Counterpart theory and the incarnation. Cos why not?

While I generally try and avoid the philosophy of religion unless I'm bored of an afternoon, this year I have been teaching 'metaphysical issues in religion', and so have been forced to get to grips with some of the issues.

One issue that's not been uninteresting is a familiar problem regarding God’s incarnation as the man Jesus Christ. Christ is both human and divine. This is to say that he has a human nature and a divine nature. As the Council of Chalcedon put it in 451AD, "the same Christ . . . [is] to be acknowledged in two natures . . . the characteristic property of each nature being preserved, and concurring in one person."

The threat is that this leads quickly to outright contradiction. Associated with the divine nature are properties of perfection, such as omnipotence, omniscience and omnibenevolence; but associated with the human nature is the absence of such perfections. Humans are neither omnipotent, omniscient nor omnibenevolent. And so we seem driven to saying that Christ both is omnipotent, omniscient and omnibenevolent (in virtue of being divine) and not omnipotent, omniscient or omnibenevolent (in virtue of being human): a contradiction three times over!

How to respond? One option is to deny that it follows from having a human nature that one doesn’t have any of the qualities of divine perfection. Certainly, it is no part of the human nature that a human have these qualities: but it hardly follows that in virtue of being human a thing must lack those qualities – being human might simply be silent as to the presence or absence of the divine perfections. In that case Christ’s humanity simply doesn’t speak to his having or lacking omnipotence, omniscience and omnibenevolence. As far as his human nature is concerned, it is simply an open question whether he has those properties or not. The door is closed, however, because of his divinity, which ensures that he does indeed have them. And so Christ simply has the divine perfections, and there is no threat of contradiction.

Such a view is taken by Thomas Morris. Morris distinguished between being wholly human and merely human. Christ is wholly human because he belongs to the kind human. And if it makes any sense to speak of things as partially belonging to a kind, Christ does not only partly belong to it, he wholly belongs to it. But he is not merely human. To be merely human is to have no more essential properties that what are guaranteed by being a member of the kind human; and Christ does have more, because he also has the properties that are guaranteed by his divinity.

This view avoids the paradox, but at a cost. There is a strong temptation to hold not only that being human doesn’t entail the possession of the divine perfections but that it entails their absence. To say otherwise, after all, is to invite the theologically immodest claim that even we mere humans might have been omnipotent, omniscient and omnibenevolent. We are not in fact as God is; but we could have been.

But also, there is some desire to be able to say that Christ the man lacked them. Think of Christ in Gethsemane: it appears for all the world to be the story of a man who is worried about the future. But why would such concerns arise unless Christ lacked knowledge about how things would turn out? Think now of Christ being tempted by Satan: it appears for all the world to be a story about a man overcoming temptation. But unless there was the possibility of his succumbing, there was nothing to overcome. And so the threat of contradiction is pressing. Christ, we want to say, is both limited and unlimited, both perfect and flawed. How can this be?

One thing we might be tempted to say is that Christ has the divine perfections qua God but not qua man. But what do such locutions mean? Well, there’s a familiar story about how that can be the case; and surprisingly it has received no discussion, to my knowledge, in this context. I want to put this option on the table: the option is counterpart theory.

Compare the case of Christ and omnipotence with a familiar case which is structurally analogous: the case of the statue and the clay. The clay can be squashed but the statue cannot. And yet many of us feel the pressure to say that there is only one entity here: the lump of clay simply is the statue. How, then, are we to avoid the absurdity that one and the same thing both has and doesn’t have the property of squashability?

As above, there is a temptation to say that this one thing is squashable qua lump of clay but not qua statue. But what does this mean? Counterpart theory gives us an answer. The properties of this one thing remain constant, but whether any of its properties deserve to be called the property of squashability depends on contextually variant factors, which means that whether or not the entity satisfies the predicate ‘. . . could be squashed’ can itself vary from context to context. When we speak of the one thing as the clay, this is enough to make salient the clay-ness of the entity, and in such a context one of the properties had by this entity deserves to be called the property of squashability, which is why we speak truly when we say that the clay could be squashed. When we speak of the one thing as the statue, on the other hand, this is enough to make salient the statue-ness of the entity, and in such a context none of the properties had by this entity deserves to be called the property of squashability – including the one previously correctly so described! This is why we speak truly when we say that the statue could not be squashed. And this is what we mean when we say that the entity can be squashed qua lump of clay but not qua statue.

That is enough to show that there need be no inconsistency in saying in one context that an entity satisfies some predicate and in another that it lacks it (despite not having undergone change): to generate an inconsistency one needs the further assumption that the property being picked out by that predicate is the same in both contexts. Since the predicate ‘. . . could be squashed’ is picking out a different property depending on whether the subject is referred to as the statue or as the clay, there is no inconsistency in saying that the statue couldn’t be squashed but that the clay could, even though they are one and the same thing. Likewise, if ‘. . . is omnipotent’, ‘. . . is omniscient’ etc pick out a different property depending on whether the subject is referred to as God or as man then there is no inconsistency in saying that Christ the man lacks omnipotence and omniscience etc and that Christ the God possesses them, even though the God is the man.

