Indeterminacy workshop, update.

The schedule is now finalised for the first metaphysical indeterminacy workshop, and follows, with paper titles. Again, let me know if you'd like to come.

Fri, Jan 21

1.00-1.15: Arrival and Registration
1.15-2.45: Antony Eagle (Oxford), The Open Future
2.45-3.00: Break
3.00-4.30: Agustin Rayo (MIT), Metaphysical Indeterminacy and the Contours of Logical Space

Sat, Jan 22

10.00-11.30: Carrie Jenkins (Nottingham), Indeterminacy and Analyticity: Blaming Semantics and Blaming the World
11.30-1.30: Lunch
1.30-3.00: Patrick Greenough (St Andrews), Truthmaker Gluts.
3.00: Conference Closes

All talks will be in G23, Baines wing. (Enter the university via the main entrance at the top of Parkinson steps, and there will be signs from there.)

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.

2 questions

Here are two questions I’d appreciate any thoughts on. Firstly, I’ve recently detected an apparent tension in my beliefs. In my paper for Phil Compass on the grounds of necessity, I argue that the Lewisian realist needn’t be worried about the epistemological objection. The objection goes: how could we know what’s (merely) possible if what’s possible is what’s true at a spatially-temporally isolated concrete world – such worlds do not interact with us causally, so how can we come to know what they’re like? Lewis responds by saying that causal interaction is necessary only when the subject matter is a contingent truth – when the claim to be known is a non-contingent matter, causal acquaintance with what the claim is about is not necessary even when the claim is about the realm of concreta. It’s not obvious to me that this is a good reply, but I thought Lewis had a simpler reply available: metaphysical priority is not conceptual priority. To say that what it is for it to be possible that p is for p to be true at some world does not commit us to saying that our epistemic access to the fact that p is possible must go via epistemic access to there being a world at which p. The Lewisian realist needn’t claim we have any way of discovering what’s true at a world independently of discovering what’s possible. Why can’t the Lewisian simply say she knows there’s a world where there’s a talking donkey because she knows that there could be talking donkeys (here appealing to whatever story about modal epistemology that any realist appeals to), and she knows that everything that could be the case is the case at some world (and here she cites the familiar Lewisian reasons for believing that claim)? What’s the problem?

That still seems convincing to me. Here’s my problem. I also find convincing an epistemological objection to consequentialism: were consequentialism true we couldn’t know what’s right or wrong because we can’t know what the full consequences of our actions would be. And it doesn’t seem to me in the least bit satisfying for the consequentialist to say: I know that murdering X will have the worst consequences because I know that murder is wrong – metaphysical priority isn’t epistemic priority, so my knowledge that it is wrong can ground my knowledge about the consequences even though what it is for it to be wrong is for it to have the worst consequences.

What I’d like is for the two cases to be disanalogous so I can consistently do what seems to me intuitive: hold the epistemological objection to consequentialism and reject the epistemological objection to Lewisian modal realism. I haven’t been able to convince myself that they’re analogous yet, so any thoughts on this are welcome (even if they’re of the form: they’re obviously analogous, and you’re wrong about the epistemological objection to ____). (Incidentally, I barely know the literature on consequentialism, so if anyone knows what consequentialists say about the epistemological objection, please enlighten me!)

Question 2. I was reminded by Brian’s post about the autonomy in logic issue. There’s a thought that every logical truth should be provable using only the rules governing the connectives in that truth. This is meant to be bad for classical logic because there are classical tautologies like Pierce’s law where the only connective is the conditional but one can’t prove Pierce’s law using only the rules for the conditional. I was thinking about this briefly, and I couldn’t see how the objection could possibly be right. We can do classical logic with just one logical connective: the Sheffer stroke, e.g. Every wff of classical logic – a fortiori every theorem – has a translation into a sentence statable using only the Sheffer stroke, and the translations of the theorems will be provable using only the rules governing the Sheffer stroke, as those are the only rules you have. But it can’t be the case that the acceptability of a logic depends on what connectives you allow yourself to use to state its theorems. The defenders of the objection are obviously going to be unimpressed with such a simplistic response, so my question to those who know more about this than me (= those who know than is written in this paragraph!) is: why not?

Substitutional Quantification and Supervaluations

(Cross-posted with Matters of Subtsance.)

Let U be the (universal) substitutional quantifier: its truth-conditions are

"UxF(x)" is true iff, for every name n, "F(n)" is true.

(Normal quotes are doing double-duty as quasi-quotes here.)

