Metaphysical Indeterminacy workshop

The first workshop of the AHRC funded project on Metaphysical Indeterminacy that Elizabeth, Robbie and I run will be held in Leeds on the 21st and 22nd of January. The speakers are

Antony Eagle (Oxford)
Patrick Greenough (St Andrews)
Carrie Jenkins (Nottingham)
Agustin Rayo (MIT)

The workshop will start at 1pm on Jan 21st and end at 2pm on the 22nd. Attendance is free, but if you are planning on coming please e-mail me (r.p.cameron@leeds.ac.uk) and let me know. We'd love to see you there!

Motivating Attitudes De Dicto and De Se

According to the Property Theory of content, the contents of our beliefs, desires, etc. aren't propositions, but properties. The contents of de se, or irreducibly first-personal, beliefs are properties we self-ascribe; if I believe that I myself am the messy shopper, I self-ascribe the property of being the messy shopper. If I merely believe de dicto (or even de re) that Jason is the messy shopper, then what I believe is the property of being such that Jason is the messy shopper. If I'm suffering from selective amnesia and have forgotten who I am, I may believe the latter without believing the former.

I like the property theory. I'd like to believe it. I've even defended it against objections. But I'm worried that it's motivations are going to over-generate. The property theory can be thought of as taking thoughts best expressed with one indexical expression -- "I" -- and inserting a slot into the content of this thought for the bit associated with that expression. (E.g., "I am the messy shopper" expresses the content ____ is the messy shopper.) I'm worried the argument that gets us to add in this slot is going to drive us to add in other slots as well.

Consider what I take to be the strongest case for the property theory: Lewis's ("Attitudes De Dicto and De Se", 1979) case of the two gods. Zeus lives at the top of the mountain; Poseidon lives at the bottom of the deepest ocean. They both know all the true propositions. But neither knows who he is. Zeus knows that Zeus is at the top of the tallest mountain; but he doesn't know that he is at the top of the tallest mountain. Since he knows all the true propositions (Lewis argues), and since if he did know that he was at the top of the mountain he'd have a (new) true belief, whatever content Zeus fails to be belief-related to must not be a proposition. But properties: those could do the job. Zeus could believe all the propositions but not believe the property being on top of the mountain.

Properties aren't the only way to handle Lewis's two-gods case. We could instead have belief as a triadic relation between, roughly, a believer, a proposition believed, and a way of presenting that proposition to oneself. Then Zeus might believe the proposition that Zeus is on top of the mountain under one mode of presentation, but not under another, first-personal, mode. Why prefer the property theory to this one? Neil Feit (Beliefs About the Self, 2008) argues (inter alia) that the property theory is just more streamlined, more elegant, than the triadic theory. We'll come back to this in a mo.

Here's the case that's worrying me. We have one god, who is sitting in front of two ghostly spheres -- call them Bo and Luke. They're intrinsic duplicates and, gosh, wouldn't you know it, they're occupying the exact same region right now. But one of them is going to move here in a minute.

Beings like us will have a hard time ostending one of the co-located spheres. But that's no problem for a god! So this god ostends one of them and says, "I wonder if that one is going to be the one that moves in a minute."

It looks like we can repeat the Lewis-style worries here. Our curious god -- call her Daisy -- might well know that Bo is going to move in a minute, but not know whether she is ostending Bo or Luke. Indeed, it looks like she might know all propositions, but still not know whether that sphere is going to move in a minute. So -- by parity of reasoning -- if Lewis's gods case drives us to add a slot in for irreducible "I"-thoughts, shouldn't the Bo and Luke case drive us to add in a slot for irreducibly demonstrative thoughts? But I take it this would be a disaster (once we see the trick, it's a good bet this will get out of hand pretty soon), so we should resist drawing the property-theory lesson from Lewis's two gods case.

I expect the property theorist to respond: "If we're already property theorists, we can find a property that Daisy doesn't believe: the property of ostending Bo. Once she comes to know that property, since she also knows that Bo will move in a minute, she will be in a cognitive state that she is not in now --- and it's one that can serve the role of 'knowing that that sphere will move in a minute'".

But the simplest version of this won't work. Suppose Daisy wonders, "Will it be that sphere or that one which moves in a minute?", respectively ostending Bo and Luke in the process. Even if she knows that she has ostended Bo during her wondering, this won't improve her cognitive state (because she has also ostended Luke). So the property theorist will have to resort to a more linguistically fine-grained property for Daisy to believe, one along the lines of "the property of having first ostended Bo and then ostended Luke", or something like that.

