Sensual quantification

I used to think that belief ascriptions – things like ‘Lois thinks Superman can fly’ and ‘Lois thinks Clark can fly’ – were very interesting and important, and that if we had a good account of them then we’d understand a lot of other things better. I still think puzzles involving coreferring names are interesting and important, but nowadays I tend to think their apparent failure of substitutivity in belief contexts is a bit of a red herring. Nonetheless, this post is about belief ascriptions.

In Ted Sider’s discussion of Mark Richard’s theory of belief ascriptions, he raises a problem. He considers these two inferences:

A1:      (i) Twain is a famous author and Odile believes that Twain is dead.

            (ii) Therefore, ∃x(x is a famous author and Odile believes that x is dead)

A2:      (i’) Twain is a famous author, and Odile does not believe that Twain is dead.

            (ii’) Therefore, ∃x(x is a famous author and Odile does not believe that x is dead)

Both inferences look okay to the untutored eye, and Sider says we ought to allow that either both are valid or neither is. Richard’s semantics for belief ascriptions validates A1 but not A2. I’m not quite as down on this as Sider is, but I agree it looks bad. The reason Richard gets this result is he wants to say that Odile can believe that Clemens is dead without believing Twain is dead, if she doesn’t know ‘Clemens’ and ‘Twain’ are two names for the same person. A lot of people want that result. It leads to trouble when quantifying in though, because ‘x’ in (ii’) takes an object as its value rather than a name. Twain and Clemens are the same object, so if Clemens satisfies ‘Odile believes x is dead’ then Twain does. One way of looking at this is that even if names have sense as well as reference, variables don’t. The sense of ‘Twain’ is needed to make (i’) true, and since it’s lost when you existentially generalise it as (ii’), (ii’) isn’t true.

One response is to say that A2 is valid, but if Odile believes Clemens is dead then (i’) isn’t true after all, because names don’t have sense any more than variables do. Believing Clemens is dead just is believing Twain is dead, because Clemens being dead just is Twain being dead. It does look a bit struthious, but plenty of people go that way. I’m sympathetic to it myself.

Another response says that A1 and A2 both commit a fallacy of equivocation. Following Frege, we say that in belief contexts a name doesn’t refer to its bearer; it refers to what is normally its sense. So in each of (i) and (i’) ‘Twain’ appears once referring to Twain and once referring to the sense of ‘Twain’. The inference is as bad as this:

A3:      (i’’) I cashed my cheques as the bank and then spent all afternoon fishing at the bank.

            (ii’’) Therefore, ∃x(I cashed my cheques at x and then spent all afternoon fishing at x)

These two responses agree with Sider that A1 and A2 are equally valid. It’d be nice though if there was a way of making them both valid and allowing that Odile can believe that Clemens but not Twain is dead. I won’t do that, but I’ll try to go one worse, and to let (i) and (i’) entail these respectively:

(iii) There is a famous author who Odile believes is dead.

(iii’) There is a famous author who Odile does not believe is dead.

Those sentences, or sentences like them, are presumably the ones driving the intuitions anyway. To make this go through, we follow Frege on the references of names in belief contexts, and introduce a quantifier ∃_s ranging over senses, and a reference function R taking senses to the referents they determine. Now we analyse (iii) and (iii’) as:

(iv)  ∃_sx(R(x) is a famous author and Odile believes that x is dead)

(iv’) ∃_sx(R(x) is a famous author and Odile does not believe that x is dead)

Now we’d like to make the inferences logically valid, rather than valid in whatever sense this inference is:

A4:      (i’’’) Twain is dead.

            (ii’’’) Therefore, ∃x(x is a name with five letters and the referent of x is dead)

For all we’ve said so far the connection between the sense of the first occurrence and reference of the second occurrence of ‘Twain’ in (i) is purely a pragmatic phenomenon, so the inference to (iii) is like A4. That isn’t what we’re after. We could complicate the semantics by taking the sense as the semantic value and covertly applying R to it outside of belief contexts but not inside them. That’d make the inferences logically valid, but the strategy wouldn’t generalise to iterated belief contexts like in ‘Odile believes that Elodie believes that Twain is dead’. (That’s because these contexts demand a hierarchy of senses going up, whereas iterations of R only allow a hierarchy of references going down.) So I’ve tried to go one worse but I’ve actually gone two worse. I’ve analysed (iii) and (iii’) differently from the way Sider and Richard did, and I’ve made the inference pragmatic instead of logical. This probably means you don’t need a primitive sensual quantifier with its own inference rules; you just define it as an objectual quantifier restricted to senses. This doesn’t constitute a grand success. Perhaps it’s a good thing I don’t think belief ascriptions are a big deal anymore.

Truth and the PWTP principle

In 'Bare Particulars' Ted Sider says that particulars, not properties, should wear the pants. In the context in which he says it, I think he’s right. He says that the proposition that you’re sitting is true because you’re sitting, and you instantiate the property of sitting because you’re sitting. Those cases seem pretty clear-cut. You could presumably have a coherent conception of reality according to which things were the other way round, but that isn’t the way we normally think.

