Graduate conference in metaphysics

See following call for papers for the CMM graduate conference
__________________________________________________________________

The Centre for Metaphysics and Mind at the University of Leeds is
hosting the 4th Annual CMM Graduate Conference on Friday 4th
September.

Submissions are welcome on any area of metaphysics. Metaphysics should
be broadly construed to include not only traditional metaphysical
topics, but also the metaphysical aspects of e.g. philosophy of mind,
philosophy of physics, philosophy of religion, and aesthetics.

Submissions of any length up to 5,000 words will be considered.

Each paper presented at the conference will be followed by a response
from a member of academic staff or PhD student from the University of
Leeds Department of Philosophy.

As with last year's conference we hope to be able to pay some or all
of the travel and accommodation costs for those people whose papers
are accepted. (This is dependent on successful funding applications.)

Please submit complete papers, preferably by e-mail, to Joanna
Pollock, joeykpollock@googlemail.com. Please mark your submission
clearly as such. Receipt will be acknowledged asap.

All papers should be suitable for blind review (we cannot guarantee
anonymised refereeing if your paper is not suitably anonymised).
Please include a cover page with title, abstract and contact details.

Deadline for receipt of submissions is Sunday 19th July 2009.

Decisions will be made by Monday 10th August 2009.

For more general details on the conference please consult:

http://www.personal.leeds.ac.uk/~phsk/cmmgc09/index.htm

or e-mail Duncan Watson at phl5dw@leeds.ac.uk

Composition as identity does not entail universalism

In my Contingency of Composition paper, I deny the commonly held claim that composition as identity (CAI) entails universalism about composition. (The entailment is defended by Sider, Merricks, et al.) My basic thought was: CAI says just that a complex object is identical to its parts – that tells us only that when you’ve got a complex object, it is identical to its parts, and this is silent about whether or not for any collection of objects there is such a complex object that they are identical to. If many-one identity makes sense then, prima facie, it makes sense to claim that for some collections of objects there’s a one that they are identical to, and some collections of objects such that there’s no one object that they are identical to. All CAI tells us is that it’s all and only the first collections that compose. To assume that every collection composes is just to assume that for any collection of objects, there’s a one to which they are identical. Why would I accept that if I doubted universalism?

In denying the entailment, I need to respond to an argument that both Sider and Merricks give for it. They argue as follows: Suppose (for reductio) the Xs don’t compose. They could do. Go to the world where they do (w). In w, there’s a one, A, that’s identical to the Xs. Given the necessity of identity, A is actually identical to the Xs. So the Xs actually compose A. Contradiction. Formally:

1) ◊(Xs=A)
2) ◊(Xs=A) -> □(Xs=A)
3) @(Xs=A)

In my paper I attempted to resist this argument with some pretty tricky moves – and while I still think they’re right, I think I haven’t exactly convinced the world! (See the earlier discussion on this blog) But I think I can actually make the point more simply than I did then.

The argument aims to prove that the Xs are actually identical to A. Thus, there is a one that the Xs are identical to: A. So since to compose is to be identical to a one, the Xs compose. But wait! All the argument shows is that it’s actually true that the Xs are A. Where do we get the claim that there’s a one that the Xs are identical to? This follows, obviously, if A is actually a one. But where does that claim come from? All we know is that A is possibly a one. Ex hypothesi A is a one in the world in which the Xs compose. But we can only conclude that A is actually a one – and hence that there’s a one that the Xs are actually identical to – if we have the assumption that anything that is possibly a one is necessarily a one. But what right do we have to make that assumption? If we’re leaving open the possibility that there’s a many that’s not a one but could be (and at this stage we must, lest we beg the question), we should also leave open the possibility that there’s a many that is a one but might not be. Since the many is the one, this is a one that might not be a one: a one that is a many, but that might have been a mere many – a many that is identical to no one. If the Xs don’t actually compose this is the status we should think A has in the world in which they do compose. So sure A is actually identical to the Xs: but A is actually just a name for the plurality, a plurality that don’t actually compose. A is only a one in the worlds in which that many do compose. And we’ve been given no reason to think we’re forced into thinking that our world is one of those.

