The problem of transobject identity

Yesterday I finished reading the first volume of David Armstrong’s Universals and Scientific Realism for the first time. It’s fun, interesting and short. I recommend it, even though some of the arguments probably aren’t the kind of thing you can get away with nowadays. Armstrong is dealing with the problem of how different things can be the same in some respect, and he argues that nominalism, Platonism and trope-theory either don’t explain what needs explaining or lead to explanatory regresses. Since these are bad things, he adopts a theory of immanent universals, which are repeatable things which crop up in different objects. If two particulars are both negatively charged, that’s because there’s a thing, negative charge, which is in both of them. I wouldn’t say I was convinced, but he makes the case pretty well.

Now, when I was reading it, I noticed a parallel between the problem Armstrong is addressing and the problem of transworld identity. Armstrong wants to know how different things can share properties, and the problem of transworld identity is about how different possible worlds can share inhabitants. Some issues in one debate have corresponding issues in the other, and this gives rise to analogies between the positions. I think at one point Armstrong even calls the thing he’s trying to explain ‘generic identity’.

Transworld identity gets explained by the worlds having either strictly identical things in them, or suitably similar things in them. Generic identity gets explained by particulars having strictly identical universals in them or suitably similar tropes. The ‘no explanation needed’ positions are magical modal realism, which reifies worlds but not possibilia, and ostrich nominalism, which reifies objects but not properties. (Both were named by their opponents.) Another parallel is that people disagree about whether particulars are bundles of properties or something besides their properties, and they also disagree about whether worlds are fusions of their inhabitants or something besides their inhabitants. The bundle theory of particulars is typically most plausible to trope theorists, and the fusion theory of worlds is typically most plausible to counterpart theorists.

When you spot a parallel between two debates it can help you in at least two ways. One is that the analogy can help us understand the more mysterious debate better. Our thinking about time became clearer when we realised it was a bit like space, and our thinking about modality became clearer when we realised it was a bit like time. I’m not sure whether we’ll be helped much in this way here: space and time really are quite like each other, whereas the relationship between a world and its inhabitants seems quite unlike the relationship between a thing and its properties, at least if the bundle theory isn't right.

The other way analogies between debates can help is more promising though. There’s some pressure to hold analogous positions in analogous areas, because a good argument for one position will often correspond to a good argument for the other. This way of killing a large number of birds with a small number of stones is particularly useful for people like me who like to make their minds up about things. For example, shortly after I came round to counterpart theory about de re modality I came round to stage theory about persistence. I’ve never really had a view about property ontology before, but maybe now I should have another look at trope theory.

How can this possibly be legal?

One of the measures which is standardly used to prevent corruption is making people in positions of power declare their interests. For example, if a politician is deciding which company gets a government contract, and the politician works for one of the companies in the running, they have to declare it and the decision may be delegated to someone else. If they don’t declare it and get found out, they get into trouble. It is fairly obvious that a system lacking this feature would be open to abuse.

One thing which seems to be allowed, however, is for a politician to take a job with a company after having used the power entrusted to them by the electorate to benefit said company. Private Eye reports on this sort of thing all the time. They call it the Revolving Door. I can’t see any principled reason to think that undeclared future interests compromise the integrity of the politicians involved much less than undeclared present interests would.

It seems to me that it would be pretty easy to put a stop to it. You say that politicians giving contracts to companies have to declare an interest or either face trouble or not take a job with the company for, say, five years. And if people keep waiting out the time limit and then immediately taking jobs with companies they’ve helped, we smell a rat and extend the time limit. But perhaps I’m missing something and a rule like this would be impossible to put into practice.

Epistemic virtue

I watched Sherlock when the BBC repeated it recently. It’s a reimagining of Sherlock Holmes set in the present, and it’s a lot of fun, even for someone like me who’s ordinarily a bit of Holmosceptic. Anyway, two of Sherlock’s most striking traits are that he’s very good at gathering evidence and inferring what’s what, and that he’s a sociopath. I’ve lately been wondering about epistemic virtues, and it seems that there’s a case to be made against the obvious position, and that the obvious position entails that we should be just like Sherlock.