Peter van Inwagen has an argument that we can't understand substitutional quantification. It goes like this:

(1) We can't understand a sentence unless we can specify what proposition it expresses.
(2) The only proposition we know of with the right truth-conditions to be expressed by "UxF(x)" is the proposition that, for every name n, "F(n)" is true. (Call this proposition "UU".)
(3) Friends of substitutional quantification say that UU is not what is expressed by "UxF(x)".
(4) There are no other candidates to be the proposition expressed by "UxF(x)".
(5) So if friends of substitutional quantification are right, we can't understand "UxF(x)".

I want to respond to this argument, but I don't know whether my response rejects premise (1) or (4). So I'll outline the basic idea, and then maybe someone can help me know which premise I'm rejecting.

Suppose some sort of supervaluationism is the right treatment of vagueness, and set aside higher order vagueness. Then a sentence like "Fido is red" doesn't express a proposition simpliciter; rather, it expresses a proposition relative to every precisification of "red".

(Since we can understand "Fido is red", this alone might be enough to lead us to deny (1). But it's not clear how this denial gives us any positive reason to think we should be able to understand substitutional quantification. I want to aim higher. So let's press on.)

The truth-conditions for this sentence with the determinacy operator are:

"Det(Fido is red)" is true iff "Fido is red" is true on every precisification of "red".

Now, we can think about precisifications in a number of ways. One of them is an explicitly semantic way: the precisifications of a term are the precise meanings it can have. But another is a bit more syntactic, relating more precise terms to less. If we have semantic precisifications, we can easily define syntactic ones as follows: T is a syntactic precisification of T* iff T's semantic value is a semantic precisification of T*. If we don't have semantic precisifications, we might take the syntactic ones as primitive, or we might be able to define them some other way (maybe by appealing to metalinguistic predicates like "admits of borderline cases" and some others).

If we have the syntactic understanding of precisification, then we have the truth-conditions

"Det(Fido is red)" is true iff "Fido is R" is true for every term R that is a precisification of "red",

which look remarkably similar to the ones we had for the substitutional quantifier.

So here's my basic idea: think of "x" as a maximally vague name --- a name such that every precise name is a (syntactic) precisification of it. Then think of "U" as a determinacy operator. This gives us essentially the truth-conditions we want.

How does van Inwagen's argument look now, with this understanding of the substitutional quantifiers? That depends, I think, on what we say about the proposition expressed by "Det(Fido is red)". I think there are very good reasons to think that this sentence does not express the proposition that "Fido is R" is true for every term R that is a precisification of red. (One very good reason is that it won't embed right at all --- it might be necessary, say, that Det(Fido is red), even though it certainly isn't necessary that "red" is even a word, much less that it has precisifications. And these thoughts extend to the truth-conditions that go via semantic precisifications, too.) But are we in any position at all to specify a proposition it expresses?

Here I don't know what to say, and this is why I don't know which premise I reject in van Inwagen's argument. On the one hand, maybe we have some recipe for specifying a proposition expressed by "Det(Fido is red)". If so, then we can use the same recipe to specify one expressed by "UxF(x)", and I deny premise (4). Maybe we think "Det(Fido is red)" expresses the conjunction of all the propositions expressed by "Fido is R", where R is a (syntactic) precisification of "red", for instance. If so, then we can say that "UxF(x)" expresses the conjunction of all propositions expressed by sentences of the form "F(a)" for some name "a".

On the other hand, maybe we can't specify any proposition expressed by "Det(Fido is red)". (Maybe we dislike the conjunction proposal for both the "Det" and "U" cases because we think it misses out on the "that's-all"-ish nature of the quantifications involved in the truth-conditions.) Nonetheless, I think it's entirely clear that we understand "Det(Fido is red)". And I also think (but I haven't argued for it) that one way we can come to understand a vague term by learning a recipe for figuring out what its precisifications are, so we can understand what the "x" in "UxF(x)" is doing. But in this case, "UxF(x)" is essentially just "Det F(x)"

There's a lot of details I've left out --- stuff about variable-binding, the viability of the syntactic characterization of precisifications, how to think of modally embedded substitutional quantifications, and so on. But setting these techy details aside, I'm wondering what the right thing to say about the argument is. Or, more to the point, I'm wondering what we should deny when we run a parody argument for our inability to understand the sentence "Det(Fido is red)".

Thoughts, anyone?

Protect research in the UK: sign this petition!

If you think the allocation of research funding should be decided on the basis of research excellence and not on the short-term and narrowly construed 'impact' it's likely to make (as decided in part by non-specialists), then please sign this petition!

