri"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">he proposition that the number of real numbers is the second smallest infinite number."</span></i></div>
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<span style="font-family: "calibri"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">The eagle-eyed and literal-minded among you will notice that this doesn’t mention sets. It mentions numbers. Since in this instance we don’t need to worry about uninstantiated numbers, we can cast CH without mentioning sets, or even mentioning infinite numbers:</span></div>
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<span id="docs-internal-guid-166efcfb-3098-3736-260b-a981b25b9ef7"><span style="font-family: "calibri"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;"><i>"There aren’t any things such that there are more of them than there are integers but fewer of them than there are real numbers."</i></span></span></div>
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<span id="docs-internal-guid-166efcfb-3098-ab76-b322-782b052df211"><span style="font-family: "calibri"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">We’ll call this CHWS, for Continuum Hypothesis Without Sets. I think that when we ask whether the continuum hypothesis is true, this is the question we’re ultimately interested in, at least under the assumption that the integers and real numbers exist. But I expect that some set theorists will like to think of the set-theoretic formulation of CH as the continuum hypothesis, and that’s fine. I’ll try to sidestep the terminological issue by giving it a slightly different name: CHWS. In deference to these imagined set theorists, from now on I’ll use CH for their set-theoretic version.</span></span></div>
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<span id="docs-internal-guid-166efcfb-3098-ef05-8cff-dd6ccad8496b"><span style="font-family: "calibri"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">I said earlier that I was a realist, and probably a Platonist, about integers and real numbers. That’s more or less true, in that it’s my working hypothesis even if I’m not fully committed to it. As I see it, if you’ve got some things, then it makes sense to talk about how many of them there are, and whether the number of them is infinite, and whether there are more of them than there are of some other things. And none of this presupposes the existence of sets. When you say there are more even numbers than prime numbers between 1 and 100 you’re saying something about numbers, not about sets. We’re able to give a precise explication of these notions in set-theoretic terms, and this explication serves for most purposes, but you might think that one lesson of the independence of CH from ZFC is that ZFC set theory can’t help us answer the question about how many real numbers there are. But if I’m a Platonist about real numbers, which I probably am, and I don’t think that there’s indeterminacy in how many of them there are, which I don’t, then CHWS can still have an answer. It’s just that set theory alone can’t help us find it. Perhaps sometimes when you ask whether there are more Xs than Ys this doesn’t always have a determinate answer, and so CHWS could be indeterminate for that reason. But I don’t see that anything we’ve learned about set theory compels us to think that. I think it’s a very strange idea, although the subject matter seems sufficiently strange that I should be open to the possibility, and so I am. But being open to the possibility that CHWS is indeterminate is very different from thinking it actually is indeterminate. And if I had to guess, I’d say it probably isn’t.</span></span></div>
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<span id="docs-internal-guid-166efcfb-30a7-a8e6-8abb-0e33298c293d"><span style="background-color: white; font-family: "calibri"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">So in summary, here are the things I said I think:</span></span></div>
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<ul>
<li><span style="font-family: "calibri";"><span style="white-space: pre-wrap;"><span id="docs-internal-guid-166efcfb-30a7-e1f9-f433-f7a4e8beecbd"><span style="background-color: white; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline;">Sets are made up, so I’m a fictionalist about sets.</span></span></span></span></li>
<li><span style="font-family: "calibri";"><span style="white-space: pre-wrap;"><span style="background-color: white; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline;"><span id="docs-internal-guid-166efcfb-30a8-0d85-13df-9dea06b4e7d5"><span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline;">Integers and real numbers aren’t made up: I’m a Platonist about those.</span></span></span></span></span></li>
<li><span style="font-family: "calibri";"><span style="white-space: pre-wrap;"><span style="background-color: white; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline;"><span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline;"><span id="docs-internal-guid-166efcfb-30a8-2c2d-c9be-70a256cc56fe"><span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline;">We can make sense of questions about whether or not there are more Xs than Ys without understanding them in terms of sets.</span></span></span></span></span></span></li>
<li><span style="font-family: "calibri";"><span style="white-space: pre-wrap;"><span style="background-color: white; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline;"><span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline;"><span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline;"><span id="docs-internal-guid-166efcfb-30a8-5cad-305d-c2c33ffda540"><span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline;">Sometimes those questions have determinate answers, and maybe they always do.</span></span></span></span></span></span></span></li>
<li><span style="font-family: "calibri";"><span style="white-space: pre-wrap;"><span style="background-color: white; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline;"><span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline;"><span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline;"><span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline;"><span id="docs-internal-guid-166efcfb-30a8-85bd-7f56-34568fa8849e"><span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline;">The continuum hypothesis can be cast as a question about how many real numbers there are, without reference to sets.</span></span></span></span></span></span></span></span></li>
<li><span style="font-family: "calibri";"><span style="white-space: pre-wrap;"><span style="background-color: white; font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline;"><span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline;"><span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline;"><span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline;"><span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline;"><span id="docs-internal-guid-166efcfb-30a8-aa96-777b-bd974e734681"><span style="font-size: 12pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline;">This question may have a determinate answer, and nothing about set theory gives us much reason to think it doesn’t.</span></span></span></span></span></span></span></span></span></li>
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<span id="docs-internal-guid-166efcfb-30a8-eed6-9c78-8be9ad3f5f05"></span></div>
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<span id="docs-internal-guid-166efcfb-30a9-d00e-08ba-036a89b4d070"><span style="background-color: white; font-family: "calibri"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">As I understand it, this isn’t a popular combination of views, and I suppose it might even be provably incoherent. Perhaps there are people who could sensibly be confident that they could prove that it’s incoherent in an afternoon. But I’ve held these views as working hypotheses for a while now, and although I don’t think I’ve converted anyone, I also haven’t noticed them leading to any problems in the general pursuit of truth, so to speak. For somebody who has the information and interests I have, they make a livable position, and livability is a source of evidence in philosophy. But I do worry that I don’t understand the issues well enough to have earned the right to hold this combination of views. Maybe my taking a position on this stuff at all is pure hubris, and my foolish, incoherent position is a result of that hubris. Or maybe I’m more or less right, and my reasons for arriving at the position are sensible enough that being right is some kind of epistemic achievement. (Or maybe I’m entitled to a view, but am nonetheless wrong.) On the one hand the Enlightenment ideal is supposed to involve having confidence in your own rational capacities and making sense of things for yourself, instead of taking things on trust from people you’re told are authorities. On the other hand, that’s exactly how people end up posting flat-earth videos on Youtube.</span></span></div>
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<span id="docs-internal-guid-166efcfb-30aa-fbe4-5936-b9b212d3410b"><span style="background-color: white; font-family: "calibri"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">So, am I being like a flat-earther? The unpopular part of my position, as I understand it, is that I’m a fictionalist about sets but I think CHWS may still have a determinate truth value. It seems to me that a couple of things differentiate me from the flat-earthers. One is that I’ve studied a lot of philosophy, including some philosophy of maths, and this should give me some protection against making really silly mistakes when thinking about this kind of thing. Another is that members of the academic establishment put quite a lot of effort into debunking flat-earthism, whereas nobody’s putting much effort into debunking the combination of set-theoretic fictionalism and realism about a version of the continuum hypothesis. Although like I say, I wouldn’t be all that surprised if a philosophically informed set-theorist with a free afternoon could do it. If there is a quick debunking to be made, the main pressure point seems to be the notion that we can make comparisons of infinite sizes without dealing with sets. More specifically, there’s the notion that we can make comparisons between </span><span style="background-color: white; font-family: "calibri"; font-size: 12pt; font-style: italic; vertical-align: baseline; white-space: pre-wrap;">uncountably</span><span style="background-color: white; font-family: "calibri"; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;"> infinite sizes without dealing with sets. Can we? It’s not obvious to me whether we can or not. Maybe that’s the question I need to answer before I’m allowed to have an opinion on this stuff.</span></span></div>
Michael Bench-Caponhttp://www.blogger.com/profile/13715068990919309271noreply@blogger.com0tag:blogger.com,1999:blog-6411624366539130337.post-47643485258310483032018-04-20T04:32:00.001-07:002018-04-20T06:16:25.761-07:00Metaphysical Whack-A-Mole<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="font-family: "verdana" , sans-serif; white-space: pre-wrap;">Here’s an argument for the existence of God:</span></div>
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<li><span style="font-family: "verdana" , sans-serif;">There’s no contradiction in an omnipotent being spontaneously coming into existence.</span></li>
<li><span style="font-family: "verdana" , sans-serif;">Nothing that was not omnipotent would be able to prevent an omnipotent being coming into existence. (Think of it like a game of metaphysical whack-a-mole.)</span></li>
<li><span style="font-family: "verdana" , sans-serif;">In a given time period, if there is no contradiction in something happening and there is nothing to prevent it from happening then there is a non-zero probability that it will happen.</span></li>
<li><span style="font-family: "verdana" , sans-serif;">So in any given time period at the beginning of which there is no omnipotent being, there is a non-zero probability that an omnipotent being spontaneously comes into existence.</span></li>
<li><span style="font-family: "verdana" , sans-serif;">So over an arbitrarily large time period the probability that an omnipotent being spontaneously comes into existence will be arbitarily close to certainty.</span></li>
<li><span style="font-family: "verdana" , sans-serif;">There has been enough time that we can be practically certain that an omnipotent being has spontaneously come into existence.</span></li>
<li><span style="font-family: "verdana" , sans-serif;">Once an omnipotent being exists, it will see to it that it continues to exist, since it is omnipotent and wants to continue to exist.</span></li>
<li><span style="font-family: "verdana" , sans-serif;">There cannot be more than one omnipotent being, since it follows from their omnipotence that they would be both able and unable to frustrate each other’s intentions, and this is a contradiction.</span></li>
<li><span style="font-family: "verdana" , sans-serif;">If there is exactly one omnipotent being, then that being is God.</span></li>
<li><span style="font-family: "verdana" , sans-serif;">So we can be practically certain that God exists.</span></li>
<li><span style="font-family: "verdana" , sans-serif;">So God exists.</span></li>
</ul>
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<span style="white-space: pre-wrap;"><span style="font-family: "verdana" , sans-serif;">What do you think? Let me know in the comments!</span></span></div>
Michael Bench-Caponhttp://www.blogger.com/profile/13715068990919309271noreply@blogger.com11tag:blogger.com,1999:blog-6411624366539130337.post-73432334478991686612017-10-03T04:49:00.000-07:002017-10-03T04:49:37.410-07:00Goat Product<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: Calibri; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;">I did a lot of maths at school, and while I’ve got a good memory and do use bits of it here and there, it’s been fifteen years and some of it’s a bit rusty. Partly in an attempt to remedy this, I recently I watched some videos on Youtube about </span><a href="https://www.youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr" style="text-decoration-line: none;"><span style="color: #1155cc; font-family: Calibri; font-size: 11pt; text-decoration-line: underline; vertical-align: baseline; white-space: pre-wrap;">calculus</span></a><span style="font-family: Calibri; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;"> and </span><a href="https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab" style="text-decoration-line: none;"><span style="color: #1155cc; font-family: Calibri; font-size: 11pt; text-decoration-line: underline; vertical-align: baseline; white-space: pre-wrap;">linear algebra</span></a><span style="font-family: Calibri; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;">. They’re by someone called Grant Sanderson, whose account is called 3Blue1Brown, and they have a friendly style with lots of neat animations. The idea of the videos is that a lot of people are taught maths in a way that involves a lot of number crunching and rule following but doesn’t get them to understand the underlying concepts, and that this leaves a gap that can be filled by presenting the ideas using visual interpretations. For example, a 2x2 matrix represents a transformation of 2D space that turns every square of size 1 into a parallelogram whose size is the magnitude of the matrix’s determinant. (If it’s negative, that means things are mirrored.) It’s possible I learned this at school, but stressing it and showing a nice animation helps you really understand what the deal is with determinants. They’re cool videos, and if you like maths then I recommend them, although they’re not really designed to teach the topics from scratch. I also recommend </span><a href="https://www.youtube.com/watch?v=AmgkSdhK4K8&t=180s" style="text-decoration-line: none;"><span style="color: #1155cc; font-family: Calibri; font-size: 11pt; text-decoration-line: underline; vertical-align: baseline; white-space: pre-wrap;">this one</span></a><span style="font-family: Calibri; font-size: 11pt; font-weight: 700; vertical-align: baseline; white-space: pre-wrap;"> </span><span style="font-family: Calibri; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;">by the same person, which shows how to give a topological proof of something that doesn’t really seem to be about topology. I watched it a while ago and it really is beautiful.</span></div>
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<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Anyway, as I was going through the linear algebra videos I wrote down some questions I still had so I could find answers to them later, and one of them was about the dot product (also known as the scalar product). The dot product of two vectors <a,b> and <x,y> is a dimensionless directionless scalar, equal to ax + by. Why? What’s it measuring? </span><a href="https://www.youtube.com/watch?v=LyGKycYT2v0&index=10&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-family: Calibri; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">The video on the dot product</span></a><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> gave it a couple of interpretations. </span></div>
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<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">One was to project <a,b> onto the line <x,y> is on via the shortest route, and then multiply the length of the new vector by the length of <x,y>. That might be OK for giving a visual heuristic for calculating or estimating the dot product, but for me it didn’t get me much of a handle on what sorts of thing it represents. Multiplying the length of two vectors is something you’d do if they were the sides of a rectangle and you wanted to find its area, but if the vectors are on the same line, where’s the rectangle? And if it’s an area, why is the dot product a scalar? It makes sense for the determinant to be a scalar because it’s the scale factor for areas, but with the projection interpretation of the dot product I couldn’t really see which areas were getting scaled up. </span></div>
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<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">The second interpretation replaced one of the vectors with a 1x2 matrix, and then visualized this as a transformation taking points in 2D space onto a number line embedded in that space. The 1x2 matrix <a,b> will take the point <x,y> in 2D space to the point ax+by on the number line. That’s great, and it shows you the nice duality between the dot product and this kind of transformation, and indeed that was the point of this part of the video. (The video was called “Dot Products And Duality”, after all.) But a 2x1 vector isn’t a 1x2 matrix, and the fact that that taking the dot product is dual to performing a process that outputs a scalar doesn’t really tell you why the dot product itself is a scalar. </span></div>
<b style="font-weight: normal;"><br /></b>
<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">There will be good reasons for the dot product to be a scalar, of course, but this video didn’t help me see what they are. I also thought it’d be good to have a better visual interpretation of the dot product, where I could point to something I could see and say “that’s the dot product”, instead of pointing at two things I could see and having to multiply them together to find the dot product, even though the multiplication didn’t correspond to anything in the picture. In the video series on calculus he </span><a href="https://youtu.be/m2MIpDrF7Es?list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr&t=219" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-family: Calibri; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">actually flags up</span></a><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> that he doesn’t have a nice picture for the derivative of 2</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 6.6pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: super; white-space: pre-wrap;">t</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> where we can point to it and say: “See? That part! That is the derivative of 2</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 6.6pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: super; white-space: pre-wrap;">t</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">!” He says he’d like one, but doesn’t know one. Perhaps there isn’t one. Although perhaps there must be one. I guess different people will have different views about how high our expectations about this sort of thing should be.</span></div>
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<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Anyway, I made a note of the question, and when I got to the end of the videos I still didn’t have an answer, so I googled things like “visual interpretation of dot product” and “why is the dot product a scalar”. And you know what? Nobody else seemed to have a decent answer either! I mean, I didn’t look very hard, but there seems to be a fair bit of mystification out there, both from people asking the question and people trying to answer it. On </span><a href="https://www.quora.com/Why-is-the-dot-product-of-two-vectors-a-scalar-number" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-family: Calibri; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">this Quora page about the question</span></a><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">, one person said that’s just how it’s defined, which isn’t helpful, and another said it was the distance between points the two vectors point at, which isn’t true on any interpretation I could work out. On </span><a href="https://betterexplained.com/articles/vector-calculus-understanding-the-dot-product/" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-family: Calibri; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">another page I found more helpful</span></a><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> someone said it was like a booster ramp in Mario Kart, which boosts you best if you drive over it in the direction of the ramp, and doesn’t boost you so well if you drive over it obliquely. I quite liked that one, but it has some problems. One is that if you drive over it backwards it still boosts you forwards, so there’s nothing much that seems to correspond to negative dot products. The other problem is that it’s not obvious what corresponds to multiplication here. It seems to me that the ramp adds a certain amount of velocity, rather than multiplying a vector from the ramp by the vector given by your initial velocity. Also the result of going on a ramp seems more like a vector than a scalar. I think these three issues are related. I did still find it helpful, and maybe I just don’t have a good enough feel for how the booster ramps work (although I have played the game quite a lot), but I wanted something better. He had one involving the angles of solar panels too but he didn’t like that as much as the Mario Kart one, and I didn’t really either. (I couldn’t see how it produced negative dot products, for example.)</span></div>