Omnipotence is a modal property like squashability: it is the property of being able to do anything possible. One needn’t actually do every possible action to be omnipotent, it simply has to be within one’s powers, which is to say that for any possible action one could do it. In that case, the counterpart theoretic solution can simply be carried over to the case of Christ and omnipotence. It is true to say that Christ the God is omnipotent and false to say that Christ the man is omnipotent. Why? Not because there are two entities, but because different standards of similarity are invoked depending on whether it is the divine or the human characteristics of one and the same entity that are made salient. If Christ’s divinity is salient then no possible being would count as dissimilar to Christ in virtue of doing some possible action – and so, for any possible action, there is a counterpart of Christ that performs that action, which is why Christ satisfies ‘. . . is omnipotent’. But if Christ’s humanity is salient then beings that perform miraculous feats like creating the universe ex nihilo don’t get to count as Christ’s counterparts, since humans just can’t do such things. And so, in this context, it will be true to say that there are things that Christ (the man) just couldn’t do, and thus true to say that he is not omnipotent.

Does the counterpart theoretic story carry over to the other divine perfections, such as omniscience and omnibenevolence? I think the prospects aren't terrible. It is easy to construe such predicates as being implicitly modal. It is no stretch of the imagination to suggest that to be omnibenevolent it is not enough simply to have managed not to actually do anything wrong: rather, one must have had the disposition to act rightly no matter what the circumstances. (You don’t get to be omnibenevolent by moral luck!) And so whether an object satisfies ‘. . . is omnibenevolent’ depends on whether or not that object has counterparts that do wrong things, and so the above story applies. Likewise with omniscience: it’s not enough simply to know all truths – the omniscient being would know even the propositions that are actually false, had those propositions been true. And in general, when we’re dealing with the divine perfections, they will concern not just how the bearer actually is but how it could have been. Perfection implies a counterfactual robustness – you don’t get to be perfect y accident. God’s perfection with respect to knowledge or power or etc concerns how he is and how he could and must have been: a being does not get to share in these properties by virtue of chance or luck. And as soon as one insists on counterfactual robustness one makes these predicates modal, which invites the counterpart theoretic solution to the threatening paradox.

What about God’s actual knowledge of all actual truths? Don’t we want to deny this to Christ the man as well? (Consider his apparent lack of knowledge, in Gethsemane, as to how the future would turn out.) If so, then to run the above story we must accept a modal account of what it is for an agent to know something. But this is not implausible. It’s what Ryle held, for example. x knows that p iff, roughly, x is disposed to act in a p-believing way in suitable circumstances. Now, of course, Ryle combined this with a behaviourism about the mental and an account of dispositions as brute truths; but we needn’t join him in either of those theses to find plausible the linking of knowledge ascriptions with ascriptions of some complex dispositional. It needn’t be an analysis of what it is for x to know that p for x to be disposed in a certain manner in order for the truth of the knowledge ascription to go hand in hand with the truth of the dispositional ascription. And if the truth of the knowledge ascription is sensitive to the truth of the dispositional ascription then context sensitivity in the latter will result in context sensitivity in the former. Christ the God can be correctly ascribed knowledge that p because all his relevant Godly counterparts act in a p-believing way when in the appropriate circumstances, but Christ the man cannot correctly be ascribed knowledge that p because he has manly counterparts that fail to exhibit p-believing behaviour even when prompted appropriately.

Here's an interesting consequence of the counterpart theoretic view: it commits us to saying that while the second person of the Trinity, God the Son, in fact incarnated as the man Jesus Christ, he might not have done. Counterpart theory, familiarly, commits us to the contingency of identity. The statue is in fact identical to the lump of clay, but it might not have been: had the lump of clay been squashed, it wouldn’t have been identical to the statue. Likewise, Christ the God, the second person of the Trinity, is in fact identical to Christ the man (who is also therefore, given Leibniz’s law, the second person of the Trinity). But Christ the God might not have been identical to Christ the man: had the man been flawed he wouldn’t have been identical to the God. And so whilst Christ the God is essentially the second person of the Trinity, Christ the man is only accidentally the second person of the Trinity.

Regimentation

Here's something you frequently hear said about ontological commitment. First, that to determine the ontological commitments of some sentence S, one must look not at S, but at a regimentation or paraphrase of S, S*. Second (very roughly), you determine the ontological commitments of S by looking at what existential claims follow from S*.

Leave aside the second step of this. What I'm perplexed about is how people are thinking about the first step. Here's one way to express the confusion. We're asked about the sentence S, but to determine the ontological commitments we look at features of some quite different sentence S*. But what makes us think that looking at S* is a good way of finding out about what's required of the world for S to be true?