CAI and SCQ

I've posted a new and expanded version of my paper arguing that composition as identity doesn't settle the special composition question. It's here; thoughts welcome.

The Northern Institute of Philosophy

The Northern Institute of Philosophy - a research centre at the University of Aberdeen directed by Crispin Wright dedicated to the core areas of analytic philospohy - now determinately exists! It is indeterminately identical to the centre I was a member of during my PhD, so is metaphysically interesting in its own right!

Their website is here, and they have a blog here. An exciting future no doubt awaits!

The REF and 'impact'

We don't often delve into the political side of things on MV, but this is an extremely important issue for philosophy in the UK. As many will know, there used to be the RAE: the research assessment exercise. This consisted of a panel of subject specialists reading and making a judgment on the (self-nominated) four best papers of every academic in the country put forward by their department (in practice, basically all the research active staff). The resulting department ratings controlled how much money they would get. Like any system, it of course had its problems, but it was beneficial in many ways. Departments could no longer afford to simply hire the person with the Oxbridge degree and ignore the non-Oxbridge person with a stack of papers in good places - it made hiring more meritocratic.

The RAE is no more. It is being replaced by the REF. It does not look like a change for the better. One bad change is that the panels are to be more coarse grained: it will no longer be simply philosophers judging philosophers, etc. But the most disturbing issue is that 25% of the grade a paper gets is now going to be on the 'impact' it makes. At least, they *say* it will be determined by the impact it makes: in practice, of course, it can't be, since no-one has a crystal ball - so the least they could do is be honest and tell us straight that 25% of the grade will be determined by its short term impact. At least wear the short-term-ism on your sleeve if that's what we're aiming for now!

"How do you determine the impact of a specific paper anyway?" one might ask. Yeah, good question. These guys need to read their Quine! The simple counterfactual account is obviously problematic (even putting aside epistemic problems). All signs point to a focus on narrow, direct, short term impact being what's going to be relevant. A disaster!

Alan Weir wrote on open response to the REF that's available here. It's well worth reading: I want to quote a section.

"The taxpayer can see how funding researchers to investigate solutions to
some immediate problem, a virus say, can be justified. But how can the
funding of pure research be justified? Well, since the research is carried
out for its own sake, those involved will think that centuries-long
traditions of transmitting a body of work of enormous intellectual,
cultural and artistic merit from one generation to the next is of great
value in its own right. But to the sceptical taxpayer we have a very
potent additional point to make. What if Albert Einstein, Max Planck,
Werner Heisenberg, Erwin Schrödinger, in trying to determine how the
mysterious sub-nuclear world of quantum physics worked, had been
constrained and directed by whether their research satisfied short-term
impact criteria? What, to move closer to my own area, if Gottlob Frege,
Bertrand Russell, and Kurt Gödel and others who devoted their lives to
investigating the nature of mathematical truth, logical consequence and
the light formal artificial languages can shed on them (and with no
thought to the possibility of automated reasoning machines of the type the
philosopher Leibniz had sketched) had been required to demonstrate the
impact their researches would have outside academe? Then no quantum
physics and modern micro-electronics, no artificial languages, recursion
theory and computer science; we would have likely remained at the level of
Victorian science and technology and all the practical, medical and
intellectual advances which microelectronics and computing have given us
would not have emerged. Even taxpayers with no desire at all to be
Socrates dissatisfied can see the enormous impact (though not on the
ludicrously short scale of ten to 15 years) these
investigations, driven by pure intellectual curiosity, have made by
comparing today’s technology with late Victorian.

It is essential to grasp that the unintended consequences which emerge
from pure disinterested research have arisen because they were precisely
that: the research was not being directed at all to go towards immediate
practical goals."

Hear hear! The 'impact' research makes is both a long term issue, and a holistic one: one simply cannot separate out the impact made by the research activity of mankind and parcel it out paper by paper. To try to do so is simply nonsense, especially on the ridiculously short time scale it would need to be for it to be relevant for funding purposes.

Let's hope sense wins out and the research community in philosophy and elsewhere is not forced to bow to the whims of petty short term thinking, looking only to immediate and foreseeable commercial gain.

Update: There's a good post on this at Logic Matters.

Update 2: Of course, it's not just philosophers who should be worried. The Guardian quoted some reasonably concerned physicists too - even the subjects where you'd expect it would be easier to demonstrate 'impact' still, sensibly, don't want to have their research agenda to be driven by that.