The Trinity and contingent identity

I got thinking about the Trinity after the workshop on the metaphysics of theism at Leeds last week, and I got to wondering: has anyone ever suggested that the Trinity is a case of contingent identity? (The good thing about a blog is you can put out those ideas that are too weird for publication! All my thoughts on the philosophy of religion are a proper subset of that category.)

So forget the Trinity for the moment and focus on the father's relationship to the son: the idea is that they are actually identical, but contingently so, and that the father is a necessary existent but the son a contingent existent. In every world in which the son exists, he is identical to the father, but there are worlds in which the father exists and is not identical to the son because there are worlds in which the son does not exist (for the son to exist depends on an act of will on the part of the father, and he might not have so willed).

So there is of course a very tight connection between the father and the son: strict numerical identity - it doesn't get much tighter! Thus vindicating Jesus's claim that that father and he are one. But we can also quite easily, on this view, make sense of Jesus's claim that the father is greater than he is: he's a mere contingent existent, the father a necessary being - that's good grounds for saying that the father is greater.

How to fit in the spirit? Well perhaps the spirit is also a contingent existent, and also actually identical to the father (and, by transitivity, the son), but that there are worlds with son but no spirit and worlds with spirit but no son. So the idea is that although the father, the son, and the spirit are each numerically identical to the others, we can distinguish them by their differing modal profiles. For any two, while they're actually identical, they might not have been. But monotheism is easily seen to be a necessary truth, on this view (whereas other views of the Trinity threaten to commit us to tritheism): necessarily, there is only one God, for necessarily any divine being is numerically identical to the father.

Objection: how can they be numerically identical if they have differing modal profiles? Reply: well, we all know the contingent identity theorist has to resist the Leibniz law argument from differing modal profiles to numerical distinctness. Whatever story they're going to tell to make sense of contingent identity in general, let them tell it here.

Objection: but isn’t there a difference in non-modal properties as well? The father is atemporal, the son temporal, the son human the father not, etc? Reply: okay, we’re going to have to say something odd here. Perhaps we just deny the atemporality of the father, or perhaps we say that God is atemporal qua father but not qua son, etc (and hopefully unpack that and say what it means!). But every view of the Trinity ends up saying something a bit odd at this point – it’s not clear that there’s a particular objection to the contingent identity view here.

So, does anyone know if this has been discussed before, or see any problems with it that aren’t faced by all accounts of the Trinity?

(Posts on sane topics will resume once marking season is over, I suspect!)

Routledge Companion to Metaphysics

The Routledge Companion to Metaphysics is now out! I'm very proud of this: I think our contributors all did an excellent job, and the volume looks excellent.

It's divided into three sections: the history of metaphysics, ontology, and metaphysics and science, and contains 53 original essays. I hope and believe it'll be a useful work of reference for the foreseeable future. You should buy it!

New research centre in Scotland!

Exciting news for philosophy in Scotland! Crispin Wright has accepted an offer to found and direct a new philosophical research centre at the University of Aberdeen. The centre will ‘go live’ Sep 1st 09, and is provisionally named ‘The Northern Institute of Philosophy’.

The NIP’s areas of remit will be: Epistemology, Formal Logic, Philosophy of Logic, Philosophy of Language, Philosophy of Mathematics, Metaphysics, Philosophy of Mind, and the History of Analytical Philosophy. A number of appointments will be made of various categories in the near future, and a bunch of the Leeds faculty will be involved as Associate Fellows, and in other respects.