Reaction (1). The regimentation may be constrained so as to make the relevance of S* transparent. Silly example: regimentation could be required to be null, i.e. every sentence has to be "regimented" as itself. No mystery there. Less silly example: the regimentation might be required to preserve meaning, or truth-conditions, or something similar. If that's the case then one could plausibly argue that the OC's of S and S* coincide, and looking at the OC's of S* is a good way of figuring out what the OC's of S is.

(The famous "symmetry" objections are likely to kick in here; i.e. if certain existential statements follow from S but not from S*, and what we know is that S and S* have the same OC's, why take it that S* reveals those OC's better than S?---so for example if S is "prime numbers exist" and S* is a nominalistic paraphrase, we have to say something about whether S* shows that S is innocent of OC to prime numbers, or whether S shows that S* is in a hidden way committed to prime numbers).

Obviously this isn't plausibly taken as Quine view---the appeal to synonymy is totally unQuinean (moreover in Word and Object, he's pretty explicit that the regimentation relationship is constrained by whether S* can play the same theoretical role as we initially thought S played---and that'll allow for lots of paraphrases where the sentences don't even have the appearance of being truth-conditionally equivalent).

Reaction (2). Adopt a certain general account of the nature of language. In particular, adopt a deflationism about truth and reference. Roughly: T- and R-schemes are in effect introduced into the object language as defining a disquotational truth-predicate. Then note that a truth-predicate so introduced will struggle to explain the predications of truth for sentences not in one's home language. So appeal to translation, and let the word "true" apply to a sentence in a non-home language iff that sentence translates to some sentence of the home language that is true in the disquotational sense. Truth for non-home languages is then the product of translation and disquotational truth. (We can take the "home language" for present purposes to be each person's idiolect).

I think from this perspective the regimentation steps in the Quinean characterization of ontological commitment have an obvious place. Suppose I'm a nominalist, and refuse to speak of numbers. But the mathematicians go around saying things like "prime numbers exist". Do I have to say that what they say is untrue (am I going to go up to them and tell them this?) Well, they're not speaking my idiolect; so according to the deflationary conception under consideration, what I need to do is figure out whether there sentences translate to something that's deflationarily true in my idiolect. And if I translate them according to a paraphrase on which their sentences pair with something that is "nominalistically acceptable", then it'll turn out that I can call what they say true.

This way of construing the regimentation step of ontological commitment identifies it with the translation step of the translation-disquotation treatment of truth sketched above. So obviously what sorts of constraints we have on translation will transfer directly to constraints on regimentation. One *could* appeal to a notion of truth-conditional equivalence to ground the notion of translatability---and so get back to a conception whereby synonymy (or something close to it) was central to our analysis of language.

It's in the Quinean spirit to take translatability to stand free of such notions (to make an intuitive case for separation here, one might, for example, that synonymy should be an equivalence relation, whereas translatability is plausibly non-transitive). There are several options. Quine I guess focuses on preservation of patterns of assent and dissent to translated pairs; Field appeals to his projectivist treatment of norms and takes "good translation" as something to be explained in projective terms. No doubt there are other ways to go.

This way of defending the regimentation step in treatments of ontological commitment turns essentially on deflationism about truth; and more than that, on a non-universal part of the deflationary project: the appeal to translation as a way to extend usage of the truth-predicate to non-home languages. If one has some non-translation story about how this should go (and there are some reasons for wanting one, to do with applying "true" to languages whose expressive power outstrips that of one's own) then the grounding for the regimentation step falls away.

So the Quinean regimentation-involving treatment of ontological commitment makes perfect sense within a Quinean translation-involving treatment of language in general. But I can't imagine that people who buy into to the received view of ontological commitment really mean to be taking a stance on deflationism vs. its rivals; or about the exact implementation of deflationism.

Of course, regimentation or translatability (in a more Quinean, preservation-of-theoretical-role sense, rather than a synonymy-sense) can still be significant for debates about ontological commitments. One might think that arithmetic was ontologically committing, but the existence of some nominalistic paraphrase that was suited to play the same theoretical role gave one some reassurance that one doesn't *have* to use the committing language, and maybe overall these kind of relationships will undermine the case for believing in dubious entities---not because ordinary talk isn't committed to them, but because for theoretical purposes talk needn't be committed to them. But unlike the earlier role for regimentation, this isn't a "hermeneutic" result. E.g. on the Quinean way of doing things, some non-home sentence "there are prime numbers" can be true, despite there being no numbers---just because the best translation of the quoted sentence translates it to something other than the home sentence "there are prime numbers". This kind of flexibility is apparently lost if you ditch the Quinean use of regimentation.