Fine on essence

I've put online a draft of a paper I'm writing for Phil Compass on the grounds of necessity. Comments on anything in it are welcome, but I'm going to post here some of the stuff I say about Kit Fine's reduction of modality to essence, since I'd especially welcome thoughts on that. So here's Fine:

"Necessity has its source in those objects which are the subject of the
underlying essentialist claim. . . We should view metaphysical necessity
as a special case of essence. . . . The metaphysically necessary truths
[are] . . .the propositions which are true in virtue of the nature of all
objects whatever."

Here are three thoughts (none intended as anything like insurmountable objections, just things to think about):

1) Prima facie, the view seems to require us to accept the existence of things like properties and relations, and thus appears to be incompatible with nominalism. For what entity can we plausibly say has a nature such as to guarantee the
truth of ‘If there are some things, there is a set of those things’ if not the
relation being a member of? No collection of actual individuals guarantees the
truth of that, because the claim says something about what happens no matter
what individuals are around.

2) If it’s necessary that there couldn’t be certain (kinds of) individuals
(universals, say, or God) then we must admit that some of the things that exist
have natures that exclude the existence of other things. You might find this
harder to accept than the claim that some things have natures that guarantee
the existence of other things. (Cf. the familiar objection to admitting
truthmakers for negative existentials: intuitively, they are true because some
things don’t exist, not because some thing does. Similarly, impossible
existents are impossible, intuitively, because there’s something about them
that’s impossible, not because, e.g., there’s something else whose essence is
such as to make them impossible.)

3) It’s easy to see how the essence of an entity e can account for the necessity of
a conditional the antecedent of which says that e exists. So my essence
grounds the truth of, hence accounts for the necessity of, ‘If Ross exists, he is
a human’. From this, it’s easy to see how unconditional necessities can be
grounded if the thing whose essence accounts for its truth has existence as part
of its essence. So were I an essential existent, my essence would account for
the necessity of the antecedent of the above conditional as well, and hence
account for the necessity of the consequent. But we might want to allow for
cases where an unconditional necessity is ‘multiply realized’ in the following
way. Suppose 2+2=4 is actually true in virtue of the essence of the numbers 2
and 4. So we account for the necessity of ‘If the numbers exist, 2+2=4’. But
it’s not just conditionally necessary that 2+2=4, ‘2+2=4’ is itself necessary.
But on this view, that’s not because the numbers exist necessarily: on this
view, while our actual world is Platonist, and mathematical truths are true
because of the numbers, structuralism is possibly true and ‘2+2=4’ is true in
virtue of the essence of certain structures, and maybe in some worlds there are
brute mathematical laws, and ‘2+2=4’ is true in virtue of these laws. So there
are multiple possible grounds for the arithmetical truth, and the truth is
necessary because it’s necessary that there is some ground or other. But what
actual things have essences such as to ground this last necessary truth? The
worry is that Fine can only account for conditional necessities or
unconditional necessities which are unconditionally necessary because there is
some essential existent that accounts for their truth in any possible circumstance.

Jobs at Leeds

Leeds will be hiring two new positions in the upcoming hiring round, at either lecturer or senior lecturer level (for US readers: roughly equivalent to a tenured assistant prof and an associate prof, respectively). Details below.

University of Leeds
Faculty of Arts
Department of Philosophy

2 Lectureships/Senior Lectureships in Philosophy
(Available from 1 September 2010)

The Department of Philosophy is one of the largest Philosophy departments in the UK, with over 30 academic staff, a large intake of undergraduate and postgraduate students and a vigorous research culture. It received a maximum 24 in the last Teaching Quality evaluation and in the 2008 Research Assessment Exercise 65% of our research was rated "world class" or "internationally excellent" (matching the percentage of leading UK philosophy departments such as Oxford and Cambridge). The Department has distinctive strengths in aesthetics, history and philosophy of science, metaphysics, and moral philosophy.

The ‘Area of Specialisation’ for this position is open, within Philosophy. Potential candidates are strongly advised to consult the department’s website for details of its research and teaching programmes.

The position will incorporate undergraduate and postgraduate teaching, some thesis supervision, and usual non-teaching duties. With a strong record of research publication, the successful candidate should be qualified to masters level or equivalent. A PhD prior to application and teaching experience are strongly preferred for a Lectureship and are essential for a position at Senior Lecturer level.

For general information see http://www.philosophy.leeds.ac.uk/

Lecturer - University Grade 7 (£32.458 – 35,469 p.a.) or University 8 (£36,532 – 43,622 p.a.) Senior Lecturer - University Grade 9 (£44,930 – 52,086 p.a.)