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<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">So anyway, I had a go at coming up with my own visualization, and I found one that I think works pretty well. You know how people share those pictures of </span><a href="https://matadornetwork.com/life/32-photos-that-prove-goats-are-the-worlds-best-climbers/" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-family: Calibri; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">goats standing on almost vertical surfaces</span></a><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">, seemingly defying gravity? Well, imagine a goat standing on one of those. It could be a very steep one like the cliffs in the pictures, or it could be shallower like a hillside. Basically any inclined plane will do. We can represent the slope with a vector u, for </span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 11pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">upslope</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">. The vector points up the slope and its magnitude is the gradient of the slope in that direction. <0,0> corresponds to a horizontal plane, which is fine, but no vector corresponds to a vertical one, which is just as well because even a goat can’t stand on a vertical plane. Now the goat sets off along the surface in a straight line, with its </span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 11pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">horizontal</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> velocity given by a vector v. It may be easiest to picture v if you look down on the goat from above. Now the dot product is the rate of change in the goat’s elevation. Positive means the goat is going up, and negative means the goat is going down. It’s a scalar, not a vector, because it’s measuring how fast the goat is moving up or down, not measuring how fast it’s moving </span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 11pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">and</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> which direction it’s moving. (Well, it’s measuring whether the goat is going up or down, but even scalars distinguish a positive and a negative direction. It’s not measuring the direction in three dimensions, or even two.)</span></div>
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<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">The sums seem to work out. Think of u = <a,b> as giving the gradient </span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 11pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">a</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> when moving north and the gradient </span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 11pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">b</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> when going east, and think of v = <x,y> as giving the velocity’s northern component </span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 11pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">x</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> and eastern component </span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 11pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">y</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">. Negative gradients are downhill, and negative velocity north or east is movement south or west. So if it goes x north and then y east it will go a*x up and then b*y up.</span></div>
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<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">It gives straightforward visual interpretations to some properties of the dot product too. To get maximum height for its horizontal displacement, the goat goes straight uphill, which means u and v have the same direction. Change in elevation for a given horizontal dispacement is proportional to gradient, and change in elevation for a given gradient is proportional to horizontal displacement. It’s clear when the dot product will be positive, negative or zero, depending on whether it’s moving uphill, downhill or along a contour. It’s a good visualization of how a difference in the angle between u and v makes less of a difference to the dot product when the angle is small than when it’s big. It’s also clear that if u = <0,0> the plane is flat and the goat won’t go up or down however much it moves horizonatally, and it’s clear that if v = <0,0> the goat is stationary so it won’t go up or down however steep the slope is. </span></div>
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<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Finally, we can think about how different vectors u can multiply by the same vector v to give the same dot product. To do that, imagine that the plane is one side of a V-shaped valley whose edges and base are horizontal, and the goat wants to get to the top or the bottom, depending on whether the dot product is positive or negative. The dot product represents the height to the top or bottom of the valley, and u represents the slope of the valley. Now imagine you’re looking at the goat from above, and it wants to get to the top. There are lots of ways it could get to its destination. It can run straight uphill, and then it won’t have gone so far horizontally. Or it can set off almost at right angles to the slope, and then it’ll go a very long way horizontally before it gets to the top. Or it can do something in between. But it can’t go at right angles or an obtuse angle to the slope, or it’ll never get to the top. And there’s also a minimum horizontal distance it has to go. Viewing from above, you can draw a little circle around the goat and see that if the circle is small enough everything inside it will still be in the valley.</span></div>
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<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">So there’s my visualization for the dot product. I like it! Commutativity holds, as it must, but it doesn’t immediately drop out of the setup the way it might if u and v represented more similar sorts of things. I won’t try making a virtue of that. But I think it’s OK, and I like it better than the other ones I found, and assuming I’ve not made mistakes with it, I think other people would like it too. I’m sure there are other adequate ones out there, but not everyone is aware of them, and coming up with these things yourself is all part of the learning process anyway. I didn’t really get what the deal was with the dot product, and now I think I do. The dot product is the goat product.</span></div>
Michael Bench-Caponhttp://www.blogger.com/profile/13715068990919309271noreply@blogger.com0tag:blogger.com,1999:blog-6411624366539130337.post-54913644080985104402017-09-12T07:47:00.000-07:002018-12-19T15:47:51.450-08:00They Do Things Differently There<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "calibri"; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;">Between 1962 and 1981, a scholar at Cambridge University called WKC Guthrie published a six-volume </span><span style="font-family: "calibri"; font-size: 11pt; font-style: italic; vertical-align: baseline; white-space: pre-wrap;">History of Greek Philosophy</span><span style="font-family: "calibri"; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;"> running from the early Presocratics to Aristotle. He was, it seems, something of an expert. In the preface to the first volume (1962: xi) he says he had plans to go further: “It is my intention, </span><span style="font-family: "calibri"; font-size: 11pt; font-style: italic; vertical-align: baseline; white-space: pre-wrap;">Deo volente</span><span style="font-family: "calibri"; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;">, to continue this history to include the Hellenistic period, stopping short of the Neoplatonists and those of their predecessors who are best understood in conjunction with them.” Six volumes is still a lot, of course, but don’t worry: he also wrote a much shorter book in 1950 covering the same period, called </span><span style="font-family: "calibri"; font-size: 11pt; font-style: italic; vertical-align: baseline; white-space: pre-wrap;">The Greek Philosophers: From Thales to Aristotle</span><span style="font-family: "calibri"; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;">. It was based on a series of lectures aimed at undergraduates who weren’t taking classics and might not know any Greek. (His six-volume work was meant to be accessible for non-Greek-readers too.) I hardly know any Greek myself, and I’ve recently been taking an interest in Anaxagoras, so when I saw it in a second hand bookshop I thought I might like it. And I did! I’ve heard the basic story a few times before, but I’m always ready to read someone else’s take on these things, and there were a few things I found kind of interesting about Guthrie’s.</span></div>
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<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">The first chapter is called “Greek Ways of Thinking”, and by page four he’s already got into a discussion about the meanings of words. He wants to stress that some of the key words ancient Greek philosophers used didn’t mean the same things to them as their usual English translations mean to us. He mentions the words translated as ‘justice’, ‘virtue’, and ‘god’ (or ‘God’), and the Greek word </span><span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">logos</span><span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> (</span><a href="https://en.wiktionary.org/wiki/%CE%BB%CF%8C%CE%B3%CE%BF%CF%82" style="text-decoration: none;"><span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">λόγος</span></a><span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">). At the start of John’s Gospel, where it says “In the beginning was the Word, and the Word was with God, and the Word was God”, the word translated as “Word” is </span><span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">logos</span><span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">. It’s also where the “-logy” in “biology” and “geology” comes from. It’s hard to translate into English, and it was already kind of slippery in Greek, which noted slippery character Heraclitus apparently took full advantage of.</span></div>
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<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Ostensibly Guthrie’s talking about this because he’s writing (and had been lecturing) for an audience of non-classicists, and he doesn’t want people who don’t read Greek to get misled by the translations. I suppose it’s quite likely that a modern reader would be liable to bring some conceptual baggage to the table even if they were able to read the original Greek, but the less Greek you’ve read the less likely you’ll be to have a feel for what they meant by these words. He wants you to understand the mindset of the Greek philosophers, and he does this, at least in part, by trying to explain what their words mean.</span></div>
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<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">It’s possible I was reading too much into it, but I kind of got the impression that casting this in terms of words was a result of the author being surrounded by British philosophers in the 1930s and 1940s. If the hip new thing is to think that philosophy is ultimately a matter of attending carefully to the meanings of words, then this is probably a smart way to present things. And of course Guthrie may have subscribed to some of this linguistic turn stuff himself too. I can vaguely recall linguistic-turn philosophers saying that while Plato, Descartes and the rest thought they were dealing with substantive non-linguistic questions they were really talking about the meanings of words, and as a result their insights can still have relevance to philosophy conceived as linguistic analysis. I wish I had an example of someone saying this for you, but I do not. </span><span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><i>[UPDATE 19/12/18: I found the thing I was vaguely recalling; it's in chapter two of Ayer [1936].] </i></span><span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Anyway, assuming they actually did say this, I kind of think they had a point except that it’s the other way round: linguistic-turn philosophers were still blundering around in much the same insight-space with much the same moves available to them as the people who came before and after, and casting their insights about causes and knowledge as insights about the words “cause” and “knowledge” doesn’t stop us using them. There’s probably a limit to how far you can take this kind of ecumenism, and some of the linguistic-turn stuff probably can trace its badness to its conception of what philosophy is. Some of it can probably trace its goodness to that too! But I think that a lot of the time it doesn’t really matter, and similarly it doesn’t really matter that Guthrie casts his discussion of the Greek philosophers’ ways of thinking in terms of the meanings of words. Just to be clear, he thinks those ways of thinking were pretty different from those of twentieth-century British people.</span></div>
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<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Another thing I thought was interesting was how he focused on the political environment. Here’s how he starts the first of two chapters on Plato:</span></div>
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<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-left: 36pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">We shall probably understand Plato’s philosophy best if we regard him as working in the first place under the influence of two related motives. He wished first of all to take up Socrates’s task at the point where Socrates had had to leave it, to consolidate his master’s teaching and defend it against inevitable questioning. But in this he was not acting solely from motives of personal affection or respect. It fitted in with his second motive, which was to defend, and to render worth defending, the idea of the city-state as an independent political, economic, and social unit. For it was by accepting and developing Socrates’s challenge to the Sophists that Plato thought this wider aim could be most successfully accomplished.</span></div>
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<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span class="Apple-tab-span" style="white-space: pre;"> </span></span><span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">The doom of the free city-state was sealed by the conquests of Philip and Alexander. It was these which assured that that compact unit of classical Greek life should be swamped by the growth of huge kingdoms on a semi-Oriental model. But they did no more than complete in drastic fashion a process of decline which had been going on for some time. (p.81)</span></div>
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<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">I was quite taken aback by this. Obviously Plato’s most famous work is called </span><span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">The Republic</span><span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">, and in it he lays out a way for a city state to be organized, and my understanding is that you’re supposed to think some of these ideas are pretty good. (I’m told it’s a sort of centrally planned natural aristocracy with philosophers running the show and a covert eugenics programme for good measure, although I blush to confess I haven’t actually read much of it.) But Plato also talks about a bunch of other things, even in </span><span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">The Republic </span><span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">itself, and I’d always been given the impression that his political ideas were a bit of an eccentric sideline, and largely independent of his much more important stuff about forms, knowledge, truth, the soul, the Euthyphro problem and so on. I was already aware that Plato’s interest in politics wasn’t entirely theoretical, and that he’d been very disappointed by the Athenian democracy that killed Socrates, and also affected by the situation with the Thirty Tyrants, about which I don’t know very much. But a person can be interested in more than one thing. Guthrie seems to think that Plato’s more purely philosophical stuff is largely in the service of his politics, and Guthrie wasn’t some kind of oddball as far as I can tell, so it’s interesting to see him saying something like that. But perhaps I’ve got the wrong end of the stick.</span></div>
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<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">The connection between politics and Plato’s less obviously political stuff is, according to Guthrie, related to the connection between religion and the state. They were, he says, closely bound together and in some ways identified. By Plato’s time the anthropomorphic paganism of Homer and Hesiod was getting challenged a lot, and the political order was getting challenged with it. The Sophists, who Plato wasn’t a fan of, were part of this. Plato wanted to find an alternative foundation for the political order, according to Guthrie, and that involved defending the idea of eternal principles of justice and a conception of the good life that would be best facilitated by city states, as long as they had plenty of central planning and a eugenics programme instead of this democracy nonsense that killed his buddy Socrates. Something like that, anyway. It makes a kind of sense, although I can't say I agree with Plato here.</span></div>
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<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">A related issue is something Guthrie says about the relationship between virtue and self-interest in ancient Greek philosophy. These days we draw a pretty sharp distinction between the two. People disagree about the extent of our moral obligations to go out of our way to help others, about how much someone’s being a bad person is an intrinsic harm to them, and about the extent to which virtue and vice are rewarded and punished after death. But we’ve still got two pretty separate concepts of doing what’s right and doing what’s best for yourself, even if we might think they line up pretty closely in practice.</span></div>
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<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Now, utilitarians these days often say that for well-off people in well-off countries morality is very demanding indeed, and that the moral life involves a level of self-sacrifice that most people don’t come anywhere near, even people we ordinarily think of as moral exemplars. Basically the idea is that people should give away practically all their disposable income to charities. Utilitarians disagree over which charities, but the consensus among them is that the charities will spend it better than you will, and that means you should hand it over. This may not have always been the case. When utilitarianism was invented there was a lot of poverty about, but there may well not have been as much an individual could achieve by throwing money at the problem, because there wasn’t the same charity infrastructure in place. The situation where the more money you give the fewer people will get malaria is new, and Peter Singer’s [1972] problem is a New Moral Problem. You could probably make a case that it existed before to an extent, but it probably wasn’t as pressing before.</span></div>
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<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">With this in mind, let’s look at what Guthrie says about the new socioeconomic realities of being an individual in a Greek city state:</span></div>
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<br />
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-left: 36pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">In early societies, where communities are small and cultural conditions simple, no conflict is observed between moral duty and self-interest. As Ritter [1933: <a href="https://www.blogger.com/null" title="In case you’re interested, Guthrie gave the page reference as page 67. I looked it up in a library copy of Ritter’s book to get the context. It wasn’t on page 67. Using the index and previews from Amazon and Google Books, I think I traced it to page 57. I can’t be quite sure because the Amazon preview didn’t include the particular page, the Google Books preview had no page numbers (I think this is to encourage academic libraries to still buy the books) and the library copy had pages 49-64 missing. It’s possible that Guthrie got the reference right and was using an edition with different pagination, but the library copy I had certainly looks like the same edition Guthrie would have been working from, although his copy presumably still had all its pages.">67 or 57?</a>] remarks: ‘He who in his relationship to his fellow men and the gods observes the existing customs is praised, respected and considered good; whereas he who breaks them is despised, disciplined and considered bad. In these conditions obedience to law brings gain to the individual, whereas transgression brings him harm. The individual who obeys customs and law is happy and contented.’</span></div>
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<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Unfortunately this simple state of affairs cannot last. The Greeks had reached the more complex state of civilization where it was forced on their attention that acts of banditry, especially on a large scale - the banditry of the conquering hero - which successfully defied law and custom, also brought gain, and that the law-abiding might be compelled to live in very modest cicumstances or even under oppression and persecution. Out of this arose the sophistic opposition of ‘nature’ to ‘law’, and the conception of ‘nature’s justice’ as not only different from man’s but something greater and finer. [pp101-2]</span></div>
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<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Now, I don’t want to get into debating the anthropology here, and Guthrie doesn’t really defend it. But the idea that there being any tension between morality and self-interest was once a New Moral Problem is interesting. Huge if true, I guess.</span></div>
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<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">I should probably clarify something here. Sometimes I’ve heard people saying that the ancient Greeks didn’t really distinguish virtue and self-interest, and they kind of rolled it all into one when they asked what the good life is, or how people should live. That’s not really what Guthrie’s saying. He’s not exactly saying the opposite either; it’s more that they were just beginning to develop concepts that could handle the distinction because political circumstances had only recently forced them to. Although Guthrie (and as far as I can tell, Ritter) also seem to say that Socrates and Plato argued that the divergence between virtue and self-interest was an illusion, that it was still in one’s interests to be virtuous, and that the illusion was created by the divergence of virtue (and thus self-interest) from doing what was immediately pleasant, and that where the Sophists had gone wrong was in identifying self-interest with immediate pleasure. They say Plato and Socrates say that when broadly enough conceived even pleasure can line up with virtue and self-interest, which I guess puts them in the same camp as the Epicureans, but not the </span><a href="https://plato.stanford.edu/entries/ethics-ancient/#6" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">Cyrenaics</span></a><span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">, who were more along the <a href="https://historyofphilosophy.net/cyrenaics" target="_blank" title="Peter Adamson's podcast about the Cyrenaics">instant-gratification</a> lines of Plato’s Socrates’s Sophist opponents.</span></div>