The obvious position is that we should proportion our credences in P to the probability of P given our evidence. The hard work is all in working out what this amounts to. You have to say where your prior probability distribution should come from, what counts as evidence, how to deal with apparently non-propositional evidence, and so on. There is also an issue about actively seeking out evidence. Maybe we should make exceptions when not proportioning our credences to the evidence will enable us to get more evidence, so our beliefs will better approximate the truth in the long run. A stock example is when the fount of all knowledge can only be reached by jumping a chasm which you’re more likely to clear if you believe you will. But it seems that the action in epistemic virtue theory is in finding out how to emulate Sherlock when it comes to gathering evidence and making proper inferences from it. We don’t expect to have to emulate his sociopathy.

Lately that’s what I’ve questioning. When a friend, spouse or what have you tells you something, you are in many circumstances supposed to believe what they say. Suppose your wife tells you she was stuck at the office until 3am and slipped in a large puddle of beer on her way home. You could add that she has said this and that she came home stinking of beer when it was already getting light to the rest of your evidence and update like a good Bayesian, but perhaps this is one thought too many. Sometimes there are conflicts between being a good husband and a good Bayesian, and skill at resolving such conflicts is one of the things distinguishing the epistemically virtuous from the rest of us.

I don’t know what people whose day job it is to think about this sort of thing have thought about it, but I can see three natural responses. One is to say that belief isn’t voluntary and all this talk about epistemic virtues is wrongheaded. I’ll put that to one side. Another response is that the epistemic virtues and the virtues of personal concern aren’t the same and can conflict. I’m quite sympathetic towards that, but if it’s true then parity of reasoning would suggest that favouring our friends isn’t any more morally virtuous than believing our wives is epistemically virtuous. The last natural response is to say we’re called upon to practise a kind of doublethink, where we separate our credences as rational inquirers from the credences which rationalise our behaviour and which we profess to have. We can’t do this with the conflicts between morality and friendship because we have only one set of actions, but with credences it seems almost feasible.

Who can you trust?

Regular readers will know that not so long ago I read and very much enjoyed Steven Pinker’s The Blank Slate, which is about the influence of genes on human psychology. That isn’t my area of expertise, but he seemed to be on the level. His reasoning was mostly reasonable and his evidential claims were backed up by sources which sounded reputable enough. The first half of chapter 18 was about psychological differences between the sexes. He argued that there was strong evidence that some psychological traits are correlated with sex and some evidence that genetic differences between men and women contribute to these correlations. As I say, he seemed to be on the level and know his stuff, so I believed him.

Last week I got some conflicting signals, though. I read Cordelia Fine’s Delusions of Gender, and I enjoyed that a lot too. Fine’s book is about the claims made about psychological differences between men and women, both by scientists and popular writers drawing on the work of scientists. I suppose if I was summarising its claims in bullet points, I’d pick these: 

• There isn’t as much evidence for psychological differences between the sexes as a lot of people make out.
• A lot of the research into this sort of thing is done very badly.
• A lot of the popular writers either misinterpret or wildly extrapolate from what evidence there is, and sometimes just make things up.
• The hypotheses getting tested tend to be based on stereotypes.
• There’s no shortage of places to look for non-genetic explanations for the differences that have been found.

Fine seemed to be on the level just as much as Pinker did, and what she said was largely pretty persuasive. Since she went into far more detail about this specific issue than Pinker did, I suppose my credences are currently balanced in her favour, and my trust in the other 20½ chapters of Pinker’s book is correspondingly undermined. Mostly though, I just don’t know what to think. Fine goes into far more detail about the methods of the research she disagrees with than those of the research she uses to support her positive claims, so I’ve no way of knowing that I won’t read another book in a few months’ time which critiques that just as severely. If she had gone into as much detail about it all it would have doubled the length of her book though, so I can kind of see why she didn’t.

I like reading non-fiction, and I particularly like reading science books pitched at about the level Pinker’s and Fine’s books are pitched at. But I sometimes wonder why I bother. I’m trying to learn but if what I end up believing depends on which persuasive-sounding books are entertainingly written and easy to get hold of, then I’m not learning at all; I’m just making myself an unwitting vehicle for the memes I happen to get infected with. That’s no good. If all I’m going to learn from reading non-fiction is that scientists disagree with each other just as much as philosophers do and nobody really knows anything about anything, then maybe I’ll just read PG Wodehouse all the time.

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.

Smaller tree

Smaller Tree

Nick Griffin

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.