Informal enquiries to philosophy-hod@leeds.ac.uk or tel: +44 (0)113 343 3260

To download an application form and job details please visit www.leeds.ac.uk and click on ‘jobs’. Alternatively these may be obtained by email from recruitment@adm.leeds.ac.uk or tel: +44 (0)113 343 5771.

Job ref 318050 Closing date Wednesday 11th November 2009

Presentations and Interviews will take place on Monday and Tuesday 18th and 19th January 2010

Applicants should submit the completed application form, full CV, and a writing sample (of no longer than 25 pages) by the closing date of 11th November.

Presentism, Truthmakers and Theoretical Virtues

I’m just back from the BSPC where I gave my Truthmaking for Presentists. I got loads of good questions of and comments, but wanted to comment on one of them. In the paper I argue that truthmaker theory can be contingently true and hence that it’s no immediate objection to my view if there are possible presentist scenarios in which my account doesn’t work, so long as we can reasonably believe that they are not actual. (The scenario in question discussed in the paper is a presentist world with an infinite past.)

One of my commentators, Caspar Hare, was pushing me on whether I thought it was similarly okay for the truthmaker principle to simply be true now. He was expecting me to say yes – but I say no, it must be true always; and he was rightly pushing me to say why one should demand that the principle be true at all times but not at all worlds when one holds a view that treats times and worlds analogously in holding that only one of each (the present time, the actual world) is real.

For me the reasons to be a truthmaker theorist concern theoretical virtues. Truthmaker theory is the theory that all the brute truths are truths about what there is, and this is theoretically more virtuous than theories that take as brute truths not only about what there is but also truths about what there was, could be, should be, etc, as well as truths about how things are, what laws hold, etc, etc. If truthmaker theory is true, God’s language only needs names and an existence predicate: that’s ideologically simpler, and hence more virtuous (other things being equal), than theories which require God to be able to make predications, express tensed facts, etc.

I think that in the absence of further information, if the only reason to believe a theory is that it is theoretically virtuous, then we should take that theory to be at best contingently true. There’s no inconsistency in a theoretical virtue selecting a necessarily true theory, but we’d need some reason to think that it does in any particular case. In general the world needn’t have cooperated with what is theoretically virtuous: being guided by simplicity, parsimony etc might have taken us badly wrong – we just hope it doesn’t actually do so. That’s why I only hold truthmaker theory to be a contingent truth. (It’s also why I hold the contingency of composition, and the contingency of whether there is a fundamental level.)

But it seems to me that satisfaction of the theoretical virtues makes a demand on how the world is across times, not just at the present time, even if the present is all that is real. Suppose we’re faced with two theories, T1 and T2. T1 says that there are always 10,000 things. T2 says that there are now only 100 things but that at all other times there are billions. It seems to me that the presentist doesn’t get even a pro tanto reason to accept T2 on the basis that it says that there are fewer things in reality. (I’m assuming quantitative parsimony is a virtue – replace talk of number of things with number of kinds of things if you don’t.) Sure, the present is all that there is, and T2 says that there are presently 100 things whereas T1 says that there are presently a hundred times as many things. But the presentist should still be moved, I think, by the fact that according to T2 reality just was, and is soon to be again, massively more unparsimonious than T1 says it is. The fact that those times aren’t real shouldn’t make us worry any less about that. (By contrast, if T3 and T4 agree on what actually exists but T4 says there are more possibilia than T3 does, this only gives us even a pro-tanto reason to prefer T3 if we are realist about possibilia.)

I think that what’s driving this thought is an idea that Kit Fine pushes in his fantastic paper ‘Tense and Reality’: that everyone should think of non-present times as part of the same ‘all encompassing reality’ whereas only the realist about possibilia should think that about worlds. Now Fine takes that as a reason to deny that the present time is privileged, and so to be a non-standard realist if you’re going to be a realist about tense; but I think that one can still accept that thought and accept a privileged present. One just needs to accept that what’s going on at other times is relevant to how we judge theories in a way that what’s going on at other worlds is not (at least, not in the same way).

So parsimony doesn’t tell the presentist to accept T2 over T1, and if the truthmaker principle is only true now it doesn’t tell the presentist to be a truthmaker theorist. The virtues of truthmaker theory are only obtained if it is always true; by contrast, whether it is necessarily true are neither here nor there, as far as securing those virtues is concerned.

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.