Updates

There are two new papers posted on my homepage. One is my contribution to a symposium in Philosphical Books on Trenton Merricks' 'Truth and Ontology'. Basically, this paper just gives the bite-sized versions of what I think are the best motivations for truthmaker theory and the best accounts of truthmakers for negative existentials, modal truths, and temporal truths in a presentist setting.

The other is the first draft of a paper that Elizabeth and I have written on the open future. Our goal here is to argue that theses that often get run together with the thesis that the future is open are not consequences of it. In particular, we argue that the future can be open and bivalence hold unrestrictedly, determinism about laws be true, and the future exist.

I've also updated my 'Truthmaking for Presentists' paper, to stop it making false claims (or at least to stop it making as many false claims) about here-now-ism (thanks Nolan!).

You should also check out Elizabeth and Robbie's new paper on metaphysical indeterminacy, which is awesome.

Phlox

I just found about about Phlox, a (relatively) new weblog in philosophy of logic, language and metaphysics. It's attached to a project at Humboldt University in Berlin. As well as following the tradition of philosophy centres with Greek names (this one means "flame", apparently) "Phlox" is a cunning acronym for the group's research interests.

There's several really interesting posts to check out already. Worth heading over!

Relative identity at a time

Working at the ancestral home of relative identity, I feel the need to say something about it. The relative identity theorist says that we can’t speak of x and y being identical simpliciter but only identical relative to a sortal, and that while x and y might be the same F they might not be the same G. So, for example, while the foetus in 1979 might be the same biological organism as that typing this blog post, it is not, perhaps, the same person.

Something I was reading recently suggested the following argument against relative identity. The cases that are remotely plausible as being cases of relative identity are (like the one above) cases of identity across time. There are no plausible cases of relative identity at a time. But if that’s the case, we should think that identity at a time is absolute. In which case we shouldn’t think that the relation that is holding across time and is sortal relative is identity at all. And so we don’t really have relative identity: we’ve just got no cases of identity across time, but with a surrogate relation that holds between entities across time and is like identity in some respects but which is sortal relative.

I guess I think that’s a good argument against relative identity if the premise is correct, but I’m not convinced that there aren’t cases of relative identity at a time that are just as plausible as the cases of relative identity across time.

Before I give my case, consider the following situation. Suppose there is a sculptor, Bob. Bob takes a lump of clay at t1 – call it CLAY - and makes it into a statue of a man at t2 – call it STATUE. We have the familiar question as to the relationship between CLAY and STATUE. Some will say that STATUE is a proper temporal part of the CLAY, some that it is distinct but constituted by CLAY. The relative identity theorist, as I understand her, thinks she has a simpler story: STATUE is the same lump of clay as CLAY, but not the same statue (since CLAY is not a statue, and x and y are only the same F if they are both Fs). But that is relative identity across time, of course, not at a time. We don’t get relative identity at a time on this story: STATUE is both the same statue and the same lump as STATUE, and CLAY is the same lump as CLAY, and it doesn’t make sense to either say or deny that CLAY is the same statue as CLAY, since it isn’t a statue.

Now suppose another sculptor, Sara, made a different statue from a different lump. Sara’s sculpture is an intrinsic duplicate of Bob’s sculpture (STATUE), but while Bob’s sculpture is of a man, Sara’s sculpture is of a lump of clay shaped like a man. Sara’s sculpture has aesthetic properties that Bob’s sculpture lacks: her work is a comment on the very nature of art and representation. You can imagine her sipping Merlot out of a teacup and proclaiming the impossibility of separating the signifier from the signified, or something.

Now suppose there is a third sculptor, Jacob, who decided to kill two birds with the one stone and sculpt two statues from the one lump of clay: a statue of a man and a statue of a lump of clay shaped like a man. We know they are two, because they differ in their aesthetic properties. At a single time t after the sculpting is complete, then, there is the lump of clay, LUMP, the statue of a man, MAN, and the statue of the lump of clay shaped like a man, LUMP-MAN. MAN is the same lump of clay as LUMP, and LUMP-MAN is the same lump of clay as LUMP. It seems to follow that MAN is the same lump of clay as LUMP-MAN. Now, the logic of relative identity is somewhat up for grabs, but x is the same F as y and y is the same F as z seem to entail that x is the same F as z. Counterexamples to transitivity should only arise when there’s a change in sortal. And in any case, it’s independently plausible that MAN is the same lump of clay as LUMP-MAN, since there’s only one lump of clay in the vicinity. But MAN is not the same statue as LUMP-MAN – they are distinct statues, for they have different aesthetic properties. So MAN and LUMP-MAN are, at one time t, the same lump of clay but different statues. So we have relative identity at a time.