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<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">But the big take-away here is that the apparent divergence of virtue and self-interest may once have been a New Moral Problem.</span></div>
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<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Close to the end of the book, Guthrie says that “Aristotle’s philosophy represents the final flowering of Greek thought in its natural setting, the city-state” (p.160). The idea is that once the political organization changed the philosophy changed with it, and so it makes sense to end the book there. I suppose this doesn’t completely square with the idea that his six-volume magnum opus ended in the same place because its author didn’t live long enough to end it later, and maybe Guthrie was making a virtue out of necessity in the face of space constraints. But given the other stuff he’s said about the interaction between Greek philosophy and its political environment, it hasn’t just come out of nowhere. He does think that Greek city states produced a distinctive kind of philosophy. (In the preface to the sixth volume, when he knew that his health wouldn’t allow him to write any more of them, he describes finishing with Aristotle as a pity but doesn’t seem to think it a catastrophe, because there were plenty of books on the subsequent period anyway, that period’s philosophy wasn’t as good as Aristotle’s, and Aristotle was ‘both the last of the ancient and the first of the modern philosophers’ [1981: ix].)</span></div>
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<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">The other thing that leapt out at me was how Guthrie emphasized the continuity between Plato and Aristotle. According to the School of Athens Caricature, Plato is interested in transcendent, celestial stuff apprehended by reason, while Aristotle is interested in everyday, terrestrial stuff apprehended by the senses. There’s a temptation to take them as exemplars of the two sides of whatever debate we’re most interested in: empiricism vs rationalism, pluralism vs monism, steady-state vs big-bang, materialism vs dualism, nominalism vs, er, Platonism. But this is usually kind of anachronistic, and it doesn’t do justice to the amount Plato and Aristotle had in common.</span></div>
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<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Some people have gone the other way, and tried to make out that Plato and Aristotle were in agreement about everything important. This reached a bit of a highpoint with Iamblichus (c.245-c.325 CE), who apparently tried to make out that both of them were essentially just writing footnotes to Pythagoras. In the late second century, when Marcus Aurelius was establishing four chairs of philosophy in Athens, the chairs represented the four main schools: Stoic, Epicurean, Platonist and Aristotelian, which I guess means Platonism and Aristotelianism were still seen as separate then. But by somewhere in the third century, Aristotelians weren’t making an effort to distinguish themselves anymore:</span></div>
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<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Alexander [of Aphrodisias] was not the first but rather the last authentic interpreter of Aristotle. Although subsequent generations of commentators were profoundly influenced by Alexander, they were motivated by a very different exegetical ideal. Their primary aim was no longer to recover and preserve Aristotle’s thought for its own sake, but for the sake of finding agreement between Aristotle and Plato and presenting them as part of one and the same philosophical outlook. [Falcon 2017]</span></div>
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<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">(I was a bit puzzled by this, but it seems what happened was that in the third century a bunch of charismatic Platonists, especially Plotinus and Porphyry, convinced everyone that Platonism was the bee’s knees. They still wanted to use Aristotle though, because he’s so useful. (They didn’t call his logical works “The Tool” for nothing. </span><span style="color: #1a1a1a; font-family: "calibri"; font-size: 11pt; font-style: italic; vertical-align: baseline; white-space: pre-wrap;">[Update 20/9/17: I recently read [Smith 2017: §2] that while they didn’t call it “The Tool” (</span><span style="color: #1a1a1a; font-family: "calibri"; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;">Organon</span><span style="color: #1a1a1a; font-family: "calibri"; font-size: 11pt; font-style: italic; vertical-align: baseline; white-space: pre-wrap;">) for nothing, they also didn’t call it that because it was useful. They called it that to stick it to the Stoics. (Those aren’t Smith’s exact words.) The Stoics thought logic (which at the time included a lot of epistemology) was one of the three branches of philosophy (which at the time included a lot of stuff now counted as science), and the Aristotelians disagreed and thought logic (including epistemology) was just a tool used by philosophy (including a lot of science). Nowadays we tend to agree with the Stoics, but it’s still called the </span><span style="color: #1a1a1a; font-family: "calibri"; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;">Organon</span><span style="color: #1a1a1a; font-family: "calibri"; font-size: 11pt; font-style: italic; vertical-align: baseline; white-space: pre-wrap;">. Oh well.]</span><span style="font-family: "calibri"; font-size: 11pt; white-space: pre-wrap;">) Eventually Platonists solved the problem by writing a bunch of commentaries on Aristotle explaining how they were both basically on the same page, although this meant reading Aristotelian ideas into Plato as much as reading Platonist ideas into Aristotle. (Or in Iamblichus’ case, reading both into Pythagoras.) The resultant synthesis dominated philosophy in the West until the Renaissance, and had a pretty impressive run in the Middle East too. I was already kind of aware that something like this had happened, but I didn’t realize it had happened so quickly.)</span></div>
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<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Anyway, Guthrie doesn’t go to either of these extremes. He’s not interested in claiming that Plato had already anticipated all of Aristotle’s contributions; it seems that this kind of tosh had already gone out of fashion among serious scholars by Guthrie’s time. But he also isn’t interested in setting them up as two giants staking out the two main sides in a debate that the rest of us have been having ever since. And I think that’s kind of important. Even if you’re not going full bore with the School of Athens Caricature, you might think that the outlines of the big philosophical debates got laid out early on and the rest is just filling in the details. It’s refreshing to see that rejected, and a little challenging.</span></div>
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<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">He starts off the discussion of Aristotle by talking about his life, and he emphasizes how Aristotle spent twenty years at Plato’s Academy, that he studied Plato’s work a lot, and that when Plato died and Aristotle left Athens he took the hardcore Platonist Xenocrates with him. Moving from the circumstantial to the more substantive, he says:</span></div>
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<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Fundamentally he remained on the side of Plato and Socrates. As Cornford put it: ‘For all this reaction towards the standpoint of common sense and empirical fact, Aristotle could never cease to be a Platonist. His thought, no less than Plato’s, is governed by the idea of aspiration, inherited by his master from Socrates - the idea that the true cause or explanation of things is to be sought, not in the beginning, but in the end’ [Cornford 1932: 89-90].</span></div>
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<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span class="Apple-tab-span" style="white-space: pre;"> </span></span><span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">In other words, the question that both can and must be answered by philosophy is the question ‘Why?’ To answer the question ‘How?’ is not enough. To speak more strictly, we may say that the permanent legacy of Platonism to Aristotle was two-fold, though its two sides were intimately connected. What he took over and retained was:</span></div>
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<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span class="Apple-tab-span" style="white-space: pre;"> </span></span><span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">(i) the teleological point of view;</span></div>
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<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span class="Apple-tab-span" style="white-space: pre;"> </span></span><span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">(ii) the conviction that reality lies in form.</span></div>
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<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">He could not give up his sense of the supreme importance of form, with which, as we have now seen, it was natural for the Greeks to include function. To know the matter </span><span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">out of which</span><span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> a thing had come to be was only a secondary consideration… The definition then must describe the form </span><span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">into which</span><span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> it had grown. [p.126-7, his emphasis]</span></div>
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<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">It’s probably fair to say this is quite different from how a lot of metaphysics is done nowadays. Teleology is unfashionable except as metaphor surrounded by disclaimers. We love poking around in the fundamental constituents of reality out of which middle-sized things arise, and the forms of the middle-sized things themselves are often a bit of an afterthought if we talk about them at all. We’ll happily try to explain how intrinsic change is possible, but to try to explain </span><span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">what intrinsic change is for</span><span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> would seem decidedly weird to a lot of us. Guthrie’s take on Aristotle’s relationship with Plato reminded me of something Jonathan Schaffer said about the Quine-Carnap debate in meta-metaphysics:</span></div>
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<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Indeed, though the textbooks cast Quine and Carnap as opponents, Quine is better understood as an antimetaphysical ally of his mentor (c.f. Price 1997). </span><span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">The Quine-Carnap debate is an internecine debate between anti-metaphysical pragmatists </span><span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">(concerning the analytic/synthetic distinction, with implication for whether the locus of pragmatic evaluation is molecular or holistic). As Quine himself says: </span></div>
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<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Carnap maintains that ontological questions, ... are questions not of fact but of choosing a convenient conceptual scheme or framework for science; and with this I agree only if the same be conceded for every scientific hypothesis. [Quine 1966: 211]</span></div>
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<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">The Quinean view of the task and method of metaphysics remains dominant. Indeed, the contemporary landscape in meta-metaphysics may be described as featuring a central Quinean majority, amid a scattering of Carnapian dissidents. Few other positions are even on the map. [Schaffer 2009: 349-50, his emphasis]</span></div>
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<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Schaffer is actually suggesting that we get a bit more Aristotelian (and not because we had previously been overly Platonist), but that’s not why I was reminded of it. It’s more just the structural point: what might seem like the two main contenders in a grand debate over an eternal cosmic question may really be two versions of a view that historically has been fairly niche. Framed in this way, perhaps it’s no wonder the late ancient Platonists were able to find so much common ground between Plato and Aristotle. (If you’re interested in when the grand synthesis of Quinean and Carnapian meta-metaphysics is coming, Carrie Jenkins is in the vanguard, responding especially to work by Amie Thomasson [2007, 2010]. Jenkins calls the resultant view </span><span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Quinapianism</span><span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">. It involves the notion of a </span><span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">serious verbal dispute</span><span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> [Jenkins 2014]. The basic idea, as I understand it, is that it’s OK to justify metaphysical claims (such as </span><span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">if there are simples arranged baseballwise then there are baseballs</span><span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">) as being entailed by the way our concepts work, like Carnapians do, but that our concepts, and thus these entailments, are still subject to revision in the light of empirical investigation, as Quineans think everything is.)</span></div>
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<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">In summary, there were three categories of thing that struck me about Guthrie’s book. First, he’s keen to emphasise that the ancient Greeks had different ways of thinking about things than we do, and he discusses this in terms of the meanings of their words. Second, he plays up the influence of the city-state political structure on ancient Greek thought up to and including Aristotle. Third, he thinks it’s reasonable to describe Aristotle as a bit of a Platonist.</span></div>
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<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">There’s a unifying theme here: the ancient Greeks were a distinctive lot who were not like us, and this comes out in their philosophy. Now, often when we’re learning about a philosophical tradition we’re used to the people not being like us. When Westerners are taught about ancient Indian or Chinese philosophy, they expect to be presented with ideas that arise out of an unfamiliar mindset, and they expect to have to learn about the mindset to understand the ideas. We’re ready to find the similarities surprising and the differences exciting. I don’t think we tend to approach the Greeks the same way. We (by which I mean Westerners; I live in the UK) see ourselves as the Greeks’ intellectual heirs. Other influences on us are tributaries; ancient Greece is the source. We expect learning what Plato and Aristotle cared about to explain what we care about, not to challenge it. We think we’re coming from basically the same place, and this affects how we interpret them. We’re more prepared to find their ideas coming naturally to us, and we’re less curious and less charitable when they don’t. To an extent this attitude probably makes sense. There really is more Plato than Confucius in Western philosophy as it’s done today. But if you’re serious about engaging with ancient Greek philosophy, you should still expect a culture shock.</span></div>
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<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">References</span></div>
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<li dir="ltr" style="background-color: transparent; color: #1a1a1a; font-family: Calibri; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; color: #333333; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: "Open Sans", sans-serif; font-size: 14px;">Ayer, A. J. (1936). </span><i style="box-sizing: border-box; font-family: "Open Sans", sans-serif; font-size: 14px;">Language, Truth and Logic</i><span style="font-family: "Open Sans", sans-serif; font-size: 14px;">. London: V. Gollancz.</span></span></div>
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<li dir="ltr" style="background-color: transparent; color: #1a1a1a; font-family: Calibri; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><span style="background-color: white; color: #333333; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span style="color: #333333; font-family: "calibri"; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline;">Cornford, Frances Macdonald (1932). </span><span style="color: #333333; font-family: "calibri"; font-size: 11pt; font-style: italic; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline;">Before and After Socrates</span><span style="color: #333333; font-family: "calibri"; font-size: 11pt; font-variant-east-asian: normal; font-variant-numeric: normal; vertical-align: baseline;">. Cambridge University Press.</span></span></li>
<li dir="ltr" style="background-color: transparent; color: #1a1a1a; font-family: Calibri; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: #1a1a1a; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Falcon, Andrea, "Commentators on Aristotle", </span><span style="background-color: transparent; color: #1a1a1a; font-family: "calibri"; font-size: 11pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">The Stanford Encyclopedia of Philosophy</span><span style="background-color: transparent; color: #1a1a1a; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> (Fall 2017 Edition), Edward N. Zalta (ed.), forthcoming URL = <</span><a href="https://plato.stanford.edu/archives/fall2017/entries/aristotle-commentators/" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">https://plato.stanford.edu/archives/fall2017/entries/aristotle-commentators/</span></a><span style="background-color: transparent; color: #1a1a1a; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">>.</span></div>
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<li dir="ltr" style="background-color: transparent; color: #1a1a1a; font-family: Calibri; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; color: #333333; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Guthrie, W. K. C. (1950). </span><span style="background-color: white; color: #333333; font-family: "calibri"; font-size: 11pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">The Greek Philosophers From Thales to Aristotle</span><span style="background-color: white; color: #333333; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">. Routledge. (Page references to 1962 Methuen reprint.)</span></div>
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<li dir="ltr" style="background-color: transparent; color: #1a1a1a; font-family: Calibri; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; color: #333333; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Guthrie, W. K. C. (1962-1981). </span><span style="background-color: white; color: #333333; font-family: "calibri"; font-size: 11pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">A History of Greek Philosophy</span><span style="background-color: white; color: #333333; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">. Six vols. Cambridge University Press.</span></div>
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<li dir="ltr" style="background-color: white; color: #333333; font-family: Calibri; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; color: #333333; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Guthrie, W. K. C. (1962). </span><span style="background-color: white; color: #333333; font-family: "calibri"; font-size: 11pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">A History of Greek Philosophy: Volume 1, the Earlier Presocratics and the Pythagoreans</span><span style="background-color: white; color: #333333; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">. Cambridge University Press.</span></div>
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<li dir="ltr" style="background-color: white; color: #333333; font-family: Calibri; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; color: #333333; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Guthrie, W. K. C. (1981). </span><span style="background-color: white; color: #333333; font-family: "calibri"; font-size: 11pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">A History of Greek Philosophy: Volume 6, Aristotle: An Encounter</span><span style="background-color: white; color: #333333; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">. Cambridge University Press.</span></div>
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<li dir="ltr" style="background-color: white; color: #333333; font-family: Calibri; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; color: #333333; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Jenkins, C. S. I. (2014). Serious Verbal Disputes: Ontology, Metaontology, and Analyticity. </span><span style="background-color: white; color: #333333; font-family: "calibri"; font-size: 11pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Journal of Philosophy</span><span style="background-color: white; color: #333333; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> 111 (9/10):454-469.</span></div>
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<li dir="ltr" style="background-color: transparent; color: #1a1a1a; font-family: Calibri; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; color: #333333; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Price, Huw (1997). Carnap, Quine, and the Fate of Metaphysics. </span><span style="background-color: white; color: #333333; font-family: "calibri"; font-size: 11pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Electronic Journal of Analytic Philosophy</span><span style="background-color: white; color: #333333; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> 5 (1).</span></div>
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<li dir="ltr" style="background-color: white; color: #333333; font-family: Calibri; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; color: #333333; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Quine, W. V. O. (1966). ‘‘On Carnap’s Views on Ontology’’, in </span><span style="background-color: white; color: #333333; font-family: "calibri"; font-size: 11pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">The Ways of Paradox and Other Essays</span><span style="background-color: white; color: #333333; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">: Harvard University Press. pp. 203–11.</span></div>
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<li dir="ltr" style="background-color: white; color: #333333; font-family: Calibri; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; color: #333333; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Ritter, Constantin (1933). </span><span style="background-color: white; color: #333333; font-family: "calibri"; font-size: 11pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">The Essence of Plato's Philosophy</span><span style="background-color: white; color: #333333; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">, Trans. R. A. Alles. London: Allen and Unwin.</span></div>