I don't have any argument the property theorist can't make this move work. I rather suspect he can. What I want to point out now is that the property theorist is now relying on properties that seem to be close to the triadic theorist's modes of presenting a proposition. That is: there will need to be some sort of quasi-syntactical specification of the thought that Daisy is having, so that Daisy can learn how parts of this thought are related to the world (e.g., that this part is related to Bo, and that one is related to Luke). This isn't the same thing as the triadic theorist's view by a long shot; but it makes use of many of the same sorts of resources.

But once we're going down this line as property theorists to deal with Daisy's ignorance, what happens to the objection to the triadic theorist's treatment of Zeus's ignorance? The triadic theorist, in essence, says that Zeus doesn't know his mental tokens of "I" pick out Zeus; the property theorist (on the envisaged response) says that Daisy doesn't know that her (particular) mental tokens of "that" pick out Bo and Luke, respectively. If we're going down this line anyway, why not be triadic theorists from the get-go? Maybe the triadic theory is ugly, but if the property theory has to partake of this same ugliness, then there's no argument from ugliness in favor of properties over modes of presentation. And the property theory in fact looks worse, because the triadic theorist can treat what seem like similar phenomena -- indexical ignorance -- in a similar fashion, whereas the property theorist treats some cases of indexical ignorance very differently than others.

AHRC studentship on metaphysical indeterminacy.

Elizabeth, Robbie and I have received a grant from the AHRC for a three year project on metaphysical indeterminacy. We are very excited about this! Part of this includes a PhD studentship. This will be an excellent opportunity, as the PhD student attached to the project will benefit from contact with the excellent group of international and UK philosophers we've got signed on to be involved! Unfortunately, there's a very short time until applications are due. Application details follow.

AHRC Project Doctoral Studentship, Metaphysical Indeterminacy

The Department of Philosophy at the University of Leeds invites applications for an AHRC-funded doctoral studentship, tenable from October 2010.

The award will be held as part of the AHRC-funded project ‘Metaphysical Indeterminacy’. The successful applicant will engage in research on a topic in the philosophy of indeterminacy, such as the metaphysics of indeterminacy, the logic or philosophy of language of vagueness, etc. The research undertaken by the award holder will contribute to the larger project, directed by Drs Elizabeth Barnes, Ross Cameron and Robert Williams. The chosen candidate will benefit from contact with national and international experts in metaphysics, the philosophy of logic and language and related fields through the programme of international visitors, seminars and workshops funded by the project.

Studentship Information

The studentship is tenable for up to 3 years (full-time) from 1 October 2010. Renewal of the studentship each year is subject to satisfactory academic progress.

AHRC regulations require that applicants must meet UK residency criteria or be ordinarily resident in the EU. EU candidates are normally eligible for a fees-only award, unless they have been ordinarily resident in the UK for 3 years immediately preceding the date of the award. Applicants should normally have, or be studying for, a Master’s degree in Philosophy. Further details concerning eligibility are available via the AHRC website. (PDF link)

Full awards cover academic fees at the standard UK rate and a maintenance grant for full-time study.

Applications

The closing date for applications is Friday 27th August 2010. You should also arrange for two academic references to be sent to us by this date.

Applications should be made using the standard postgraduate research degree application form, which is available for download (Word doc link). The following documents should be submitted with your application: 500 word PhD proposal; a copy of your degree transcripts (or a transcript of your marks to date if you are currently completing a degree); a sample of written work, consisting of a philosophical essay on a question of your choice, not less than 3000 words in length; CV.

All applications and references should be sent to Jenneke Stevens, Postgraduate Secretary, Department of Philosophy, University of Leeds, Leeds LS2 9JT, email: J.M.Stevens@leeds.ac.uk, tel: +44 113 343 3263.

Intending applicants should contact Dr Ross Cameron (r.p.cameron@leeds.ac.uk) for information about the studentship.

Lewisian realism and modal reduction

I’ve posted a draft of a new paper that, among other things, defends Lewis against the charge that he needs to employ primitive modality in order for his modal realism to be successful, thus undermining his claims to reduction. One thing I argue is that Lewis’s objectors fail to adequately distinguish two tasks: giving an account of what possibility is, and giving an account of the extent of possibility. The tasks are crucially different and, in my opinion, neither requires for its success the meeting of the other. In particular, an account of what possibility is can stay silent on the extent of what is possible.