Arbitrary Reference

I posted a while back toying with a view of vagueness whereby there was a sharp cut-off in any sorites series as a result of there always being a unique most meaning among the candidate meanings (i.e. those that fit equally well with usage) for any vague expression; since naturalness is a reference magnet – and since it is ex hypothesi not trumped by usage – this is the meaning we will in fact mean, thus determining that the cut-off is where it is. (I further toyed with the idea that it is ontically indeterminate which meaning is the unique most natural, thus yielding the conclusion that it’s determinate that there’s a sharp cut-off in the sorites series but that it’s ontically indeterminate where it is – but forget about this complication for now.)

I’ve also been thinking about this with respect to arbitrary reference. What’s going on when we reason as follows? Let n be an arbitrary multiple of 4. n is a multiple of 2, all multiples of 2 are even, so every multiple of 4 is even. In particular, what, if anything, is referred to by ‘n’ throughout? Maybe it doesn’t refer; but then it’s hard to see how the sentences could be truth-apt, and we get a kind of Frege-Geach problem. Maybe it refers to a special kind of entity: the arbitrary multiple of 4; but that’s kind of weird. Ofra Magidor and Wylie Breckenridge have a really interesting paper where they argue that n actually refers to some particular multiple of 4 – we just cannot know which one. But in virtue of what do I refer to this particular multiple of 4 rather than some other? In virtue of nothing, they say: this is a brute fact. The semantic facts, on their view, are not fixed by the non-semantic facts: all the non-semantic facts could have been just the same but you have referred to some other multiple of 4 by ‘n’. I don’t like brute semantic facts, but I like a lot about their account, so I am quite attracted to extending the above account of vagueness to cases of arbitrary reference: ‘n’ refers to the most natural arbitrary multiple of 4. (Psst! – and it’s ontically indeterminate what this is. But again, forget this just now.)

There are two problems, one of which is encountered by both Magidor and Breckenridge and myself, the other of which might be thought to tell in favour of Magidor and Breckenridge’s view over my variant. I’d appreciate any thoughts on what I have to say about these.

First the common problem. Any view that takes us to genuinely refer to an F when we aim to refer to an arbitrary F has to have something to say about the case where there can be no Fs. For example, suppose we reason as follows. Let n be an arbitrary even prime greater than 2. n is (because it’s even) divisible by 2. So n is divisible by a number other than itself or 1. So n is not prime. Reductio: there is no such n. This chain of reasoning is perfectly good; but it’s obviously hopeless to take ‘n’ to refer to any even prime greater than 2, precisely because there are no such things. (I guess we could go Meinongian, and claim that there are such things, and ‘n’ refers to one, but that n doesn’t exist. But let’s not.) So what’s going on in this case? This is a case where those who postulate special entities as the referents in the cases of arbitrary reference – the arbitrary F – are at an advantage over those who take us to refer to an F; for if the arbitrary even prime greater than 2 isn’t really an even prime greater than 2, there can be no objection to its existence on these grounds. But of course, such views face other problems: such as, if the arbitrary F isn’t an F, what is it? I think we should treat cases like this as not really being cases of arbitrary reference after all. Despite their surface similarity to such cases, these cases, I suggest, are really reductios on the hypothesis that we have a case of genuine reference. So when we say ‘Let n be an arbitrary even prime greater than 2’, I suggest we are really supposing for reductio the hypothesis that ‘an arbitrary even prime greater than 2’ refers. Then, of course, we need some principle that lets us semantically descend, and conclude that there are no even primes greater than 2 if that expression cannot refer.

Now to the other problem. While I might not know what the most natural F is when I refer to an arbitrary F, there are some things I do know. I do know, for example, that if I refer to an arbitrary property I do not refer to grue, because grue is less natural than green. So when I say ‘Let F be an arbitrary property’, I can conclude that F is not identical to grue. But can’t I then conclude that all properties are not identical to grue, for isn’t one of the rules we’re trying to capture the one that says that if x is an arbitrary F and x is G then all Fs are G? But this rule would then take us wrong, for it’s not true that all properties are not identical to grue, for grue is identical to grue.