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<li dir="ltr" style="background-color: transparent; color: #1a1a1a; font-family: Calibri; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; color: #333333; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Schaffer, Jonathan (2009). On what grounds what. In David Manley, David J. Chalmers & Ryan Wasserman (eds.), </span><span style="background-color: white; color: #333333; font-family: "calibri"; font-size: 11pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Metametaphysics: New Essays on the Foundations of Ontology</span><span style="background-color: white; color: #333333; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">. Oxford University Press. pp. 347-383.</span></div>
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<li dir="ltr" style="background-color: white; color: #333333; font-family: Calibri; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; color: #333333; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Singer, Peter (1972). Famine, affluence, and morality. </span><span style="background-color: white; color: #333333; font-family: "calibri"; font-size: 11pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Philosophy and Public Affairs</span><span style="background-color: white; color: #333333; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> 1 (3):229-243</span></div>
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<li dir="ltr" style="background-color: white; color: #333333; font-family: Calibri; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><span style="background-color: white; color: #333333; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><span id="docs-internal-guid-37eefbaf-a3f5-937f-af11-00305e9ba3a9"><span style="background-color: transparent; color: #1a1a1a; font-family: "calibri"; font-size: 11pt; line-height: 1.7999999999999998; vertical-align: baseline;">Smith, Robin, "Aristotle's Logic", </span><span style="background-color: transparent; color: #1a1a1a; font-family: "calibri"; font-size: 11pt; font-style: italic; vertical-align: baseline;">The Stanford Encyclopedia of Philosophy </span><span style="background-color: transparent; color: #1a1a1a; font-family: "calibri"; font-size: 11pt; vertical-align: baseline;">(Spring 2017 Edition), Edward N. Zalta (ed.), URL = <</span><a href="https://plato.stanford.edu/archives/spr2017/entries/aristotle-logic/" style="text-decoration-line: none;"><span style="background-color: transparent; color: #1155cc; font-family: "calibri"; font-size: 11pt; vertical-align: baseline;">https://plato.stanford.edu/archives/spr2017/entries/aristotle-logic/</span></a><span style="background-color: transparent; color: #1a1a1a; font-family: "calibri"; font-size: 11pt; vertical-align: baseline;">>.</span></span></span></li>
<li dir="ltr" style="background-color: white; color: #333333; font-family: Calibri; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: white; color: #333333; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Thomasson, Amie L. (2007). </span><span style="background-color: white; color: #333333; font-family: "calibri"; font-size: 11pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Ordinary Objects</span><span style="background-color: white; color: #333333; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">. Oxford University Press.</span></div>
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<span style="background-color: white; color: #333333; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Thomasson, Amie L. (2010). The controversy over the existence of ordinary objects. </span><span style="background-color: white; color: #333333; font-family: "calibri"; font-size: 11pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Philosophy Compass</span><span style="background-color: white; color: #333333; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> 5 (7):591-601.</span></div>
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<br />Michael Bench-Caponhttp://www.blogger.com/profile/13715068990919309271noreply@blogger.com0tag:blogger.com,1999:blog-6411624366539130337.post-73812113716934288122017-09-10T10:15:00.001-07:002017-09-11T03:01:03.542-07:00Closing The Altruism Loophole<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "calibri"; font-size: 11pt; white-space: pre-wrap;">The prisoner’s dilemma is one of the best known puzzles in game theory. Here’s a version of it. </span></div>
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<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Two criminals, Alice and Betty, have been captured and imprisoned in separate cells. The guards want them to talk. If one talks and the other doesn’t, the talker goes free and the non-talker gets a long sentence. If both talk, both get mid-length sentences. If neither talks, both get short sentences. Alice and Betty only care about the lengths of their own sentences. Should they talk?</span></div>
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<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Whatever Alice does, Betty does better if she talks. Whatever Betty does, Alice does better if she talks. So if they’re acting self-interestedly, talking is a no-brainer. But both talking works out worse for each of them than neither talking. The point is that it seems self-interest alone should be able to get them from the both-talk situation to the neither-talk situation, because it’s better for both of them. But it also seems there’s no rational way for them make this happen. That’s the puzzle.</span></div>
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<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">One thing people sometimes suggest is that the solution is to be altruistic. The fact that if Alice talks and Betty doesn’t then Betty will get a longer sentence gives </span><span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Alice</span><span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> a reason not to talk, if she cares about Betty. In a way, people bringing this up is annoying. It’s either a misunderstanding of the problem or a refusal to engage with the problem. Part of the set-up is that Alice and Betty only care about the lengths of their own sentences. But on the other hand, the prisoner’s dilemma is supposed to be structurally similar to some real-life situations, and in real life people do care about each other, at least a bit. Also, we sometimes like to do experiments to see how people behave in real-life prisoner’s dilemma situations. If the prisoner’s dilemma has self-interested subjects and our test subjects are somewhat altruistic, as people tend to be, then we’re testing it wrong.</span></div>
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<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">There are at least three ways round the problem. One is to make Betty a less sympathetic character, who cares about something Alice doesn’t care about at all. One option I’ve heard is to make Betty a robot who only cares about increasing the number of paperclips in the world. Alice’s payoffs are money, and Betty’s payoffs are paperclips. But this introduces an asymmetry into the situation, and it also means we’re not dealing with two humans anymore; we’re dealing with a robot. And the robot doesn’t behave according to general principles of rationality; it behaves how we’ve programmed it to behave. If we can’t formulate a principle, we’ll struggle to program the robot to follow it. If we tell the robot to apply the dominance reasoning, it’ll talk. If we tell the robot to assume everyone picks the same option in symmetrical situations with no indistinguishable pairs of options, it won’t talk. (This principle is very close to what Wikipedia calls </span><span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><i><a href="https://en.wikipedia.org/wiki/Superrationality" target="_blank">superrationality</a></i>.)</span><span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> We don’t learn anything from this. It’d be better if we could test it with people.</span></div>
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<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">A second way to try to avoid the altruism loophole is to set the payoffs so the participants would have to be very altruistic for it to affect what they did.</span></div>
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<table style="border-collapse: collapse; border: none;"><colgroup><col width="65"></col><col width="86"></col><col width="138"></col><col width="143"></col></colgroup><tbody>
<tr style="height: 0pt;"><td style="border-bottom: solid #000000 1pt; border-left: solid #000000 1pt; border-right: solid #000000 1pt; border-top: solid #000000 1pt; padding: 5pt 5pt 5pt 5pt; vertical-align: top;"><br /></td><td style="border-bottom: solid #000000 1pt; border-left: solid #000000 1pt; border-right: solid #000000 1pt; border-top: solid #000000 1pt; padding: 5pt 5pt 5pt 5pt; vertical-align: top;"><br /></td><td style="border-bottom: solid #000000 1pt; border-left: solid #000000 1pt; border-right: solid #000000 1pt; border-top: solid #000000 1pt; padding: 5pt 5pt 5pt 5pt; vertical-align: top;"><div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Betty</span></div>
</td><td style="border-bottom: solid #000000 1pt; border-left: solid #000000 1pt; border-right: solid #000000 1pt; border-top: solid #000000 1pt; padding: 5pt 5pt 5pt 5pt; vertical-align: top;"><br /></td></tr>
<tr style="height: 0pt;"><td style="border-bottom: solid #000000 1pt; border-left: solid #000000 1pt; border-right: solid #000000 1pt; border-top: solid #000000 1pt; padding: 5pt 5pt 5pt 5pt; vertical-align: top;"><br /></td><td style="border-bottom: solid #000000 1pt; border-left: solid #000000 1pt; border-right: solid #000000 1pt; border-top: solid #000000 1pt; padding: 5pt 5pt 5pt 5pt; vertical-align: top;"><br /></td><td style="border-bottom: solid #000000 1pt; border-left: solid #000000 1pt; border-right: solid #000000 1pt; border-top: solid #000000 1pt; padding: 5pt 5pt 5pt 5pt; vertical-align: top;"><div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Talks</span></div>
</td><td style="border-bottom: solid #000000 1pt; border-left: solid #000000 1pt; border-right: solid #000000 1pt; border-top: solid #000000 1pt; padding: 5pt 5pt 5pt 5pt; vertical-align: top;"><div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Doesn’t talk</span></div>
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<tr style="height: 0pt;"><td style="border-bottom: solid #000000 1pt; border-left: solid #000000 1pt; border-right: solid #000000 1pt; border-top: solid #000000 1pt; padding: 5pt 5pt 5pt 5pt; vertical-align: top;"><div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Alice</span></div>
</td><td style="border-bottom: solid #000000 1pt; border-left: solid #000000 1pt; border-right: solid #000000 1pt; border-top: solid #000000 1pt; padding: 5pt 5pt 5pt 5pt; vertical-align: top;"><div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Talks</span></div>
</td><td style="border-bottom: solid #000000 1pt; border-left: solid #000000 1pt; border-right: solid #000000 1pt; border-top: solid #000000 1pt; padding: 5pt 5pt 5pt 5pt; vertical-align: top;"><div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Alice gets £2</span></div>
<div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Betty gets £2</span></div>
</td><td style="border-bottom: solid #000000 1pt; border-left: solid #000000 1pt; border-right: solid #000000 1pt; border-top: solid #000000 1pt; padding: 5pt 5pt 5pt 5pt; vertical-align: top;"><div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Alice gets £7</span></div>
<div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Betty gets nothing</span></div>
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<tr style="height: 0pt;"><td style="border-bottom: solid #000000 1pt; border-left: solid #000000 1pt; border-right: solid #000000 1pt; border-top: solid #000000 1pt; padding: 5pt 5pt 5pt 5pt; vertical-align: top;"><br /></td><td style="border-bottom: solid #000000 1pt; border-left: solid #000000 1pt; border-right: solid #000000 1pt; border-top: solid #000000 1pt; padding: 5pt 5pt 5pt 5pt; vertical-align: top;"><div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Doesn’t talk</span></div>
</td><td style="border-bottom: solid #000000 1pt; border-left: solid #000000 1pt; border-right: solid #000000 1pt; border-top: solid #000000 1pt; padding: 5pt 5pt 5pt 5pt; vertical-align: top;"><div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Alice gets nothing</span></div>
<div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Betty gets £7</span></div>
</td><td style="border-bottom: solid #000000 1pt; border-left: solid #000000 1pt; border-right: solid #000000 1pt; border-top: solid #000000 1pt; padding: 5pt 5pt 5pt 5pt; vertical-align: top;"><div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Alice gets £3</span></div>
<div dir="ltr" style="line-height: 1.2; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Betty gets £3</span></div>
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<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Suppose Betty talks. By not talking Alice would give up her only £2 to get Betty an extra £5. That would be awfully nice of Alice. Supposing Betty doesn’t talk, by not talking Alice would give up an additional £4 so Betty could keep her £3. That seems rather nice of her too. If Alice truly loves Betty as she loves herself, she probably won’t talk however we set it up, or at least she won’t know which to do because she doesn’t know what Betty will do. (Since the total payoff in nobody-talks is higher than in both-talk, not talking must increase the total either when the other doesn’t talk, when they do, or both.) But most people don’t love the other participant as they love themselves, and fiddling with the payoffs can make it so that more altruism is needed not to talk.</span></div>
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<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">A third way is cleaner. I hadn’t heard it before, so when I came up with it I thought I’d tell you about it. The problem was that Alice might allow her behaviour to be affected by concern for what happens to Betty. To avoid this, we start by roping in three other people Alice cares about just as much as Betty (let’s just assume none of the participants know anything much about the others). There are four possible outcomes for Betty, so we </span><span style="font-family: "calibri"; font-size: 14.6667px; white-space: pre-wrap;">randomly</span><span style="font-family: "calibri"; font-size: 11pt; white-space: pre-wrap;"> divide up the three outcomes Betty avoids among the three other participants. Since Alice is indifferent between Betty, Bertha, Bernice and Belinda, she doesn’t care which prize goes to Betty as it’s still the same four prizes distributed among the same four people. The only variable left for Alice to care about it what happens to her. Similarly, we divide the outcomes Alice avoids among Althea, Annabel and Albertine, so Betty will be indifferent between outcomes except insofar as they affect Betty. Alice and Betty won’t keep quiet out of altruism now, and if they can’t think of another reason to keep quiet, they’ll end up both talking and wishing neither of them had.</span></div>
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<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">So, introducing the other people closes the altruism loophole. I guess it doesn’t close the </span><span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">justice</span><span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> loophole, if there is one. The problem there is that Alice might not talk because she is concerned that Betty might not either and she doesn’t want to punish Betty for doing her a favour. Or maybe Alice will think she has some special responsibility towards Betty as a fellow player. But at least we’ve closed the simplest version of the altruism loophole. If we haven’t tried testing the prisoner’s dilemma this way, I guess we should. Maybe we’ll get different results. Or maybe we’ll get results we’d previously attempted to explain through altruism, and we won’t be able to explain them away through altruism anymore. Of course, we may already be doing this. I don’t know. It's not my area.</span></div>
Michael Bench-Caponhttp://www.blogger.com/profile/13715068990919309271noreply@blogger.com0tag:blogger.com,1999:blog-6411624366539130337.post-73799748496158527562017-09-08T02:28:00.000-07:002017-10-16T16:03:59.283-07:00Reviewing Non-Fiction Is Hard<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Sometimes I read non-fiction books, and really enjoy them. “What an awesome book,” I’ll think. But it’s actually quite hard to tell if non-fiction books are any good or not. At least, it’s hard to tell just by reading them. I guess you could read a review. But someone has to write the reviews.</span></div>
<b id="docs-internal-guid-5873c737-60c4-c5a9-1805-d00d7ef4fc2a" style="font-weight: normal;"><br /></b>
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<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">The reason it’s hard is that you’ll usually be in one of two situations. Either you’ll be an expert in the topic the book is about, or you won’t be. Suppose you’re not, and so a lot of the stuff in the book is new to you. You don’t know if the book is any good or not, because you don’t know whether the stuff in the book is right or not. You can try factchecking it, but even if you can track down the sources they’ll often be buried in difficult academic writing of a sort you’re not really competent to understand. And if the book you’re reading is any good, a lot of what it’s telling you won’t be checkable facts, but rather a kind of expert insight and analysis that you wouldn’t be able to reconstruct yourself. And of course some books contain original research, in which case they can’t really be checked because in a way they </span><span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">are</span><span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> the source. These three all blur into each other, but they all make it very hard for a non-expert to tell if a non-fiction book is any good just by reading it. (And if we’re being strict about “just by reading it”, you’re not allowed to factcheck it anyway! But let’s not be strict. It's hard in any case.)</span></div>
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<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">A good example of this danger is Daniel Kahneman’s </span><span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Thinking, Fast and Slow</span><span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">. Kahneman is one of the world’s top psychologists, he did pioneering work on cognitive biases with Amos Tversky, and he won the economics Nobel "for having integrated insights from psychological research into economic science, especially concerning human judgment and decision-making under uncertainty". The book is about cognitive biases and decision-making under uncertainty, and the title refers to two styles of thought, one automatic and not very conscious and the other fairly carefully thought through and more conscious. It tells you about lots of cool little findings from psychological research, like how people are more likely to believe something they read if it’s written more legibly (pp62-3), and it integrates the anecdotes into a general narrative about the different ways people think.</span></div>
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<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">When that book came out, it was very well received by people who weren’t already experts on the topic. I vaguely remember experts being more divided on it, but I’m not an expert and I thought it was awesome. I was entertained by the anecdotes, and I really felt like I was learning something. I told my friends the anecdotes as if we could be confident that they were true, and I recommended the book to them. But since it came out, psychology has had a bit of an existential crisis based on the fact that lots of its little findings don’t replicate. A lot of effects people found may well have been flukes that only seemed representative of how people behave because when psychologists have done experiments and not found anything cool they haven’t told anyone about them. Or they have but nobody has listened, which makes them less likely to bother telling people next time. Kahneman himself is very concerned about the whole thing, and he thinks he was a bit too credulous about some of the stuff in the book.</span></div>
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<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Now, I don’t want to set Kahneman up as some kind of fall-guy here. It may still be a good book, and the issues with some of the anecdotes may be kind of minor. He’s still a great psychologist and communicator, he was writing in good faith, and his willingness to publicly address problems with his own work is impressive and an example to his colleagues. The point is that I wasn’t competent to judge how good his book was. And to be honest, I still couldn’t tell you.</span></div>
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<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">So, it’s hard to tell if a non-fiction book is good if you’re not already very familiar with the subject. Well, duh! But what if you are an expert? What if you could have written the book yourself? In that case you have a different problem: </span><span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><b>The Curse Of Knowledge</b></span><span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">. In his book </span><span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">The Sense of Style</span><span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">, Steven Pinker argues that the reason people often write badly is they struggle to imagine what it’s like not to know things that they in fact do know. You know what you want to say, but your reader has to try to work it out from what you’ve written, and it’s hard to put yourself into their mind and work out whether what you’ve written would still be clear. And if you’re trying to explain something you already understand but they don’t, you have to put yourself into their mind and work out whether they can understand the thing you’re trying to explain on the basis of what you’ve written. That’s hard too. Now, imagine you’re an expert reading a book by another expert on the same thing, and you’re trying to work out whether a non-expert will be able to understand the thing the book is about on the basis of what the book says. It’s not easy to do.</span></div>
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<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">So, who should be reviewing books, if both experts and novices face systematic obstacles? Three suggestions come to mind.</span></div>
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<li dir="ltr" style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 700; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Someone who is neither an expert nor a novice. </span><span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">What you want is someone who doesn’t already know what the book says, and so doesn’t have the curse of knowledge, but who’s competent enough in the sort of thing the book is about to be able to check if it’s right, once they’ve been told the things the book says. In general it’s often easier to check an answer to a question than find the answer. While I wasn’t competent to check if Kahneman’s book was any good, maybe a psychologist in a different field could have done it.</span></div>