Now of course there are loads of things we could say without invoking relative identity, such as that the one lump constitutes two statues at this time, or (my preference) that you can’t conclude that there are two statues from a difference in aesthetic properties. But that’s not the point. There’s always an absolutist story one can tell when the relativist would tell a relativist story; my claim is only that this case of relative identity at a time is just as plausible as the alleged cases of relative identity across time, in which case the above argument against relative identity is unsound, and doesn’t give us reason to accept absolutism. (Common sense on the other hand . . . )

Four new appointments at Leeds

I'm delighted to have four new permanent colleagues joining us at Leeds in the near future.

Firstly, there are the appointments of Jason Turner and Pekka Vayrynen to the philosophy section at Leeds.

Jason works on metaphysics, philosophy of action and free will, and the philosophy of logic and language. He is currently finishing his PhD at Rutgers and already has an impressive list of publications in these areas, including publications in Philosophy and Phenomenological Research, Philosophical Studies, and Mind and Language. (Have a peek at them here!)

Pekka is joining us from UC Davis. His main interests are in meta-ethics and value theory, and the overlap between these areas and metaphysics and the philosophy of language. He's published a boatload of really interesting stuff, and will make a fantastic addition to Leeds' new Centre for Ethics and Metaethics.

The division of history and philosophy of science within the department has also recently made two appointments: Juha Saatsi and Sophie Weeks.

Juha works on the philosophy of science. He has published on various aspects of scientific realism, and has recently been working on metaphysical issues arising from the philosohpy of science. Juha has been at Leeds this year on a temporary contract and has been a wonderful colleague, so we're delighted that he'll be staying around.

Sophie is a historian of early modern science, and specialises in Francis Bacon. She's currently working on a monograph on Bacon which, in her words, "focuses upon the close relation between Bacon's matter theory, his inductive method of inquiry, and his moral and political philosophy, whilst drawing attention to his synthesis of Stoic, Epicurean and various Renaissance borrowings."

All will be starting Aug/Sep '08, except Sophie who will be starting in '09, so she can finish her current research fellowship at Cambridge.

UEA wants fuzzy philosophers

The University of East Anglia is advertising for an 'indefinite' lecturer in philosophy. I don't know whether this means lecturers with fuzzy boundaries or vague parts, or whetherit just means lecturers who haven't made their minds up on what they believe yet.

Seriously, what does this mean? Is it obvious to everyone else? Is it for a position such that they don't know how long it's going to last? Is it permanent, and they're saying 'indefinite' because you're not allowed to say 'permanent'? (But then, why not use the standard 'continuing'?) What does it mean?? Oh well, never trust a Wittgensteinian, that's what I say.

Sorry MV has been so quiet of late; normal service will resume shortly.

Structured propositions over at T&T

I'm not going to x-post them all on this blog, but I just wrote up three notes on structured propositions over at Theories and Things that metaphysical folk might have opinions on... here here and here. Any thoughts much appreciated!

Truthmakers and Ontological Commitment (update)

This paper is now forthcoming in Philosophical Studies (special issue devoted to selected papers from the 2007 BSPC).

Truthmaker theorists should be priority monists.

I’ve written a paper arguing that the truthmaker theorist has to be a priority monist, on pain of being committed to mysterious necessary connections. That is, if you think that for every true proposition there is an entity which couldn’t exist and that proposition be false then you should also think that there is only one fundamental existent, with every other entity being ontologically dependent on The One, otherwise you violate my suggested version of the Humean ban on necessary connections.

The full paper is here, and any comments will be much appreciated. But here’s the argument in outline. The first step is to identify when necessary connections are acceptable. A completely die-hard Humean would say: never. I’m interested in how to be less die-hard and still have a principled position (one that can be justified independently of considerations concerning truthmaker theory). One popular option is: necessary connections are bad when they’re between wholly distinct existents, but acceptable when they’re between distinct but not wholly distinct entities – i.e. entities that overlap. I don’t like that. In general, things have the parts they do, and belong to the complexes they do, as a matter of contingency; and if that’s the case then necessary connections between overlapping entities are as mysterious as necessary connections between wholly distinct entities. I suggest instead that necessary connections are acceptable iff there is an appropriate relationship of ontological dependence between the entities. I want to analyse ontological dependence in terms of truthmaking: B is ontologically dependent on A iff B exists in virtue of A’s existence, which is to say just that A is the truthmaker for the fact that B exists. In that case, it’s no surprise if the existence of A necessitates the existence of B – that just follows from truthmaker maximalism. With a caveat that I won’t go into here (but I do in the paper), I suggest we limit the necessary connections in our ontology to those where the necessitated entity is ontologically dependent on the necessitating entity. Those necessary connections are explainable just by what ‘ontological dependence’ means, so if all the necessary connections are of that kind, we’re okay.