If this is a problem for my view, however, there is as much of a problem with Magidor and Breckenridge’s view. Indeed, any view that takes you to refer in a case of arbitrary reference has such a problem, including views that take you to refer to a special kind of entity (the arbitrary F), for the above rule would tell you to infer that all the Fs have the property of having being referred to by you when you said ‘Let n be an arbitrary F’. If I, at time t, say ‘Let n be an arbitrary number’ then, if ‘n’ refers – no matter what it refers to, or how the reference fact is determined – then n has the property having been referred to by me at t. If we follow the rule that tells us to infer that all Fs are G if the arbitrary F is G, it follows that all numbers were referred to by me at t. This is false: either I referred to a particular number, or to a special entity that is the arbitrary number, but I certainly didn’t refer to each number.

So anyone who takes cases of arbitrary reference to really be cases of reference can’t admit that rule in full generality. But views which take us to refer to an F (rather than to a special entity, the arbitrary F) when we say ‘Let a be an arbitrary F’ obviously needed to restrict this rule in any case. Suppose I say ‘Let n be an arbitrary multiple of 4’. We want to be able to reason as follows: n is even, hence every multiple of 4 is even. But suppose, as a matter of fact (putting aside why this is the case), ‘n’ refers, arbitrarily, to 28. 28 is a multiple of 14. So can’t we now conclude, mistakenly, that all multiples of 4 are multiples of 14? The rule had better be restricted so that we cannot so infer. Magidor and Breckenridge respond to this problem by modifying the rule to say that we can only conclude that every number is F if we can prove that the arbitrary number n is F. Because you can’t know that n is 28, you can’t prove that n is a multiple of 14, and hence you can’t conclude that all multiples of 4 are multiples of 14.

I think Magidor and Breckenridge are basically right to restrict the rule so that the properties we can conclude that all Fs have aren’t the ones that n has if n was our arbitrary F but rather just those ones that we can prove that n has from a certain basis. But the basis can’t be the properties we know that n has: for while that would deal with the problem immediately above, since we can’t know that n, our arbitrary multiple of 4, is a multiple of 14, even if it is, this won’t deal with the prior problem, since we can know that n was referred to at t when I said at t ‘Let n be an arbitrary multiple of 4’. I think instead we should restrict the rule as follows: if a is an arbitrary F, then if you can prove that a is G from facts that are true solely in virtue of a being an F (i.e. excluding those facts that are true in virtue of a being the particular F that it is), conclude that all Fs are G. 28 isn’t a multiple of 14 in virtue of being a multiple of 4, it’s a multiple of 14 in virtue of being that particular multiple of 4, but it is even in virtue of being a multiple of 4, and that’s why we conclude that all multiples of 4 are even but why we can’t conclude that they’re all multiples of 14. Nor was 28 the referent of ‘n’ solely in virtue of being a multiple of 14: on my view, it is true in virtue of being the most natural multiple of 14; on Magidor and Breckenridge’s view it is not true in virtue of anything. Either way, the move to ‘all multiples of 14 were referred to by ‘n’ at t’ is blocked.

This also lets me respond to what would otherwise have been an advantage of Magidor and Breckenridge’s approach over my own (I owe the objection to Ofra). Suppose we say ‘let n be an arbitrary number and let m be an arbitrary number’? If the reference facts are just brutely settled, they might be brutely settled so that ‘n’ and ‘m’ co-refer and they might not be. Either way, we can’t prove either that n is identical to m or that n is distinct from m, so we can’t ever conclude that arbitrary Fs a and b are identical (unless we can prove that there’s only one) or that they are distinct: and of course, that’s exactly as it should be. But the worry is that I can know that n=m because I know that ‘n’ and ‘m’ co-refer: they must both refer to the most natural number.