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<li dir="ltr" style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 700; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">A great teacher. </span><span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">The curse of knowledge essentially arises because a certain kind of imaginative exercise is difficult. But some people seem to be quite good at it. Being good at it is part of the skillset of a great teacher: they need to be able to get into the minds of the students and tell whether what they’re saying would communicate the material to someone who wasn’t already familiar with it.</span></div>
</li>
<li dir="ltr" style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 700; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">A novice and an expert working together. </span><span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">The two problems are pretty separate, so in theory the expert ought to be able to read the book to check that what it says is sound, while the novice reads it to see if they feel like they’re learning something. And after they’ve both read it, the novice and the expert can talk to each other so the expert can check that the novice really did learn the things they felt like they were learning.</span></div>
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</ul>
<br />
<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "calibri"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">My favourite one is the last one. While an expert in an adjacent field might be able to do a decent job of factchecking, they won’t do as good a job as an expert, and it’ll be harder for them. Their transferable research skills will also mean they still have to do a bit of difficult imagining to get into the minds of the intended audience. A great teacher might be able to do the job, but we don’t even have enough great teachers to fill all the teaching jobs, let alone all the reviewing jobs as well. This leaves the last option. Unlike great teachers, experts are ten a penny, and novices are twenty a penny. Of course, you do need two people. But it’s still my favourite option, and it’s kind of odd that it practically never happens.</span></div>
Michael Bench-Caponhttp://www.blogger.com/profile/13715068990919309271noreply@blogger.com2tag:blogger.com,1999:blog-6411624366539130337.post-23274554334561749762017-08-01T07:51:00.000-07:002018-10-25T01:57:36.697-07:00Avicenna vs Turtles<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="font-family: Calibri; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">Anglophone metaphysicians, and perhaps some other metaphysicians too, fairly recently started thinking about things in terms of </span><span style="font-family: Calibri; font-size: 12pt; font-style: italic; vertical-align: baseline; white-space: pre-wrap;">ontological dependence</span><span style="font-family: Calibri; font-size: 12pt; vertical-align: baseline; white-space: pre-wrap;">. The idea is that some things depend on other things, or are grounded in those things; some facts are true in virtue of other facts, some things are fundamental while some things depend on the fundamental things, and so on. There’s a whole mess of concepts in the vicinity and we still haven’t sorted it all out, but it seemed like a useful way to think. It still does. I still think like that myself, sometimes.</span></div>
<b style="font-weight: normal;"><br /></b>
<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">One question you might ask about this framework is this:</span></div>
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<li dir="ltr" style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Must there be a funamental level? Couldn’t it just be turtles all the way down?</span></div>
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<b style="font-weight: normal;"><br /></b>
<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Ross Cameron addressed this question in a paper a few years ago (</span><a href="https://philpapers.org/rec/CAMTAT" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">Cameron 2008</span></a><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">). He basically came to the conclusion that he couldn’t find anything incoherent about everything being grounded in something further down, but it’s an inelegant set-up and we should expect the world not to be like that. When I’ve come across people citing his paper it has mostly been to agree with his conclusion, although this impression may be unrepresentative or at least out of date. I like the paper too, and I’m pretty sympathetic to his take on the issue: metaphysical systems don’t have to be incoherent to be implausible.</span></div>
<b style="font-weight: normal;"><br /></b>
<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Now, Cameron wasn’t the first person to think about this sort of thing. He mentions some predecessors in the paper, but today I’m going to talk about one he doesn’t mention. About a thousand years ago </span><a href="https://plato.stanford.edu/entries/ibn-sina/" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">Avicenna</span></a><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> was coming up with a proof of the existence of God, like you do, and his proof involved thinking about something structurally quite similar to the turtles question and coming to the opposite conclusion over whether there has to be something at the bottom. He thought the infinite descent scenario really was incoherent. Since one can count the people cleverer than Avicenna on the fingers of one hand, if he’s challenging our contemporary consensus we should probably take a look at what he had to say.</span></div>
<b style="font-weight: normal;"><br /></b>
<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">I’m not an Avicenna scholar, unfortunately. My knowledge of Avicenna comes mostly from </span><a href="http://historyofphilosophy.net/" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">a podcast</span></a><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> by one Avicenna scholar (Adamson 2010-, especially #138-142) and a book by another (McGinnis 2010). I’ve also read a few passages from Avicenna’s own work in translation, including one on the argument I’m talking about here (McGinnis and Reisman 2007, especially pp214-5). It’s not nothing, but you probably won’t find me trying to turn this blogpost into a paper. (But if you’re an Avicenna scholar and think there’s something here worth tackling properly together, I’m not busy.) You might wonder why I’m writing about it at all, given my incompetence to do the topic justice; it’s basically because it seemed like there was something there and nobody else seemed to be writing about it. Maybe that’s because the medieval-philosophy-in-Arabic crowd and the contemporary-analytic-metaphysics crowd don’t overlap much. Anyway, if you think I’m talking rubbish but not such irredeemable rubbish as not to be worth engaging with, we can have a discussion in the comments or wherever and try to understand the issue better.</span></div>
<b style="font-weight: normal;"><br /></b>
<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">So, here’s Avicenna’s argument as I understand it.</span></div>
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<li dir="ltr" style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">He’s got a distinction between things which are </span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">necessary through </span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">(or</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> in</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">)</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> themselves</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> and things which are </span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">necessary through another</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">. He’s not understanding necessity the same way philosophers do nowadays - possible worlds and all that - but I wouldn’t like to try to explain exactly how he is understanding it. It seems at least to be structurally a bit like something related to our contemporary concept of ontological dependence, though.</span></div>
</li>
<li dir="ltr" style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">He thinks that everything is either one or the other, and nothing is both. In terms of ontological dependence, you can think about things that depend on something else, and things that don’t.</span></div>
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<li dir="ltr" style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">He wants to show that at least one thing must be necessary in itself. He’s going to go on to argue that various things follow from something being necessary in itself, and that there can only be one such thing, and he’s going to say that this necessary existent is God. But for the moment he just wants to show that there’s at least one.</span></div>
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<li dir="ltr" style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">We know that something exists. Look around yourself, look within yourself, whatever. Something exists.</span></div>
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<li dir="ltr" style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Now gather everything together that is necessary through another. If there aren’t any such things, then since something exists, something must be necessary in itself. But if there are, then gather them together into one big object. (We should resist the temptation to call this object The Great Mumkin.)</span></div>
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<li dir="ltr" style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Is this object necessary in itself, or through another? If it’s necessary in itself, then we’re done. If not, then what is it necessary through? (I’ve seen this step presented in different ways, and Avicenna may have presented it himself in different ways. He actually thinks it’d be absurd for the sum of all things necessary through another to be necessary in itself, but it’s worth noting that we don’t have to agree about that for his argument to work.)</span></div>
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<li dir="ltr" style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">If it’s necessary through a part of itself, that’s either absurd or counts as the part being necessary through itself. (I’m not really sure how this step goes, and it seems to me that it’s where most of the action is.)</span></div>
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<li dir="ltr" style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">If it’s necessary through something that isn’t part of it, then that thing must be necessary in itself, because everything else is a part of it.</span></div>
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<li dir="ltr" style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">So whichever option we go for, something is necessary in itself.</span></div>
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</ol>
<b style="font-weight: normal;"><br /></b>
<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Now, I expect I’ve garbled the argument somewhere. The bit where we say that things can’t be necessary through a part of themselves seems especially dodgy. Here’s a worry: take the sum of everything that exists. Is that necessary in itself, or through another? If anything besides God exists, then it can’t be necessary in itself, at least according to Avicenna, because he` thinks only one thing is, and that thing is God and doesn’t have proper parts. But if it’s necessary through another, then that other thing must be a part of it, because everything is. But that’s not supposed to be allowed. So I don’t really get what’s going on there. (I guess he could say that in this case we choose the option at step 7 of the part being necessary in itself. But I do think I’m missing something here.)</span></div>
<b style="font-weight: normal;"><br /></b>
<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">One way of patching this is to say that everything is either necessary in itself, or is necessary through another, or is the sum of something necessary in itself and something necessary through another. (I’m using a pretty classical-mereology framework, because Avicenna seems to be. To call Avicenna a classical mereologist would be anachronistic by 900 years or so, but the argument helps itself to principles that are accepted by classical mereology but rejected in some non-classical mereologies. If classical mereology rules out turtles all the way down, that’s interesting in itself. Investigating which mereological principles are essential to the argument and which aren’t would be interesting too, and if the argument has something in it then it’s something we should do.) If we make this assumption, the argument still goes through much the same. You just include the mixed option in step six, and note that the mixed option also entails that something is necessary in itself. The sum of all things would be the sum of the Necessary Existent, which is necessary in itself, and Creation, which is necessary through another, viz. the Necessary Existent.</span></div>
<b style="font-weight: normal;"><br /></b>
<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">With different mereological assumptions you might also try constructing the sum-of-all-dependents object by removing everything necessary in itself and taking what’s left. That relies on a complementation principle you might want to reject (but which classical mereology accepts), but it’s worth noting the option. That object might not contain all dependents - if there’s a dependent object that is part of a necessary object, for example - but if it depends on something outside itself then something is outside it, and so something is necessary in itself because everything outside it is part of the sum of things necessary in themselves.</span></div>
<b style="font-weight: normal;"><br /></b>
<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Anyway, let’s adapt Avicenna’s argument to the question of whether everything might be dependent on something else. We’ll call things that are dependent on something else </span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">dependent</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">, and other things </span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">independent</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">. We’ll allow mixed cases, and assume classical mereology (though not atomicity - there could be </span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">gunky</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> things all of whose parts have proper parts).</span></div>
<ol style="margin-bottom: 0pt; margin-top: 0pt;">
<li dir="ltr" style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Something exists.</span></div>
</li>
<li dir="ltr" style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">If there are no dependent things, something is independent and we’re done. Otherwise take the sum of all dependent things.</span></div>
</li>
<li dir="ltr" style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">If it’s independent or mixed, we’re done. So assume it’s dependent. What’s it dependent on?</span></div>
</li>
<li dir="ltr" style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">If it’s dependent on something that isn’t part of it, that thing must be independent or mixed, and we’re done.</span></div>
</li>
<li dir="ltr" style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: decimal; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">If it’s dependent on something that is part of it, that’s either absurd or counts as it being independent or mixed. (This is the dodgy step.)</span></div>
</li>
</ol>
<b style="font-weight: normal;"><br /></b>
<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">In Cameron’s paper, he does sort of address a version of the summing-the-dependents objection, although not with particular reference to Avicenna. Let’s look at what he says:</span></div>
<b style="font-weight: normal;"><br /></b>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-left: 36pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Another potential justification for the intuition is familiar from the debate between Leibniz and Hume. Here, the thought is that if there could be an infinite chain of entities e</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 7.199999999999999pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: sub; white-space: pre-wrap;">1</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">, e</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 7.199999999999999pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: sub; white-space: pre-wrap;">2</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">, e</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 7.199999999999999pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: sub; white-space: pre-wrap;">3</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">, ... such that e</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 7.199999999999999pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: sub; white-space: pre-wrap;">1</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> is ontologically dependent on e</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 7.199999999999999pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: sub; white-space: pre-wrap;">2</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">, and e</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 7.199999999999999pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: sub; white-space: pre-wrap;">2</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> ontologically dependent on e</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 7.199999999999999pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: sub; white-space: pre-wrap;">3</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> etc, then, while every entity in the chain is grounded, nothing grounds the chain itself. Even if there needn’t be a first member of the chain – an independent entity that provides the ultimate ontological grounding for every member of the chain - there must be an ontologically independent entity to ground the existence of the chain itself. </span></div>
<b style="font-weight: normal;"><br /></b>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-left: 36pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">But that’s unconvincing. Grant for the sake of argument that not only must every being on the chain have an ontological grounding but the chain itself must have an ontological grounding. This doesn’t entail that anything is an independent entity. Perhaps the chain of entities e</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 7.199999999999999pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: sub; white-space: pre-wrap;">1</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">, e</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 7.199999999999999pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: sub; white-space: pre-wrap;">2</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">, e</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 7.199999999999999pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: sub; white-space: pre-wrap;">3</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">, ... depends on a further entity e</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 7.199999999999999pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: super; white-space: pre-wrap;">a</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 7.199999999999999pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: sub; white-space: pre-wrap;">1</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> which depends on e</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 7.199999999999999pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: super; white-space: pre-wrap;">a</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 7.199999999999999pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: sub; white-space: pre-wrap;">2</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">, which depends on e</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 7.199999999999999pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: super; white-space: pre-wrap;">a</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 7.199999999999999pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: sub; white-space: pre-wrap;">3</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> etc? And if someone asks “but what about the chain e</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 7.199999999999999pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: super; white-space: pre-wrap;">a</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 7.199999999999999pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: sub; white-space: pre-wrap;">1</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">, e</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 7.199999999999999pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: super; white-space: pre-wrap;">a</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 7.199999999999999pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: sub; white-space: pre-wrap;">2</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">, e</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 7.199999999999999pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: super; white-space: pre-wrap;">a</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 7.199999999999999pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: sub; white-space: pre-wrap;">3</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">...?” we can appeal to a new entity e</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 7.199999999999999pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: super; white-space: pre-wrap;">b</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 7.199999999999999pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: sub; white-space: pre-wrap;">1</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> which is the ontological ground of this new chain, and which depends on e</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 7.199999999999999pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: super; white-space: pre-wrap;">b</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 7.199999999999999pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: sub; white-space: pre-wrap;">2</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> which depends on e</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 7.199999999999999pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: super; white-space: pre-wrap;">b</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 7.199999999999999pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: sub; white-space: pre-wrap;">3</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> etc. And so on. In each case, the infinite chain of entities is dependent on an entity which is itself the first member of another infinite chain. Provided we’re prepared to postulate more and more entities, one for every cardinal number, then nothing will go ungrounded. (Cameron 2008: 11)</span></div>
<b style="font-weight: normal;"><br /></b>