Sometimes you want to say that the abstracta are wearing at least some of the pants. I’ve got a prime number of arms because two is a prime number and I’ve got two arms. The reason the number two gets to do some work here is that we’re talking about primeness, and primeness is a property of numbers. There’s a related property which my arms have, namely the property of being a prime number of arms, but this property is derivative from the property of primeness, which belongs in the realm of abstracta. This seems an unproblematic violation of the principle.

Now a lot of people seem to think that the property of truth, as applied to utterances, inscriptions and beliefs, is a derivative property, like the property of being a prime number of arms. Consider this sentence-token:

S          Snow is white.

It’s not obviously barmy to think that S is true because it expresses the proposition that snow is white and that proposition is true. On the other hand, it’s also not obviously barmy to think that S is true because it says that snow is white, and snow is white. But if ‘says’ means ‘expresses’, and ‘that snow is white’ names a proposition, and that proposition is true because snow is white, then these two views aren’t really in conflict. The second view has just used different words and followed the explanation a bit further.

However, I also don’t think it’s obviously barmy to think that S is true because the subject refers to snow and the predicate expresses the property of being white and snow is white. We haven’t talked about a proposition at all there, and I don’t think we need to. We’ve talked about a property, and I’m not sure how to avoid it, but I’m not too concerned about that. The important thing is that the proposition isn’t doing any work.

So there are two ways of looking at truth as applied to utterances and inscriptions. (I think similar considerations apply to beliefs, but I’ll stick to more obviously sentence-like things at the moment.) On one view, truth is primarily a property of abstracta, and utterances are only true derivatively. On the other view, utterance-truth isn’t derivative in this way: it’s a non-derivative property of concrete things down here in the world. I’m much more inclined towards the latter view, but I don’t know how to go about arguing for it, so I won't do that. The point is that these are two pretty different ways of thinking about truth and the role of propositions, and I don't know which is the right one.

*ADDED 11/02/2014*

Since I wrote this post, I've come across complaints elsewhere that the 'wearing the pants' metaphor might be sexist, or heteronormative, or cisnormative. I've used it here because Sider used it, and I've come across it used by philosophers in conversation a fair bit. But I do see the point, and if anyone's been offended by it here, then I'm sorry, and when I'm choosing metaphors in future I expect I'll try to avoid this one.

Counterpart theory

The other day I was trying to explain to another philosopher what counterpart theory was in terms which didn’t make me sound like a maniac for sympathising with it, and it wasn’t that easy.

I said that according to a counterpart theorist, she could have been a chef because the world could have contained somebody who was very like her, except she was a chef. (I glossed over technicalities about multiple counterparts and multiple good candidates.) This contrasts with a transworld identity theorist, who says that she could have been a chef because the world could have had her in it being a chef. Similarity is vague and context dependent and identity isn’t, so counterpart theory makes de re modal predication vague and context dependent, and transworld identity theory doesn’t.

I think this is more or less right, but there’s a problem with it. In my explanation of counterpart theory I talked about how the world could have been, and taken at face value that’s a de re modal predication of the world. Now, some people don’t think the world exists, like compositional nihilists, and for them I suppose there’s a difference between a de dicto modal statement and a de re modal predication of the world. Either way you’re having to talk about ways things could have been. If we give a counterpart-theoretic gloss of how I could have been, why don’t we give the same sort of gloss of the way things in general could have been? And if we take ways the things in general could have been as primitive, why not do the same with ways I could have been?

Well, if you’re a modal reductionist you’ve got an answer to this. David Lewis had a bunch of spatiotemporally connected mereological sums representing ways things could have been. Yagisawa had the same things as Lewis but let you cut them up however you like, pretty much making the accessibility relation a counterpart relation. Ersatzists had abstract possible worlds. Once you’ve got ways things could have been you’re up and running and can give your counterpart-theoretic account of who could have been a chef. This keeps the reductive isthmus small, just like Mark Schroeder tells us to.

But what about me? I don’t want to sound like a maniac and I don’t see how ersatz worlds could bear much explanatory weight, so I’ve got nothing to reduce ways things could have been to. I need to take them as primitive, and that means I can’t be a counterpart theorist all the way down.

Perhaps this isn’t so bad. It’s pretty much what Ted Sider does in ‘the ersatz pluriverse’, taking overall possibilities as primitive and doing the rest with counterparts. What intrigues me is whether we’ve any reason to think, after letting in primitive possibilities and necessities for the world, that there aren’t primitive possibilities and necessities for me as well. I guess what I’m pushing is a kind of essentialism: there are some context-independent facts about possibility given by the essences of things, and the rest is counterparts. It’s inspired by a footnote to Naming and Necessity, though I suppose Kripke would be upset if he knew.