But once the rule isn’t restricted to the properties we can prove n has from the basis of facts we know about n but rather, as it has to be to deal with the reference problem, to the properties we can prove n has on the basis of facts that hold solely in virtue of n being a number, this problem dissolves. n is not identical to m, if it is, solely in virtue of being a number. It is in virtue of n being the particular number that it is, i.e. m, that it is identical to m. Likewise if n is in fact distinct from m, this is true in virtue of n being the particular number that it is - one other than m. With this restriction on the rule – and let me re-emphasise that any account that takes us to refer in cases of arbitrary reference must place some such restriction – I think there will be no unwelcome consequences to my approach. (At least, no additional unwelcome consequences over the brute facts view!) And the advantage is that, at the price of accepting these facts about naturalness, we avoid both brute semantic facts and the postulation of weird entities like the arbitrary number.

Ontological Cheating and Ockham's Razor

I’ve written a brief reply to Jonathan Tallant’s forthcoming Analysis paper, 'Ontological Cheats Might Just Prosper', that argues in favour of being the kind of ‘cheating’ presentist and actualist that simply takes truths concerning the past, or what could have been, to be ungrounded. Tallant argues that Ockham’s razor suggests we should be cheats, because if we can do without past or merely possible ontology, Ockham’s razor says we should. Don’t multiply entities beyond necessity, so since it’s possible not to believe in such things, you shouldn’t believe in them.

I argue that this has to be a bad understanding of Ockham’s razor: were it good, we should be Ontological Nihilists and believe that nothing exists. Since it’s possible to believe in nothing at all, believing in anything multiplies entities beyond what’s necessary, hence we shouldn’t believe in anything! Since we’re not Ontological Nihilists, we can’t be operating with this version of the razor.

Why aren’t we Ontological Nihilists? Because while it’s ontologically parsimonious, it’s ideologically extravagant. (See Jason’s paper.) Ockham’s razor has to allow that ontological parsimony needn’t be purchased if the cost is extravagant! But once we allow this, we’re just back to the old game of weighing up the admitted ontological benefits of cheating against what should be the admitted costs in its ideology and/or in its account of how truth depends on reality. The debate hasn’t progressed any.

I argue that every theory owes us an account of three things: what exists, what is true, and how truth links up to ontology. Ockham’s razor tells us, I suggest, that we shouldn’t accept a theory that postulates the existence of some things that don’t, according to its own view of how truth depends on ontology, do any work in accounting for what it itself says is true. That principle is going to tell us not to say, e.g., both that truths about the past are brute but yet there are nevertheless past entities. And that’s as it should be: that’s a bizarre combination of views to hold. But it’s never going to let us decide between two theories just by looking at their ontologies. And I think that’s as it should be: we have to look at the other two components as well, and see if the ontological advantage is being paid for at an appropriate price. And I can’t see any version of the razor that will mandate accepting the ‘cheating’ theories that won’t also mandate accepting Ontological Nihilism.

(I’ve also written a reply to a forthcoming paper by Stefano Predelli which argues against my view that there are no musical works. It’s here.)

Leeds metaphysicians sweep Oxford Studies in Metaphysics prize!

Some fantastic news for the Leeds metaphysicians: Jason Turner has won the the Younger Scholar Prize in Metaphysics, for his paper 'Ontological Nihilism'! This was after a record number of submissions. Well done Jason!

And the joint runners-up are Robbie Williams and Elizabeth Barnes for their paper 'A Theory of Metaphysical Indeterminacy' and me for my 'Truthmaking for Presentists'. So a clean sweep for Leeds!

These three papers will all be appearing in a forthcoming volume of Oxford Studies in Metaphysics.

Update: Jason's paper is now available on-line: check it out via the link above!

Further update: It looks like the above three papers will be published alongside Richard Woodward's earlier accepted paper 'Metaphysical Indeterminacy and Vague Existence'. So it looks like Leeds is really going to dominate that issue of OSM! Maybe it should be called 'Oxford Studies in Leeds Metaphysics'.

(Both Rich's and my paper make use of the way of thinking about metaphysical indeterminacy in the way Elizabeth and Robbie tell us to - so this journal will also see three papers defending the Elizabeth/Robbie plan. Metaphysical indeterminacy's day is here!)