<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">I don’t think this works against Avicenna’s version of the objection. The problem is that mereology isn’t like set theory. (The reference to “one for every cardinal number” is talking about the way set theory deals with this kind of thing.) In set theory you can’t just gather all the things of a certain kind into a set and ask questions about it. You get Russell’s paradox and others if you allow that. But in mereology you can gather all the dependents together into a sum and ask questions about it. You don’t get the paradoxes, and in fact accepting unrestricted mereological composition is fairly popular among people who work on the topic. (The difference basically arises because the set of all Xs can’t have members that aren’t Xs, but the sum of all Xs can have parts that aren’t Xs. For example, the sum of all cars has parts that are wheels, not cars.) Since mereology allows this kind of comprehension principle, it doesn’t help to postulate more and more entities as Cameron suggests. Anything you postulate will either be part of the sum-of-all-dependents already or won’t be a dependent. There are issues about infinite extensibility and unrestricted quantification which might apply here, but our understanding of that is much less settled than our understanding of set theory, and moving from </span><a href="http://ndpr.nd.edu/news/absolute-generality/" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">the difficulties of unrestricted quantification</span></a><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> to the impossibility of unrestricted composition is a leap that would need some heavy-duty justification. I think it’s fair to say that in light of Avicenna’s version of the argument, Cameron hasn’t really said enough here to fend off the objection.</span></div>
<b style="font-weight: normal;"><br /></b>
<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">So I guess bringing Avicenna into the debate wasn’t a complete waste of time. But might there be something else wrong with Avicenna’s argument? The argument looks pretty solid, at least given the assumptions about mereology, except for the step at the end. Why shouldn’t an object be dependent on something that’s part of it? There are a couple of structures we can imagine as challenges to Avicenna’s picture.</span></div>
<b style="font-weight: normal;"><br /></b>
<ul style="margin-bottom: 0pt; margin-top: 0pt;">
<li dir="ltr" style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Gunk</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">: everything is dependent on its proper parts taken together, and everything has proper parts. So everything is dependent on something.</span></div>
</li>
<li dir="ltr" style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: italic; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Turtles</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">: reality is made of the earth sitting on top of an infinite descending series of turtles. Everything is dependent on the sum of the things its parts depend on, and everything is dependent on any segment of the series unbounded below and wholly strictly lower than it, if any. So the earth is dependent on the sum of the turtles, the top turtle is dependent on the sum of the other turtles, and the whole of reality is dependent on the sum of the turtles but not on itself (since nothing depends on the earth), and the sum of the turtles is dependent on the sum of the turtles other than the top one. (There are some issues to go into about overdetermination, joint dependence and so on, but I think it should be possible to fill in these details in this general picture.)</span></div>
</li>
<ul style="margin-bottom: 0pt; margin-top: 0pt;">
<li dir="ltr" style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: circle; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">If you prefer, you can work with </span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Simple Turtles</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">: reality is a mereologically simple earth above a (not densely ordered) infinite descending series of mereologically simple turtles. Everything depends on the sum of everything strictly below its top part.</span></div>
</li>
</ul>
</ul>
<b style="font-weight: normal;"><br /></b>
<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">That wasn’t so hard. What was Avicenna thinking? Three possibilities come to mind:</span></div>
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<li dir="ltr" style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">He had a notion of necessity-in-itself which rules out these structures.</span></div>
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<li dir="ltr" style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">He had a notion which doesn’t rule out these structures but he didn’t think of them.</span></div>
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<li dir="ltr" style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">He had a notion which doesn’t rule out these structures but had other substantive commitments that do.</span></div>
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<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">All are prima facie plausible, though the second is uncharitable. Avicenna scholars will have views, but I’m not in a position to say what those views would be. But we can still think about how we should respond to these cases.</span></div>
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<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">It’s worth taking the gunk and turtle cases separately. With </span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">gunk</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> I think the best thing to do is just admit defeat if we’re allowing that things can depend on their proper parts. I think composition is identity, and things don’t depend on their parts: things </span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">are</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> their parts. (Gunk is a bit weird if composition is identity, but I don’t see that it’s incoherent. Indeed, I don’t see that you couldn’t have gunky pluralities even if composition isn’t identity. Regular readers will be familiar with gunky pluralities from </span><a href="http://michaelbenchcapon.blogspot.co.uk/2017/07/gunky-pluralities.html" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">the previous post</span></a><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">.) If you don’t think composition is identity - and if you’ve worked in the area then you probably don’t - then you might adopt some other substantive commitment linking mereology and dependence, like saying if an object depends on a part of x it depends on x, and so if things depended on their parts they would depend on themselves, which tends not to be allowed. But if you think things can depend on their parts, I guess you’re welcome to think the </span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">gunk</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> example undermines the Avicennan argument. (And Avicenna does seem to think things depend in some way on their proper parts, which is part of why the necessary existent can’t have proper parts. I definitely feel like I’m missing something.)</span></div>
<b style="font-weight: normal;"><br /></b>
<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">With </span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Turtles</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> and </span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Simple Turtles</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> there isn’t really a ready-made metaphysical thesis like composition as identity that I can wheel out to undermine the argument. So what can we say? Well, I don’t have a great answer, but I do think that even being able to ask the question moves the debate forward a bit in terms of where you can apply pressure. The problem Cameron had with turtles all the way down was that it’s theoretically uneconomical: you can’t have one base explaining everything, because the base needs a separate explanation, and so on forever. It’s inelegant. But now we have a different objection: </span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Turtles</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> isn’t just inelegant; it’s </span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">weird</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">. And where there’s weirdness, there might be Rationally Compelling Metaphysically Necessary Principles to rule it out. If you can think of one, feel free to put it in the comments.</span></div>
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<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">References:</span></div>
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<li dir="ltr" style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: white; color: #333333; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Adamson, Peter (2010-present): </span><span style="background-color: white; color: #333333; font-family: Calibri; font-size: 12pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">The History of Philosophy Without Any Gaps</span><span style="background-color: white; color: #333333; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">. Podcast. Historyofphilosophy.net.</span></div>
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<li dir="ltr" style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: white; color: #333333; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Cameron, Ross P. (2008). Turtles all the way down: Regress, priority and fundamentality. </span><span style="background-color: white; color: #333333; font-family: Calibri; font-size: 12pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Philosophical Quarterly</span><span style="background-color: white; color: #333333; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> 58 (230):1-14.</span></div>
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<li dir="ltr" style="background-color: white; color: #333333; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: white; color: #333333; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">McGinnis, Jon (2010). </span><span style="background-color: white; color: #333333; font-family: Calibri; font-size: 12pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Avicenna</span><span style="background-color: white; color: #333333; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">. Oxford University Press.</span></div>
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<li dir="ltr" style="background-color: white; color: #333333; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: white; color: #333333; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">McGinnis, Jon & Reisman, David C. (eds.) (2007). </span><span style="background-color: white; color: #333333; font-family: Calibri; font-size: 12pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Classical Arabic Philosophy: An Anthology of Sources</span><span style="background-color: white; color: #333333; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">. Hackett.</span></div>
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Michael Bench-Caponhttp://www.blogger.com/profile/13715068990919309271noreply@blogger.com2tag:blogger.com,1999:blog-6411624366539130337.post-10787953490074438132017-07-27T09:56:00.000-07:002018-10-30T03:38:17.057-07:00Gunky Pluralities<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="font-family: Calibri; font-size: 12pt; white-space: pre-wrap;">Philosophers have been squeezed out of most traditional areas of physics by fancy scientists with their “experiments” and their “research budgets”, but one thing they’ve managed to cling on to is mereology. We’ve even reclassified it as metaphysics so the physicists won’t accidentally stumble across it when looking for a book on something more important. Mereology is the theory of parts and wholes. Mereologists try to answer questions like these:</span></div>
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<li dir="ltr" style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Is there a great big object which all the other objects are parts of?</span></div>
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<li dir="ltr" style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">When x is a proper part of y, is there always another object z which is the rest of y?</span></div>
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<li dir="ltr" style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Does anything even have proper parts? (A proper part of x is a part of x that isn’t x itself.)</span></div>
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<li dir="ltr" style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Could there be two different objects made out of the same parts at the same time?</span></div>
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<li dir="ltr" style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Could there be something all of whose parts had multiple parts?</span></div>
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<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">The last question is about</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> gunk</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">. I wrote here </span><a href="http://michaelbenchcapon.blogspot.co.uk/2010/11/hume-vs-gunk.html" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">once before</span></a><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> about gunk, when describing an argument by David Hume against the possibility of gunk. You have to be a little bit careful when defining gunk, because what seem like equivalent definitions might not be equivalent if you accept some other exotic principles about parthood, or at least reject some mundane ones. One fairly careful definition of gunk would be “something all of whose parts have proper parts”, but that doesn’t really get at what we had in mind if we allow that things can be proper parts of each other.</span></div>
<b style="font-weight: normal;"><br /></b>
<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Now, parts and wholes aren’t the only game in town when it comes to gathering objects together. Somebody once told me that Bolzano identified like fifteen different ways of gathering objects together. Maybe it wasn’t fifteen, but I’m pretty sure it was a lot. Although perhaps this person was pulling my leg.</span></div>
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<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Anyway, one alternative to making a whole out of some objects is to make a plurality out of them. A broom is an object made of a brush and a handle. A brush and a handle are a plurality whose members are a brush and a handle. (Sets are different again; two things </span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><i>form</i> a set, but they <i>are </i>a plurality.)</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> Now, you might think that there’s no distinction here: a broom just is a brush and a handle. If that’s what you think then I’m actually on your side, but most people who work on this stuff don’t think that’s right. (One person who works on this stuff and thinks it </span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">is</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> right is <a href="http://www.uky.edu/~mwa229/" target="_blank">Meg Wallace</a>, of whose work on both this and other things I am a fan.) The mainstream view is that a broom can’t be a brush and a handle, because (apart from anything else) a broom is one thing and a brush and a handle are two things. Anyway, let’s make the distinction.</span></div>
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<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">It turns out that a lot of the candidate principles governing wholes and their parts are analogous to candidate principles governing pluralities and their subpluralities. Let’s say that Tom and Harry are </span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">among</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> Tom, Dick and Harry. Let’s also say that Tom is among Tom, Dick and Harry, and that Tom, Dick and Harry are among Tom, Dick and Harry, but not </span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">properly among</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> them. And let's allow that "some things, the xs, are F" can be true even if only one thing is F, so some things are (each!) Buzz Aldrin. Now we have a language in which to ask similar questions about pluralities and subpluralities to the ones we asked about parts and wholes.</span></div>
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<li dir="ltr" style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Are there some things, the xs, such that whenever there are some things they’re among the xs?</span></div>
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<li dir="ltr" style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">When the xs are properly among the ys, are there always some things, the zs, that are the rest of the ys?</span></div>
</li>
<li dir="ltr" style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Are any things properly among any other things?</span></div>
</li>
<li dir="ltr" style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Could there be some things, the xs and the ys, such that any things among the xs were also among the ys and vice versa, but the xs weren’t the ys?</span></div>
</li>
<li dir="ltr" style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Could there be some things, the xs, such that whenever some things the ys were among the xs there were some things, the zs, properly among the ys?</span></div>
</li>
</ul>
<b style="font-weight: normal;"><br /></b>
<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Call some xs that fit the definition in the last question a </span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">gunky plurality</span><span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">. Could you have gunky pluralities? Are they ridiculous? I asked Twitter if they were ridiculous, and the eight respondents were evenly split on the matter.</span></div>
<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><br /></span></div>
<table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody>
<tr><td style="text-align: center;"><img alt="Gunky pluralities twitter poll results.png" height="224" src="https://lh3.googleusercontent.com/_e-HT_qrDcP2T_Kq3vouKgpO0_CA1eIJM0iEgkLfwsXIxiXil7BDKvXzY39aMXabC_n9SNPzwet3XuK70evPe1QZp7396J-jiCQzV6Aq03JbXWbgdgmmhGmLKMda4zU5IVLjbNgT" style="border: none; margin-left: auto; margin-right: auto; transform: rotate(0rad);" width="541" /></td></tr>
<tr><td class="tr-caption" style="text-align: left;"><i>Am I an experimental philosopher yet?</i></td></tr>
</tbody></table>
<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><br /></span></div>
<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">I was a little bit surprised. I think gunky pluralities are coherent, but in the past I’ve never detected much enthusiasm for them. While a Twitter poll with eight respondents doesn’t give much of an indication of the frequency of a position among any population apart from the people who responded to it, I was quite surprised to see that four people, not including me, saw the tweet who don’t think gunky pluralities are ridiculous. Maybe they didn’t understand the question. I did phrase it in terms of membership instead of in terms of amongness, but if anything I’d expect that to make the position seem more ridiculous, not less.</span></div>
<b style="font-weight: normal;"><br /></b>
<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Now, I’m invested in gunky pluralities being coherent because I think composition’s identity and amongness is parthood, and so if gunky pluralities are incoherent then gunk is incoherent, and nobody wants to be committed to that. (Someone with a fancy research budget might come along and make a fool of you.) But even if you don’t think composition’s identity, and I suppose even if you don’t think merelogical gunk is possible, you can still make sense of the question about gunky pluralities. Are they ridiculous or aren’t they?</span></div>
<b style="font-weight: normal;"><br /></b>
<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">I think that Hume and Leibniz probably took the view that they were ridiculous. Hume may well have been thinking only about mereological gunk, and I’m pretty sure Leibniz was, but it would have been kind of weird to endorse their arguments for the mereological case and not the analogous arguments for the pluralities case. It’s possible of course that they didn’t really see a distinction, Bolzano not having arrived on the scene until the following century. Hume credited his argument to a Monsieur Malezieu, who I guess is probably <a href="https://en.wikipedia.org/wiki/Nicolas_de_Mal%C3%A9zieu" target="_blank">this guy</a>, although his English Wikipedia article could use some work and his French one doesn't mention Hume. Here are some quotes for you:</span></div>
<b style="font-weight: normal;"><br /></b>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-left: 36pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">It is evident, that existence in itself belongs only to unity, and is never applicable to number, but on account of the unites, of which the number is composed. Twenty men may be said to exist; but it is only because one, two, three, four, &c. are existent, and if you deny the existence of the latter, that of the former falls of course. It is therefore utterly absurd to suppose any number to exist, and yet deny the existence of unites; [...]</span></div>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-left: 36pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">But the unity, which can exist alone, and whose existence is necessary to that of all number, is of another kind, and must be perfectly indivisible, and incapable of being resolved into any lesser unity. </span><a href="http://www.gutenberg.org/files/4705/4705-h/4705-h.htm#link2H_4_0015" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">(Hume, </span><span style="background-color: transparent; color: #1155cc; font-family: Calibri; font-size: 12pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">Treatise on Human Nature</span><span style="background-color: transparent; color: #1155cc; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">, 1.2.2)</span></a></div>
<b style="font-weight: normal;"><br /></b>
<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-left: 36pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">And there must be simple substances, since there are compounds; for a compound is nothing but a collection or aggregatum of simple things. </span><a href="http://philosophy.eserver.org/leibniz-monadology.txt" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">(Leibniz, </span><span style="background-color: transparent; color: #1155cc; font-family: Calibri; font-size: 12pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">Monadology</span><span style="background-color: transparent; color: #1155cc; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;">, translated by Robert Latta, proposition 2)</span></a></div>
<b style="font-weight: normal;"><br /></b><br />