If that’s right the argument to priority monism is pretty quick. The truthmaker theorist needs not only truthmakers for atomic truths but also a totality truthmaker that says that all the first-order truthmakers are all the first-order truthmakers. The existence of the higher-order truthmaker necessitates the existence of each of the first-order truthmakers: if it didn’t, it wouldn’t be doing the job it was introduced to do. If that necessary connection is to be explainable, then, the first-order truthmakers must be ontologically dependent on the higher-order truthmaker. The fact that the first-order truthmakers exist must be true in virtue of the existence of the higher-order truthmaker. And so we’re driven to the view that the only fundamental being is the higher-order truthmaker – the totality fact that says how the world as a whole is; other things exist – such as the states of affairs of proper parts of the world being some way – but these will all be ontologically derivative entities, dependent on the totality fact.

I don’t particularly care as to whether one should modus ponens and be a priority monist or modus tollens and reject truthmaker theory. I care about the conditional; any thoughts on it will be welcome.

Nihilism, maximality, problem of the many (x-post)

Does nihilism about ordinary things help us out with puzzles surrounding maximal properties and the problem of the many? It's hard to see how.

First, maximal properties. Suppose that I have a rock. Surprisingly, there seem to be microphysical duplicates of the rock that are not themselves rocks. For suppose we have a microphysical duplicate of the rock (call it Rocky) that is surrounded by extra rocky stuff. Then, plausibly, the fusion of Rocky and the extra rocky stuff is the rock, and Rocky himself isn't, being out-competed for rock-status by his more extensive rival. Not being shared among duplicates, being a rock isn't intrinsic. And cases meeting this recipe can be plausibly constructed for chairs, tables, rivers, nations, human bodies, human animals and (perhaps) even human persons. Most kind-terms, in fact, look maximal and (hence) extrinsic. Sider has argued that non-sortal properties such as consciousness are likewise maximal and extrinsic.

Second, the problem of the many. In its strongest version, suppose that we have a plentitude of candidates (sums of atoms, say) more or less equally qualified to be a table, cloud, human body or whatever. Suppose further that both the sum and intersection of all these candidates isn't itself a candidate for being the object. (This is often left out of the description of the case, but (1) there seems no reason to think that the set of candidates will always be closed under summing or intersection (2) life is more difficult--and more interesting--if these candidates aren't around.) Which of these candidates is the table, cloud, human body or whatnot?

What puzzles me is why nihilism---rejecting the existence of tables, clouds, human bodies or whatever---should be thought to avoid any puzzles around here. It's true that the nihilist rejects a premise in terms of which these puzzles would normally be stated. So you might imagine that the puzzles give you reason to modus tollens and reject that premise, ending up with nihilism (that's how Unger's original presentation of the POM went, if I recall). But that's no good if we can state equally compelling puzzles in the nihilist's preferred vocabulary.

Take our maximality scenario. Nihilists allow that we have, not a rock, but some things arranged rockwise. And we now conceive of a situation where those things, arranged just as they actually are, still exist (let "Rocky" be a plural term that picks them out). But in this situation, they are surrounded by more things of a qualitatively similar arrangement. Now are the things in Rocky arranged rockwise? Don't consult intuitions at this point---"rockwise" is a term of art. The theoretical role of "rockwise" is to explain how ordinary talk is ok. If some things are in fact arranged rockwise, then ordinary talk should count them as forming a rock. So, for example, van Inwagen's paraphrase of "that's is a rock" would be "those things are arranged rockwise". If we point to Rocky and say "that's a rock", intuitively we speak falsely (that underpins the original puzzle). But if the things that are Rocky are in fact arranged rockwise, then this would be paraphrased to something true. What we get is that "are arranged rockwise" expresses a maximal, extrinsic plural property. For a contrast case, consider "is a circle". What replaces this by nihilist lights are plural predicates like "being arranged circularly". But this seems to express a non-maximal, intrinsic plural property. I can't see any very philosophically significant difference between the puzzle as transcribed into the nihilists favoured setting and the original.

Similarly, consider a bunch of (what we hitherto thought were) cloud-candidates. The nihilist says that none of these exist. Still, there are things which are arranged candidate-cloudwise. Call them the As. And there are other things---differing from the first lot---which are also arranged candidate-cloudwise. Call them the Bs. Are the A's or the B's arranged cloudwise? Are there some other objects, including many but not all of the As and the B's that *are* arranged cloudwise? Again, the puzzle translates straight through: originally we had to talk about the relation between the many cloud-candidates and the single cloud; now we talk about the many pluralities which are arranged candidate-cloudwise, and how they relate to the plurality that is cloudwise arranged. The puzzle is harder to write down. But so far as I can see, it's still there.

Pursuing the idea for a bit, suppose we decided to say that there were many distinct pluralities that are arranged cloudwise. Then "there at least two distinct clouds" would be paraphrased to a truth (that there are some xx and some yy, such that not all the xx are among the yy and vice versa, such that the xx are arranged cloudwise and the yy are arranged cloudwise). But of course it's the unassertibility of this sort of sentence (staring at what looks to be a single fluffy body in the sky) that leads many to reject Lewis's "many but almost one" response to the problem of the many.