So consider the Lycan/Shalkowski objection that Lewis needs a modal understanding of ‘world’ to ensure that there is the correct correspondence between worlds and possibilities, necessary for the material adequacy of Lewis’s account of possibility as truth at a world. Lycan says that Lewis needs ‘world’ to mean ‘possible world’ to rule out the inclusion of impossible worlds in Lewis’s ontology. Shalkowski says Lewis needs the notion of a world to be modal to ensure that the space of worlds is complete: that there are no worlds missing.

I think that’s wrong. What ensures that there are no impossible worlds is Lewis’s account of what possibility is. To be possible just is to be true at a world, so there’s simply no question of there being an impossible world for Lewis. Whatever worlds there happen to be, those worlds will all be possible and none of them impossible, because that’s just what possibility is. Similarly, there’s no question of there being a world missing – of there being a possible circumstance with no corresponding world. But what accomplishes this is not a modal understanding of ‘world’ but, again, Lewis’s account of what possibility is.

It just falls out from Lewis’s analysis that there’s no impossible world, and no possible circumstance unrepresented by a world. Now, here’s what doesn’t fall out from the analysis: that there’s no world with a round square as a part, or that there’s a world with a talking donkey as a part. But contra what Lycan and Shalkowski think, this doesn’t mean that Lewis’s analysis leaves it open that there are impossible worlds or not worlds enough for possibility. If it turns out that there’s a world containing round squares then this is not for it to turn out that there’s an impossible world, according to Lewis’s analysis – it’s for it to turn out that round squares are possible after all! Likewise, mutatis mutandis, if it turns out that there’s no world containing a talking donkey.

Now, Lycan and Shalkowski might complain that any analysis of modality that says that round squares are possible and talking donkeys impossible is not acceptable. Well maybe that’s right. But Lewis’s analysis of course doesn’t say this: it just doesn’t settle that round square are impossible or talking donkeys possible. But that’s fine: the account of what possibility is needn’t settle these claims about the extent of possibility. To demand that Lewis’s analysis settle these facts is to demand too much of analysis: it’s to confuse the two tasks that should be kept separate.

You might think that we need to be able to acquire warrant for thinking that there are no worlds with round squares and that there are worlds with talking donkeys if Lewis’s analysis is to be warranted in the first place. Well, again, that’s fine: Lewis has given us an argument for thinking that the space of worlds is like this. (Namely, that the posit that it is so is theoretically beneficial.) But it’s nothing about the meaning of ‘world’ or the nature of worlds that settles that the space of worlds is so, and nor need it be, since an account of what possibility is needn’t entail an account of the extent of possibility.

I think a similar thing is going on in Divers and Melia’s objection to Lewisian realism. Their argument is as follows. They assume that it’s possible for there to be alien natural properties, and so Lewis’s principle of recombination doesn’t give us a complete account of what worlds there are. Now, it seems that if there could be alien natural properties, there should be no finite bound on the number of possible alien natural properties out there. It seems ad hoc to say there are exactly 17, or a billion, alien natural properties in the multiverse; and so it seems that if we accept the possibility of alien properties in the first place, we should hold that for any finite natural number n, there are at least n alien properties to be found across the space of worlds. But once this is granted, argue Divers and Melia, there is no way to give in non-modal terms a complete account of what worlds there are. For we can’t just say that there are infinitely many alien natural properties spread across the worlds; or that for any finite n there is a world where n distinct alien natural properties are instantiated. Why not? Well, to satisfy those tenets there has to be, across the space of worlds, a denumerable sequence of alien natural properties P1, P2, . . ., Pn. Now, let S be the set of all the worlds that there are. S satisfies both those tenets, of course; but so does the set S* which is the subset of S containing all the members of S except those worlds where, say, P1 is instantiated. Because with P1 missing, there are still of course infinitely many alien properties left; so any tenet you laid down to tell you that there were infinitely many alien natural properties out there in the space of worlds won’t be able to discriminate between it being P1, P2, . . ., Pn that exist across the worlds or merely P2, . . ., Pn that exist. And so there is no tenet you can lay down that will completely yield all the worlds that there are. Unless, of course, we say something like ‘All the possible alien natural properties are instantiated somewhere across the space worlds’. And so the only way to completely say what worlds there are is to invoke primitive modality.

I think Divers and Melia’s argument that the Lewisian is not going to be able to give a complete account of the space of worlds in non-modal terms is pretty convincing. But unlike them, I see no reason to think this casts doubt on the reductive ambitions of the theory. Why should we demand that the Lewisian be able to give a complete non-modal account of what worlds there are? Given the Lewisian analysis, that’s to demand a non-modal account of the space of possibilities. But why should we demand this? To say what it is to be possible is one thing, to say what is possible another. Maybe no complete account of the space of possibility can be given: that should lead us only to epistemic humility, not to abandon a reductive account of what it is to be possible.