<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Calibri; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">It’s also true that our language gets a bit strained when we try to talk in a way that never presupposes that the thing we’re referring to is just one thing. You’ll have noticed that when I was trying to do it earlier. On the other hand, there doesn’t seem to be any reason you can’t construct a logic that can accommodate gunky pluralities. You might struggle to get a model theory in terms of sets that didn’t make a certain kind of person a bit grumpy, but this kind of person is already grumpy about variable-domain model theory for modal logic, so you’ll be in good company. (It may be that their grumpiness is warranted, but my impression is that even if the objection in the case of modal logic succeeds, the analogous objection would be question-begging in the case of gunky pluralities. But I’m pretty open to being wrong about that.) One possibility is that the idea of gunky pluralities is one of those things that’s ridiculous without being incoherent. I don’t really get what the problem is supposed to be, though. If you think they’re ridiculous, and it seems at least four of you do, let me know why in the comments!</span></div>
Michael Bench-Caponhttp://www.blogger.com/profile/13715068990919309271noreply@blogger.com0tag:blogger.com,1999:blog-6411624366539130337.post-14463841961830597392017-07-23T11:32:00.000-07:002017-08-11T03:10:33.874-07:00Four Ways To Misuse Words<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "arial"; font-size: 11pt; white-space: pre-wrap;">There are lots of ways to misuse words. Today I’m only going to talk about four. I’m interested in the situation that occasionally arises with emotionally or politically charged terms. It’s been happening for a long time with “terrorist”, we all watched it happen over the last year or two with “fake news”, and yesterday I heard someone say that it’s happening with “gaslighting”, although I haven’t noticed that one myself. Sometimes people talk about the phenomenon by saying “when people say [word] what they really mean is [concept]”. Here the concept is not what you’d expect a dictionary to say the word meant; it’s the concept that applies to the things these people in fact apply the word to. For example:</span></div>
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<li dir="ltr" style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">‘When people say “terrorist” what they really mean is “enemy combatant”.’</span></div>
</li>
<li dir="ltr" style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">‘When people say “fake news” what they really mean is “news unfavourable to me”.’</span></div>
</li>
<li dir="ltr" style="background-color: transparent; color: black; font-family: Arial; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">‘When people say “gaslighting” what they really mean is “saying things I don’t agree with”.’</span></div>
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</ul>
<b style="font-weight: normal;"><br /></b>
<br />
<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">I don’t think this is usually the best way of putting it, and I think it obscures the distinction between at least four ways of misusing words.</span></div>
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<br />
<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Ignorance:</span><span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> The word conventionally means one thing, but I use it to mean something else, because I’m mistaken about the convention. For example, if I thought that “cat” meant what “octopus” means, and so I said “cats live underwater and have eight tentacles”. Or I might think that “fake news” meant what “untrue news” means, and use the term “fake news” to describe any news story I don’t think is true.</span></div>
<b style="font-weight: normal;"><br /></b>
<br />
<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Lying:</span><span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> I know what concept the word conventionally expresses, but I use it for things that concept doesn’t apply to because I want to mislead people. For example, I might want people to think that cats live underwater and have eight tentacles, and so I’d say “cats live underwater and have eight tentacles”. Or a news story might come out which wasn’t favourable to me, and so I’d mislead people into thinking it was deliberately made up by saying “that’s fake news”.</span></div>
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<br />
<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Bullshit:</span><span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> I don’t really care what the word means, and I may not know what it means, but I do think that it’d be rhetorically advantageous to apply the word to it so I go ahead and do it. For example, I might have heard people calling stories “fake news” and getting some rhetorical mileage out of it, so I call stories I don’t like “fake news” as well.</span></div>
<b style="font-weight: normal;"><br /></b>
<br />
<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 700; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Inflation/Defining Down: </span><span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">I know that using the word for something stretches the conventions governing the word without necessarily breaking them, but I use the word anyway because I want people to categorize it with the central cases. For example, I might refer to something as fake news when it was really a result of a combination of sloppy reporting and wishful thinking, because I want people to lump the reporter in with people who deliberately make stories up.</span></div>
<b style="font-weight: normal;"><br /></b>
<br />
<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">There’s probably some overlap here, and one kind of use might shade into another. But I think only the first one is properly a case of using a word when what you really mean is something else. Maybe, when people say “when people say X they just mean Y” they’re usually being metaphorical and just mean “when people say X </span><span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">it</span><span style="background-color: transparent; color: black; font-family: "arial"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> just means Y”. But maybe not. And there’s a difference between what someone means by a word and what you can infer from the fact they’re using the word. I don’t think people who talk this way always have that distinction clearly in mind. It’s a pretty fuzzy distinction in a lot of cases, so that’d be understandable, but the distinction’s there. I think in at least some cases this is part of the irksome tendency on the part of a certain kind of person to attribute all the ills of the world to the imprecise use of language.</span></div>
Michael Bench-Caponhttp://www.blogger.com/profile/13715068990919309271noreply@blogger.com0tag:blogger.com,1999:blog-6411624366539130337.post-81762478408967830542017-07-15T00:40:00.000-07:002017-07-15T00:40:21.215-07:00A Load Of Rubbish<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="font-family: Cambria; font-size: 12pt; white-space: pre-wrap;">A crash of rhinos. A parliament of owls. I’m not above leafing through a book of miscellaneous lists once in a while, and such books occasionally have a list of collective nouns. I’ve got views about collective nouns.</span></div>
<b style="font-weight: normal;"><br /></b>
<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Cambria; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Sometimes a collective noun will have become a word in one of the normal ways, and it will be used when people aren’t actually talking about collective nouns, and competence in speaking the language involves knowing what it’s used for. A certain kind of social grouping among lions is called a pride, and a different kind of grouping among ants is called a colony. If you call the lions a colony and the ants a pride then you’re making a linguistic mistake. I’m not sure exactly what kind of mistake it is. I think it’s probably a worse mistake than if you talked about a swarm of sheep or a flock of bees. It’s more or less just unidiomatic to talk about a swarm of sheep, but an ant colony really isn’t a pride. Maybe I’m being too harsh or not harsh enough on one of these kinds of mistake, but the point is that they’re mistakes. You’re flouting the conventions internalized by competent language users if you talk about a pride of ants, unless something very odd is going on.</span></div>
<b style="font-weight: normal;"><br /></b>
<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Cambria; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Anyway, that’s not what a lot of collective nouns are like. Basically what happens is this. People know that there are collective nouns for some things, like lions, ants and bees. Glossing over the fact that a pride of lions isn’t just any old group of lions gathered into the same place at the same time, they notice that lots of things don’t have collective nouns. So they make them up. They make suggestions that are supposed to be fitting or satirical or simply euphonious, and congratulate each other when someone comes up with a good one. It’s a parlour game. As an extension of the parlour game, people will sometimes propose more or less comprehensive lists of the things. They don’t usually catch on, of course. The parlour game produces proposals for established usages, not established usages. Perhaps “murder of crows” is one that caught on. But usually they don’t catch on.</span></div>
<b style="font-weight: normal;"><br /></b>
<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Cambria; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Now, part of the parlour game is that it begins with someone asking “what’s the collective noun for a group of lions/larks/ostriches?” If it was lions, someone could rightly say “a pride of lions”, and they’d be right. That </span><span style="background-color: transparent; color: black; font-family: Cambria; font-size: 12pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">is</span><span style="background-color: transparent; color: black; font-family: Cambria; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> the established word for a kind of group of lions. You only move to phase two of the parlour game, where people make proposals, if you can’t come up with an answer at phase one. And one thing you might do in phase one is try to look it up. To meet this need, people make lists and put them in the kind of miscellany books I talked about at the beginning of the post. Now, a scrupulous listmaker would do what lexicographers do: look at established usage and see if there is a collective noun being used for a group of ostriches. If there used to be but it’s out of fashion, they’ll let you know it’s archaic or worse. And if there’s never been an established term for a group of ostriches, they don’t put one in the list. Alternatively, the listmaker could piggy-back on the efforts of a scrupulous lexicographer by looking through a dictionary written by one.</span></div>
<b style="font-weight: normal;"><br /></b>
<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Cambria; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">But our listmakers are not scrupulous. They want a nice long list with nice funny entries. </span><span style="background-color: transparent; color: black; font-family: Cambria; font-size: 12pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Unfamiliar</span><span style="background-color: transparent; color: black; font-family: Cambria; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> entries. So instead of looking at established usage or the records of it found in dictionaries, they copy the lists of proposals made by people who wanted to play the parlour game but had no friends to play it with. I once heard that there was a vogue at one point for sending such lists to magazines, though I don’t know if this is true. So now we have two kinds of lists. Lists of proposals which someone might send in to a magazine as an extension of a parlour game, and the </span><span style="background-color: transparent; color: black; font-family: Cambria; font-size: 12pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">plagiarized lists of lies</span><span style="background-color: transparent; color: black; font-family: Cambria; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> that turn up in miscellany books.</span></div>
<b style="font-weight: normal;"><br /></b>
<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Cambria; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Now, I know what you’re thinking. We’re all descriptivists now, and in the case of language, when a lie is repeated often enough it becomes the truth. I don’t know if that’s what we ought to say or not. So in the interests of science, I’ll look up “parliament”, “crash” and “exaltation” in the OED, to see if they give a usage meaning a group of owls, rhinos or larks respectively. I’m excited!</span></div>
<b style="font-weight: normal;"><br /></b>
<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Cambria; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Parliament: it does mention “a parliament of owls” as an example of this extended usage:</span></div>
<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Cambria; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><img alt="Parliament definition owls OED.png" height="121" src="https://lh5.googleusercontent.com/AXa02L5G8yK7ftweBHE_O2wtrrTZPDDK9zaeuXyFeY9uMcw2yGn0IzyQrRCFlTeDKsJk3XAvc13Ypz_mfNUNnuEmCmHRcvxU8gPfe5LFqGZyzFZ9f46gD9MVmIriaeW3mEa8nd7i" style="border: none; transform: rotate(0rad);" title="" width="640" /></span></div>
<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Cambria; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">The usage of “a parliament of owls” they give is from a book called </span><span style="background-color: transparent; color: black; font-family: Cambria; font-size: 12pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">An Exaltation of Larks</span><span style="background-color: transparent; color: black; font-family: Cambria; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> by James Lipton, which is of course a book about collective nouns. (There may be nothing objectionable about the book. I haven’t read it, and as you can see I don’t have a problem with all instances of people writing about collective nouns.) Note that in the definition the OED gives there’s nothing that makes “parliament” any more appropriate to owls than to larks, and it’s less appropriate to either than to rooks, which the lists invariably say come in murders.</span></div>
<b style="font-weight: normal;"><br /></b>
<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Cambria; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Crash: the entry doesn’t mention rhinos at all.</span></div>
<b style="font-weight: normal;"><br /></b>
<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Cambria; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Exaltation: here’s the screenshot so you can judge for yourself:</span></div>
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<span style="background-color: transparent; color: black; font-family: Cambria; font-size: 12pt; font-style: normal; font-variant-caps: normal; font-variant-ligatures: normal; font-weight: 400; margin-left: 1em; margin-right: 1em; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><img alt="Exaltation larks definition OED.png" height="126" src="https://lh5.googleusercontent.com/2oNNrHx_c98LkBDzMJb_IkAw-croULFAnQBIhic5PhBKU5PoBtxi1m_TMkaqV8D4yc-u0dFcse6l860X1ujLCgKwviyww9oZdpsQBl16F-sFxftmv4nvuonJEBKJOUN0C_kwPOar" style="border: none; transform: rotate(0rad);" width="640" /></span></div>
<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
</div>
<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Cambria; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">I too can judge for myself, and I’d point out that the OED’s authors have not found any usages which were clearly not in the context of discussing collective nouns, and they also appear to think that the established way of referring to such a group of larks is as a </span><span style="background-color: transparent; color: black; font-family: Cambria; font-size: 12pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">flight</span><span style="background-color: transparent; color: black; font-family: Cambria; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">. But of course </span><span style="background-color: transparent; color: black; font-family: Cambria; font-size: 12pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">A Flight Of Larks</span><span style="background-color: transparent; color: black; font-family: Cambria; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> would not have been a good title for James Lipton’s book.</span></div>
<b style="font-weight: normal;"><br /></b>
<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Cambria; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">(The entry for “pride”, of course, has a definition as “</span><span style="background-color: transparent; color: #333333; font-family: Cambria; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">A group of lions forming a social unit,” and gives several examples of it being used outside the context of discussing collective nouns. It says it’s an extended usage, but that’s probably accurate.)</span></div>
<b style="font-weight: normal;"><br /></b>
<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Cambria; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">So the scrupulous lexicographers at the OED present us with a bit of a mixed bag. A parliament can be a group of birds but isn’t specific to owls. A crash of rhinos isn’t a thing. An exaltation of larks is a thing but not to my mind a very honourable one, though your mileage may vary.</span></div>
<b style="font-weight: normal;"><br /></b>
<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt; text-align: justify;">
<span style="background-color: transparent; color: black; font-family: Cambria; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Now, up until recently I had the very negative attitude towards this whole collective noun nonsense that astute readers will have detected in the foregoing. However, the other day I saw some medievalists playing the parlour game on Twitter - they were still on a high from a conference in Leeds, where I live, and wanted a collective noun for medievalists - and I must say it seemed like fairly harmless fun. So I don’t know what to think. I guess if all you’re doing is making suggestions, that’s fine. And if you make a really good suggestion at the right time, say you’re at a medievalist conference and you think of a good one for a group of medievalists, then it might end up as an established term like “pride” or “colony”. That's fine too. But don’t make lists of lies, and certainly don’t go correcting someone when they call a group of rhinos a colloquium just because you read somewhere that we’re supposed to call it a crash.</span></div>
Michael Bench-Caponhttp://www.blogger.com/profile/13715068990919309271noreply@blogger.com3tag:blogger.com,1999:blog-6411624366539130337.post-50965781701440523542017-05-21T05:29:00.000-07:002017-06-02T07:53:57.431-07:00Bad Deal Or No Deal<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "verdana"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Consider these two statements:</span></div>
<ul style="margin-bottom: 0pt; margin-top: 0pt;">
<li dir="ltr" style="background-color: transparent; color: black; font-family: Verdana; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "verdana"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Eating no bread is better than eating any mouldy bread.</span></div>
</li>
<li dir="ltr" style="background-color: transparent; color: black; font-family: Verdana; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "verdana"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Any bread at least as good to eat as no bread is not mouldy.</span></div>
</li>
</ul>
<b id="docs-internal-guid-3c4ee276-2af9-8ecf-7d85-564efd7105e3" style="font-weight: normal;"><br /></b>
<br />
<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "verdana"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">To avoid ambiguity, let’s put them into Mickey Mouse first order logic:</span></div>
<ul style="margin-bottom: 0pt; margin-top: 0pt;">
<li dir="ltr" style="background-color: transparent; color: black; font-family: Verdana; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "verdana"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">(x)[[Mouldy(x) & Bread(x)] → Better(eatingNoBread,eating(x))]</span></div>
</li>
<li dir="ltr" style="background-color: transparent; color: black; font-family: Verdana; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "verdana"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">(x)[[Bread(x) & ¬Better(eatingNoBread,eating(x))] → ¬Mouldy(x)]</span></div>
</li>
</ul>
<b style="font-weight: normal;"><br /></b>
<br />
<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "verdana"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">The two formulations are equivalent: they are both false iff there is some mouldy bread the eating of which is no worse than eating nothing. But there’s a difference of emphasis. The first formulation is something you might say if you were taking an uncompromising line on bread: if mouldy bead is all there is, you’d rather have nothing. The second formulation is something you might say if you were taking a compromising line on mouldiness: it can’t be mouldy or you wouldn’t recommend eating it at all. But a difference in emphasis is not a difference in commitment. Asserting either commits you to the same things.</span></div>
<b style="font-weight: normal;"><br /></b>
<br />
<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "verdana"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Now, the government’s line on the Brexit negotiations is apparently that no deal is better than a bad deal. People take this as meaning that they’re taking an uncompromising line on deals, and they take it to embody an attitude of cavalier intransigence. But consider these two statements:</span></div>
<ul style="margin-bottom: 0pt; margin-top: 0pt;">
<li dir="ltr" style="background-color: transparent; color: black; font-family: Verdana; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "verdana"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Reaching no deal is better than reaching any bad deal.</span></div>
</li>
<li dir="ltr" style="background-color: transparent; color: black; font-family: Verdana; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "verdana"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Any deal at least as good as no deal is not bad.</span></div>
</li>
</ul>
<b style="font-weight: normal;"><br /></b>
<br />
<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "verdana"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">And in MMFOL:</span></div>
<ul style="margin-bottom: 0pt; margin-top: 0pt;">
<li dir="ltr" style="background-color: transparent; color: black; font-family: Verdana; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "verdana"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">(x)[[Bad(x) & Deal(x)] → Better(reachingNoDeal,reaching(x))]</span></div>
</li>
<li dir="ltr" style="background-color: transparent; color: black; font-family: Verdana; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; list-style-type: disc; text-decoration: none; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "verdana"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">(x)[[Deal(x) & ¬Better(reachingNoDeal,reaching(x))] → ¬Bad(x)]</span></div>
</li>