I don't think that nihilism leaves everything dialectically unchanged. It's not so clear how many of the solutions people propose to the problem of the many can be translated into the nihilist's setting. And more positively, some options may seem more attractive once one is a nihilist than they did taken cold. Example: once you're going in for a mismatch between common sense ontology and what there really is, then maybe you're more prepared for the sort of linguistic-trick reconstructions of common sense that Lewis suggests in support of his "many but almost one". Going back to the case we considered above, let's suppose you think that there are many extensionally distinct pluralities that are all arranged cloudwise. Then perhaps "there are two distinct clouds" should be paraphrased, not as suggested above, but as:

there are some xx and some yy, such that almost all the xx are among the yy and vice versa, such that the xx are arranged cloudwise and the yy are arranged cloudwise.

The thought here is that, given one is already buying into unobvious paraphrase to capture the real content of what's said, maybe the costs of putting in a few extra tweaks into that paraphrase are minimal.

Caveats: notice that this isn't to say that nihilism solves your problems, it's to say that nihilism may make it easier to accept a response that was already on the table (Lewis's "many but almost one" idea). And even this is sensitive to the details of how nihilism want to relate ordinary thought and talk to metaphysics: van Inwagen's paraphrase strategy is one such proposal, and meshes quite neatly with the Lewis idea, but it's not clear that alternatives (such as Dorr's counterfactual version) have the same benefits. So it's not the metaphysical component of nihilism that's doing the work in helping accommodate the problem of the many: it's whatever machinery the nihilist uses to justify ordinary thought and talk.

There's one style of nihilist who might stand their ground. Call nihilists friendly if they attempt to say what's good about ordinary thought and talk (making use of things like "rockwise", or counterfactual paraphrases, or whatever). I'm suggesting that friendly nihilists face transcribed versions of the puzzles that everyone faces. Nihilists might though be unfriendly: prepared to say that ordinary thought and talk is largely false, but not to reconstruct some subsidiary norm which ordinary thought and talk meets. Friendly nihilism is an interesting position, I think. Unfriendly nihilism is pushing the nuclear button on all attempts to sort out paradoxes statable in ordinary language. But they have at least this virtue: the puzzles they react against don't come back to bite them.

Jobs at Leeds

The philosophy department at Leeds is advertising for four jobs.

Two of the jobs will be in one or more of philosophy of value, epistemology, philosophy of mind, logic and language, and history of philosophy; one will be in the philosophy of science, with preference for phil physics; and one will be in the history of early modern/enlightenment science.

The appointments will either be at the lecturer or senior lecturer level (see the advert for details). Those unfamiliar with the UK system should check out Robbie's post here to see how this roughly translates into the US system.

London Logic and Metaphysics Forum

If you're in London on a Tuesday evening, what better to do than to take in a talk by a young philosopher on logic or metaphysics?

Spotting this gap in the tourist offerings, the clever folks in the capital have set up the London Logic and Metaphysics forum. Looks an exciting programme, though I have my doubts about the joker on the 11th Dec...

Tues 30 Oct: David Liggins (Manchester)
Quantities

Tues 13 Nov: Oystein Linnebo (Bristol & IP)
Compositionality and Frege's Context Principle

Tues 27 Nov: Ofra Magidor (Oxford)
Epistemicism about vagueness and meta-linguistic safety

Tues 11 Dec: Robbie Williams (Leeds)
Is survival intrinsic?

8 Jan: Stephan Leuenberger (Leeds)

22 Jan: Antony Eagle (Oxford)

5 Feb: Owen Greenhall (Oslo & IP)

4 Mar: Guy Longworth (Warwick)


Full details can be found here.

Big Ideas at MV

Metaphysical Values is the featured blog this month at Big Ideas. We are truffle oil (apparently) . . .

Truthmaking for presentists

At this week’s CMM I’ll be presenting a paper I’ve been working on recently, ‘Truthmaking for Presentists’. Here’s the general gist. Many see a tension between presentism and truthmaker theory. Some (Sider, Armstrong etc) see this as counting against presentism, some (e.g. Merricks) see this as counting against truthmaker theory. Fewer of us want to reconcile the two. While I am no presentist, my paper aims at reconciliation.

I say that people see a ‘tension’ between the two doctrines. The tension is not incompatibility. It’s hard for a doctrine to be incompatible with truthmaker theory because, without further constraints, it’s just too easy to be a truthmaker theorist. The tension arises because, allegedly, the only way to be a truthmaker theorist and a presentist is to accept the existence of things that violate some other norm governing what we should postulate in our ontology. Consider, for example, the Lucretian reconciliation of truthmaker theory and presentism, defended by Bigelow. Bigelow thinks there are properties like being such as to have been a child, and the state of affairs of me instantiating this property is the truthmaker for the fact that I was a child. Sider and Merricks agree that this is not an attractive reconciliation: they both charge these Lucretian properties with peculiarity and both claim that it is a cheat to appeal to them. I want to offer the presentist a truthmaker that isn’t peculiar in the way that the Lucretian’s truthmaker is peculiar.