The paper goes into these issues in more detail, as well as making some methodological remarks about how to assess whether something can appropriately be included in a reductive basis. Comments on any of it would be welcome.

Yagisawa Book

I've written a critical study of Takashi Yagisawa's Worlds and Individuals, Possible and Otherwise for Analysis Reviews. Mostly, I try to get clear on the differences between Yagisawa and Lewis, and argue that Lewis has the upper hand: if anyone's interested, it's here. Comments welcome.

An argument against Platonism

Here’s a quick argument against Platonism about mathematical ontology.

Premise 1: For everything that exists, it is conceptually possible that it not exist.

Premise 2: If Platonism is true then the truth of ‘9 is not prime’ depends on the existence of the number 3.

Premise 3: If the truth of p depends on condition X and it is conceptually possible that X not obtain, then it is conceptually possible that p is false.

Premise 4: No conceptual truth is such that it’s conceptually possible that it’s false.

Argument:

1. Platonism is true. (Assumption.)

2. The truth of ‘9 is not prime’ depends on the existence of the number 3. (From (1) and Premise 2.)

3. It is conceptually possible that the number 3 not exist. (From (1) and Premise 1.)

4. It is conceptually possible that ‘9 is not prime’ is false. (From (3) and Premise 3.)

5. ‘9 is not prime’ is a conceptual truth. (Assumption.)

6. Contradiction. (From (4), (5) and Premise 4.)

7. Platonism is not true. (From (1) and (6).)

This argument is valid and rests only on premises 1-4 and the assumption that it’s a conceptual truth that 9 is not prime. I won’t consider challenging that assumption here: it seems to me absurd to deny that it’s a conceptual truth about 9 that it is divisible by a factor other than itself or 1. So the Platonist must deny one of the four premises. Premise 4 is analytic, so it’s premises 1-3 that are of interest.

Premise 3 seems to me to be overwhelmingly plausible. How could it be conceptually necessary that something be true whilst being conceptually possible that the conditions required for its truth not obtain? If it’s conceptually necessary that a thing, A, is a certain way, F, then the truth of ‘A is F’ is guaranteed by our very concept of what A (and F) is; so if there is any further condition on the truth of ‘A is F’ it simply must be the case that the fact that this condition obtains is also guaranteed by our very concept of what A (and F) is. If it’s conceptually possible that this condition not obtain then either it’s not a condition on A’s being F after all or we should hold off on a judgment as to whether A is in fact F until we know whether the condition is met, in which case ‘A is F’ is not conceptually necessary.

So I think the real action is on premises 1 and 2. Premise 1 is the claim that there’s nothing such that our very concept of that thing guarantees its existence. It would be denied by proponents of the ontological argument for the existence of God – but that doesn’t bother me, since that argument is hopeless. And in any case, defenders of it will likely hold that God is the only being that constitutes such a counterexample, and so the argument will still go through if we build in the assumption that the number 3 is not God. (Even Trinitarians, in declaring that God is 3, probably don’t literally mean that God and the number 3 are numerically identical!) The possible exception of God aside, Premise 1 seems plausible to me. Even if the existence or otherwise of mathematical ontology is a metaphysically non-contingent matter, it still seems to me that it is a conceptually contingent matter: whatever the truth of the matter is between nominalism and Platonism, nothing about our concepts of mathematical ontology rules out that it be otherwise.

Premise 2 is, I think, the best premise to give up. But the thought in favour of it is very simple: when a number is not prime we explain why by appealing to an existential – there is some number other than it or 1 that is its factor. But if existence is in general a conceptually contingent matter then we can make sense of all the numbers existing except those factors. As far as our concepts go, we can make sense of all the numbers existing except 3, in which case there simply is no factor of 9 other than 1 or 9 itself. Were that the case, 9 would be prime. Now, of course, the Platonist can rightly insist that this is metaphysically impossible – but the argument here is that the conceptual possibility is worrying enough.

I think the best thing for the Platonist to do is to resist the thought that the non-primeness of 9 is hostage to fortune to the existence of the number 3: that is, to deny the dependence claim. This would be to claim that the existence of the factors is not a necessary condition on it being true that the number in question is so divisible. So the conceptual possibility of the non-existence of 3 doesn’t threaten the conceptual necessity of 9’s being divisible by 3. But once one does this, one starts to pull apart the truth of mathematical claims from the apparent ontological demands of those truths, which undercuts the motivations for Platonism in the first place. If ‘9 is divisible by 3’ doesn’t depend for its truth on the existence of 3, why think it depends on the existence of 9 either? If we start going down this route, why not just follow it to its natural non-Platonistic end, where the truth of mathematical claims doesn’t depend on the existence of mathematical ontology?