</ul>
<b style="font-weight: normal;"><br /></b>
<br />
<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "verdana"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">The second formulation seems to embody an attitude of roundheaded compromise. Don’t criticize this underwhelming deal, they say, because it’s better than nothing. But the two formulations are formulations of the same commitment. In the mouldy bread case the speaker enjoys a certain amount of latitude because of whatever vagueness and subjectivity there is in the word “mouldy”. In the Brexit case the speaker enjoys latitude because of whatever vagueness and subjectivity there is in the word “bad”. </span></div>
<b style="font-weight: normal;"><br /></b>
<br />
<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "verdana"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Now with the mouldy bread case, the speaker is at least committing themselves to something. That’s because some bread is determinately mouldy. Suppose the only food available is determinately mouldy bread, and you say that eating no bread is better than eating any mouldy bread. Half the party eats the bread, against your advice, and half the party goes hungry. One half has a better time and you are open to praise or criticism as a result. </span></div>
<b style="font-weight: normal;"><br /></b>
<br />
<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "verdana"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Now consider the Brexit case. While we don’t have a whole party to divide up into people taking your advice and people not taking it, we can still compare the actual world with our dimly assigned probability distributions over the space of counterfactual situations. But the government can always evade criticism, whatever consensus history arrives at on the relative merits of no deal and the available deals. Obviously the government are also the people taking the decision, unless they lose the election, and so they could be open to criticism for taking one option if history judges that other available options would have turned out better. There’s no escaping that. But the particular claim that no deal is worse than a bad deal is entirely hedged.</span></div>
<b style="font-weight: normal;"><br /></b>
<br />
<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "verdana"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Take any deal you like. If we decide that it’s worse than no deal, the government says it’s bad and takes the credit for being right. If we decide that it’s better than no deal, the government can just say that it wasn’t a bad deal. Similarly, nobody needs to praise the government however things turn out either. If history judges that the available deal was worse than no deal, the opponent can say that of course there are </span><span style="background-color: transparent; color: black; font-family: "verdana"; font-size: 11pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">some</span><span style="background-color: transparent; color: black; font-family: "verdana"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> deals worse than no deal, but there are plenty of bad deals better than no deal too, and if we’d been able to get one of those then the government would have turned it down and been wrong to do so. The word ‘bad’ and the associated concept are flexible enough that nobody ever needs to admit they were wrong about whether no deal is worse than a bad deal. The government shouldn’t be criticized for taking a bad line; they should be criticized for empty, commitment-free rhetoric.</span></div>
Michael Bench-Caponhttp://www.blogger.com/profile/13715068990919309271noreply@blogger.com0tag:blogger.com,1999:blog-6411624366539130337.post-52352112152327468052017-05-01T04:44:00.001-07:002017-05-01T04:44:25.603-07:00The After Dinner Circuit<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: "verdana"; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;">It was recently reported that </span><a href="http://www.telegraph.co.uk/news/2017/04/25/barack-obama-criticised-400000-wall-street-speech-fee/" style="text-decoration-line: none;"><span style="color: #1155cc; font-family: "verdana"; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;" target="_blank" title="telegraph.co.uk: Barack Obama criticised for '$400,000 Wall Street speech fee'">Barack Obama is getting paid $400,000 to give a speech to a Wall Street bank</span></a><span style="font-family: "verdana"; font-size: 11pt; vertical-align: baseline; white-space: pre-wrap;">. Obama’s a great speaker, but a lot of people seem to think nobody’s $400,000 great, and so the transaction smacks of corruption. The thinking is that the bank must be getting more than just a speech for their money.</span></div>
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<span style="background-color: transparent; color: black; font-family: "verdana"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Now, I don’t know if it’s true that the speech alone isn’t worth that much to the bank. There’s a lot of money flying around in banking, and the stakes are high. Maybe if people come to your dinner rather than your competitor’s dinner, you might get a big deal that makes the money back. Or maybe hosting dinners with Obama attracts employees that could otherwise only be attracted with those enormous banker’s bonuses that we love reading about.</span></div>
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<span style="background-color: transparent; color: black; font-family: "verdana"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">But let’s suppose that the speech isn’t worth that much to the bank, and they’re getting something else. Or maybe it is worth it to them but they're still getting something else, because that's how the after dinner speech market works. One possibility is that Obama made a shady deal where he did the bank some kind of regulatory favour while he was in office, on the understanding that they would pay him $400,000, which they are now laundering as a speaking fee. I think that's unlikely, but it’s beyond the scope of this blogpost to persuade you to agree with me that it's unlikely.</span></div>
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<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "verdana"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">What I think is much more likely is that there’s a general understanding that Wall Street banks, and other big businesses, are willing to pay massive speaking fees to politicians after they leave office, and that they offer the gigs to politicians who are friendly to Wall Street and so on while they’re in office, and that on some level this influences the way politicians govern. This kind of thing is insidious and I can see it affecting basically everyone to some extent, without anyone doing anything they could be prosecuted for. That’s not ideal.</span></div>
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<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "verdana"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">What can we do about this? </span><a href="http://michaelbenchcapon.blogspot.co.uk/2011/09/how-can-this-possibly-be-legal.html" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-family: "verdana"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;" target="_blank" title="My Blog: How Can This Possibly Be Legal?">One thing we could do</span></a><span style="background-color: transparent; color: black; font-family: "verdana"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> is demand that politicians declare future conflicts of interest. If you’re taking a gig in the medium-to-near future that would constitute a conflict of interest if you had it now, then you need to declare it as if you had it now. I don’t see that it makes sense to have laws or strong norms about present conflicts of interest while relying on the honour system for future conflicts of interest. But let’s assume that’s not going to happen. What can individuals do?</span></div>
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<a href="http://www.vox.com/policy-and-politics/2017/4/25/15419740/obama-speaking-fee" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-family: "verdana"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;" target="_blank" title="Matt Yglesias">Some people</span></a><span style="background-color: transparent; color: black; font-family: "verdana"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> think Obama shouldn’t take this kind of gig. He should set an example, he needs to go high where other people go low, and so on. Even if his governing wasn’t influenced by the prospect of lucrative speaking gigs, he needs to extinguish any suspicion that it was.</span></div>
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<a href="http://www.hollywoodreporter.com/news/trevor-noah-obama-wall-street-speech-colbert-998506" style="text-decoration: none;"><span style="background-color: transparent; color: #1155cc; font-family: "verdana"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: underline; vertical-align: baseline; white-space: pre-wrap;" target="_blank" title="Trevor Noah">Some other people</span></a><span style="background-color: transparent; color: black; font-family: "verdana"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> think Obama should take the money. Everyone takes the money, and it’s unfair to demand he make all the sacrifices, especially when the new president brazenly doesn’t care about all his own conflicts of interest and spends government money at his own businesses all the time.</span></div>
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<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "verdana"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Here’s what I think. It’s too late for Obama. Whatever influence the speaking fees had on his presidency, they’ve had it already. We know he wasn’t planning to eschew the speaking fees, and changing his mind now won’t change whatever decisions he took during his presidency. If he was running for future office, things would be different. But he probably isn’t, and so it’s too late. Obama showed a lot of things were possible, but he can’t show that saving politics from the after dinner circuit is possible. And if he had been planning to do this, regulating Wall Street on the merits and to hell with the speaking fees, then he should have said something about it sooner. Like, when he was in office, or even before that.</span></div>
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<span style="background-color: transparent; color: black; font-family: "verdana"; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">It’s not too late for everyone. If you’re in office now, or you’re running for office in the future, and you don’t want politicians to be influenced by the prospect of future speaking fees, pledge not to take them. Or if you aren’t willing to go that far, then at least pledge not to take the really big fees. It’s simple, it’s easy for people to understand, and it doesn’t rely on backwards causation. </span></div>
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<br />Michael Bench-Caponhttp://www.blogger.com/profile/13715068990919309271noreply@blogger.com3tag:blogger.com,1999:blog-6411624366539130337.post-2471358449730544122017-04-15T07:01:00.000-07:002017-04-15T07:07:02.614-07:00Meet Me Halfway<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "cambria"; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">A logician goes to an island of knights and knaves. Knights always tell the truth; knaves always lie. One of the locals says “either I’m a knave or there’s gold on this island”. Is there gold on the island?</span></div>
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<b id="docs-internal-guid-90556ace-71e0-61dd-4ae1-dc0fa31719c1" style="font-weight: normal;"><br /></b></div>
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<span style="background-color: transparent; color: black; font-family: "cambria"; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">This kind of puzzle is a staple of the puzzle books of Raymond Smullyan, and </span><span style="background-color: transparent; color: black; font-family: "cambria"; font-size: 12pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Forever Undecided: A Puzzle Guide To Gödel</span><span style="background-color: transparent; color: black; font-family: "cambria"; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> is no exception. This isn’t just a compendium of brainteasers intended solely for entertainment though; Smullyan has a serious purpose. He’s explaining some of the main results in provability logic by recasting them in terms of the beliefs of logicians with various characteristics when faced with this sort of knight/knave puzzle. It’s a clever idea, and very much the kind of clever idea you would expect Raymond Smullyan to have.</span></div>
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<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "cambria"; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">It’s helpful to cast results like Gödel’s incompleteness theorems and Löb’s theorem in different terms, and especially in fairly concrete terms about things people say or the output of a computer program. It helps to explain the content of the results, and helps readers understand their significance. One thing Smullyan is pretty keen to get across is that the impossibility of a system of arithmetic proving its own consistency doesn’t give </span><span style="background-color: transparent; color: black; font-family: "cambria"; font-size: 12pt; font-style: italic; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">any</span><span style="background-color: transparent; color: black; font-family: "cambria"; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> reason for thinking such systems aren’t consistent. This makes sense, since we already knew that an inconsistent system could prove its own consistency - inconsistent systems prove everything - so if a system says it’s consistent that’s no reason to think it is. If you ask a resident of the knight-knave island if they’re a knight, knights and knaves will both say they are. Similarly, if you want to know if a system’s consistent, you shouldn’t ask the system itself, and the fact people didn’t properly figure this out until Gödel discovered that consistent systems wouldn’t answer the question doesn’t change that.</span></div>
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<span style="background-color: transparent; color: black; font-family: "cambria"; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">As well as discussing the results, the book also contains lots of exercises, with reasonably generous solutions. These are analogous to the kind of exercises you might get in a textbook on provability logic, except they’re expressed in different terms. Now, you might think that doing it in terms of knights and knaves and so on would make the whole thing so much fun that the hard work of getting your head round this material wouldn’t feel like hard work, and before you knew it you’d have all the proofs of the main results in provability logic at your fingertips. This was not my experience. The material is just as hard, and now you have to learn a bunch of new terminology. It isn’t Smullyan’s fault that this stuff is hard, but there are things I think he could have done to make it a bit easier.</span></div>
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<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "cambria"; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">First, the book doesn’t have an index, and the chapter headings are often whimsical (“It ain’t necessarily so!”), vague (“More Consistency Predicaments”), or related to the island-hopping framing device (“In Search of Oona”). This makes it difficult to go back and remind yourself of material when it comes up again. This is bad enough when reading a novel, but in a textbook it’s not really excusable. Smullyan hasn’t set out to write a textbook, but he wanted the material to be comprehensible to someone who (unlike me) was approaching it for the first time, and an index and analytic table of contents would have helped with that a lot.</span></div>
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<span style="background-color: transparent; color: black; font-family: "cambria"; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Second, the book introduces a lot of new terminology: reasoners of type 1, 2, 3, 4, 1*, G, G* and Q; normal, regular, peculiar, modest, conceited, reflexive and stable reasoners; Gödelian systems, Löbian systems, and so on. Being a doofus, I wasn’t able to keep all the definitions in my head. Since there was no convenient way of looking them up, a lot of the time I couldn’t understand the exercises until I looked at the solutions to see what followed from a reasoner being regular or stable or of type 3 or whatever. This isn’t really satisfactory, so I skipped a lot of the exercises and solutions, and when I didn’t skip the exercises I often didn’t really know what I was being asked. An appendix in the back saying what all these definitions mean would have been a great help. The last chapter gives a summary of the main results, but that’s not the same thing and doesn’t make the exercises more comprehensible. I’m considering writing an appendix myself and sticking it in the back in case I or anyone else reads my copy of the book again. It’d take some work though, as the definitions are scattered throughout the book and there’s no index.</span></div>
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<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "cambria"; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">So, who’s the book for? I think you’d really enjoy the book if you liked whimsical logic puzzles and were already very familiar with the technical material. (I like whimsical logic puzzles but was only reasonably familiar with the technical material.) You’d also probably get some scholarly benefit from reading the book if your understanding of the proofs of the results was better than your understanding of what the results amount to. I’m the opposite, and I expect that’s normal for people who encounter it through studying philosophy. I guess if you encountered it through studying maths then things might be the right way round for you. Who else would like the book? Well, someone who liked puzzles and would be interested in provability logic but hadn’t seen any of the results before would probably like the book at first but find it became a bit of a slog about 100 pages in. If they’re the sort of person who can read a maths textbook without looking at the index, the contents page or a list of definitions used in the book, then they’d probably be fine. Here’s what Smullyan says about the target audience in the preface:</span></div>
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<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-left: 36pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: "cambria"; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">I have lectured a good deal on all this material to such diverse groups as bright high school students and Ph.D.’s in mathematics, philosophy, and computer science. The responses of both groups were equally gratifying - they were intrigued. Indeed, any neophyte who is good at math or science can thoroughly master this entire book (though some application will be needed), yet many an expert will find here a wealth of completely new and fresh material.</span></div>
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<span style="background-color: transparent; color: black; font-family: "cambria"; font-size: 12pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">I think that’s a bit optimistic, and if he wanted neophytes to apply themselves and master the entire book then he should have met them halfway with an index, and appendix and a better contents page. But I’ve no doubt people enjoyed the lectures.</span></div>
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Michael Bench-Caponhttp://www.blogger.com/profile/13715068990919309271noreply@blogger.com0tag:blogger.com,1999:blog-6411624366539130337.post-87557582553432868082017-04-12T07:50:00.001-07:002017-04-12T07:50:08.997-07:00Lost Voices Of History<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="font-family: Verdana; font-size: 11pt; white-space: pre-wrap;">Bertrand Russell was a great philosopher, and he also had a great voice. Since he was a celebrity who died in 1970, he was on TV a lot and you can have a listen to his voice on Youtube. If you hear a voice in your head when you read, as I do but as not everyone does, then I recommend reading Russell in Russell’s voice. It’s fun! With a lot of great philosophers, of course, we don’t have this luxury. There aren’t any recordings of their voices and nobody knows what they sounded like. This seems to me an avoidable shame. </span></div>
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<span style="background-color: transparent; color: black; font-family: Verdana; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">People will presumably continue to do Michael Caine impressions for at least a while after Michael Caine dies, and my understanding is that most people’s Michael Caine impression owes at least as much to copying other people’s impressions as to copying Caine himself. That’s why they all sound the same but they don’t sound like Michael Caine. The Michael Caine impression voice is easy to do, and Michael Caine’s voice is hard to do, and here we are.</span></div>
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<span style="background-color: transparent; color: black; font-family: Verdana; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">It seems to me that the Michael Caine impression voice could be preserved indefinitely, even if all the recordings of his voice and the impression voice were destroyed and no more were ever produced. People would copy each other, and hundreds of years into the future people would still be doing impressions of Michael Caine. And that would be a fine thing.</span></div>
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<div dir="ltr" style="line-height: 1.7999999999999998; margin-bottom: 0pt; margin-top: 0pt;">
<span style="background-color: transparent; color: black; font-family: Verdana; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">At least as fine a thing would be if this had actually happened with historical public figures: people had done impressions of them for the amusement of people familiar with the original, the way the impression sounded had become common knowledge, the ability to do the impression had become part of every self-respecting person’s conversational repertoire, and then 470 years on we were all still doing impressions of Henry VIII. </span></div>
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<span style="background-color: transparent; color: black; font-family: Verdana; font-size: 11pt; font-style: normal; font-variant: normal; font-weight: 400; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">I can’t think of anyone this has happened with in the Anglosphere. All the impressions we do nowadays are of people we have recordings of. Perhaps there are or have been communities who did preserve their ancestors’ voices over the centuries in this way; if you know of any then tell us about it in the comments. It would seem strange to me if that hadn’t happened, but English speakers seem not to have preserved any, so maybe that’s how things are.</span></div>
Michael Bench-Caponhttp://www.blogger.com/profile/13715068990919309271noreply@blogger.com0