Truthmakers survey

I've posted a draft of a survey-ish paper on truthmakers I've been writing for the Oxford Handbook of Truth; comments welcome!

Truthmaking and In Virtue Of

Suppose you believe in both truthmaking and metaphysical dependence. That is, you believe both that for some true proposition p there is some thing or things which make p true, and that for some true propositions q and r, q is true in virtue of r. Neither relationship, you think, is to be analysed modally: the truth of ‘Necessarily, if A exists then p’ is a necessary condition for A’s making p true, but it is not a sufficient one; likewise for ‘Necessarily, if q then r’ and ‘r is true in virtue of q’.

If you believe all that, it’d be nice if one of truthmaking or in virtue of could be defined in terms of the other, so that we only have one primitive here rather than two. I think the prospects of defining truthmaking in terms of in virtue of are better than vice-versa, and I’d welcome thoughts on this.

How might one define the in virtue of relation that can hold between two true propositions in terms of the makes true relation that holds between a thing and a true proposition? Here are some of the obvious things that come to my mind, and why I don’t like them.

(1) p is true in virtue of q iff q makes p true

Okay, this one is obviously hopeless. For starters, if propositions are necessary existents, this entails that no contingent truth is true in virtue of anything. But even if propositions are contingent existents, presumably their existence is not contingent on them being true; they can exist and be false, and so this definition is still hopeless. Suppose 'X is wrong' is, as the consequentialist says, true in virtue of 'X has bad consequences'; the definition tells us that the latter proposition makes it true that X is wrong. But that proposition can exist and be false (X might have had good consequences), so now we’re committed to thinking that in a world where X has good consequences, X is still wrong, which is exactly the opposite of what the consequentialist wants.

(2) p is true in virtue of q iff the truth of q makes p true

This solves the above problem, but at the cost of admitting weird entities. What type of entity is the truth of q? A truth trope: the particularized truth of the proposition q? Nasty.

(3) p is true in virtue of q iff the state of affairs that q makes p true

That might be okay if there were a state of affairs that p for every true proposition p. But there’s not.

(4) p is true in virtue of q iff (necessarily) whatever makes q true makes p true

No: it’s no part of the definition of truthmaking that every truth has a truthmaker, and we should allow for the possibility that one proposition is true in virtue of another even though neither have truthmakers, as well as the possibility that two propositions lack truthmakers but where one is not true in virtue of the other. And if every truth does have a truthmaker, the definition will entail the wrong result that is true in virtue of any true negative existential, such as , since whatever makes the negative existential true necessarily makes it true that there is something, since everything that makes anything true necessarily makes it true that something exists, since it makes it true that it itself exists.

It doesn’t look to me like there’s a good way of defining in virtue of in terms of truthmaking; but I think truthmaking can be defined in terms of in virtue of. Truthmaker theory says that what is true is grounded in what there is: as I understand it, this is the claim that the totality of truths are ultimately true in virtue of just those truths that are concerned solely with ontology – that is, that any truth at all is ultimately true in virtue of some truth(s) concerning (solely) what there is.

Call the set containing all and only the brute propositions – that is, those that are not true in virtue of anything – BRUTUS. Consider also the set – call it EXISTS – of propositions whose entire content is that some thing, or some things, exist(s): call these propositions pure existence claims. (Pure existence claims will be expressible by sentences of the form ‘a exists’ or ‘the Xs exist’, where ‘a’ is a rigid designator and ‘the Xs’ a rigid plurally referring expression (i.e. it plurally refers in every possible world to the things that are actually the Xs if they exist, and it fails to refer if any of the actual Xs fail to exist.)

We can define truthmaking as follows.

(*) A proposition p is made true by X, or the Xs, just in case either (i) p belongs to BRUTUS & p belongs to EXISTS & p says that X (or the Xs) exist(s) or (ii) There is an x such that (p is true in virtue of x & x belongs to BRUTUS & x belongs to EXISTS & x says that X (or the Xs) exist(s)).

That is: a proposition is made true by some things, the Xs, if and only if it is the brutely true pure existence claim that the Xs exist or it is true in virtue of the brutely true pure existence claim that the Xs exist.

I’d welcome any thoughts on this. Especially if you think there’s a problem with the proposed definition of truthmaking in terms of in virtue of or if you think there’s a good way to define in virtue of in terms of truthmaking.