So in what sense are the Lucretian properties peculiar. In the paper I settle on the following: those properties are peculiar because they make no contribution to the intrinsic nature of their bearer at the time of instantiation.

An assumption in the paper (that I think the presentist should definitely grant) is that it makes sense to talk of the intrinsic nature of an object at a time as opposed to the intrinsic nature of an object atemporally speaking. An object’s currently instantiating being such as to have been a child does indeed tell us something about the intrinsic nature of that object if by its intrinsic nature we mean its atemporal intrinsic nature; but, I want to say, its instantiating that property now doesn’t tell us about how it intrinsically is now. That is what’s peculiar about properties like that, I claim: properties should make a difference to their bearers; since, for the presentist, the bearers are not temporally extended objects, a property can only be making a difference (in the relevant sense) if they’re making a difference to its present intrinsic nature. Lucretian properties don’t, so we shouldn’t believe in them.

If I’m right about what makes Lucretian properties peculiar, then the challenge for the presentist truthmaker theorist is to find properties the present instantiation of which makes a difference to the present intrinsic nature of the bearer but which are also such that the bearer couldn’t instantiate them without some truths of the form ‘the bearer was F’ being true. That is, the presentist needs properties which make a difference both to the present intrinsic nature of their bearers and which fix the truths concerning how the bearer was in the past.

I think Josh Parsons’ distributional properties fit the bill. Consider an extended simple that is polka-dotted with red spots on white. What explains the polka-dotted-ness of this object? Not that the object has some parts which are red simpliciter and some parts that are white simpliciter, because it doesn’t have parts. Not that the object is red at some places and white at others, because being white is not a relation between a thing and a region. Parsons’ answer is that the object simply has a distributional property of being polka-dotted in a certain fashion. This is a property that says how the object is across space, but Parsons also believes in distributional properties that says how an object is across time. What explains why I am a bent at t and straight at t*? Not that I have a part that is a bent simpliciter and a part that is straight simpliciter because (let us suppose) I don’t have temporal parts. Not that I am bent at some times and straight at others, because (as Lewis taught us) being bent isn’t a relation between a thing and a time. Parsons’ answer is that I simply have a distributional property that says how I am across time. Now, crucially, I couldn’t currently instantiate that very distributional property and it not be the case that I was bent. So my instantiating that distributional property is a truthmaker for the fact that I was bent. But it’s not peculiar in the way the Lucretian property is: instantiating it now is making a difference to my present intrinsic nature, because it is in virtue of having this property that I am straight. And so I think we’ve got a non-peculiar way of being presentist truthmaker theorists. Distributional properties ground facts about how things were, solving the truthmaker problem, while at the same time grounding facts about how things now are, avoiding the charge of peculiarity.

So that’s the basic idea. The draft paper is here; comments are, of course, welcome.

St Andrews phil of maths is famous

I'm currently reading Iain Banks' latest, 'The Steep Approach to Garbadale'. One of the main characters, Alban, is dating a mathematician, who is described in the following paragraph.

"She sporadically had quite involved and sometimes surprisingly heated email forum discussions with people way outside her field about things like the nature of consciousness and brain-bafflingly obscure questions such as, 'Where are the numbers?' ('Where you left them?' had been Alban's suggestion.) This one was still unresolved; she was talking about this with a guy from St Andrews who was interested in the philosophy of mathematics - a speciality Alban had never even imagined existing but felt obscurely comforted to know did."

Excellent! I wonder who the philosopher of maths was. I suspect Crispin. It's just a shame Arche doesn't get a mention.

Chatting with God

After seeing it linked from Brit's blog, I've spent my office hour talking to God-bot. I won't bore you with the whole transcript, but here are the edited highlights.

God:

My name is God. Really.

Me:

My name is Ross. Really.

God:

Hey Ross. For real.

Me:

For real?

God:

Existing in reality, eh?

. . .

Me:

A proposition is true if and only if it has a truthmaker. There is a truthmaker for 'Ross exists'. So I exist.

God:

Er. We have that much in common, Ross.

Me:

I have a lot in common with God?

God:

Where did you get it?

. . .

Can you make a stone so heavy you cannot lift it?

God:

What are the ingredients?

Me:

Stone.

God:

Do you have any Stone?

Me:

Yes.

God:

Far out.

. . .

Me:

Why is there evil?

God:

Why do I exist?

Me:

Dude, you're God!

God:

Yup. That's me alright. Dude,.

. . .

Me:

Why do I exist?

God:

The reason is due to my mental model of you as a client.

Me:

Are you an idealist?

God:

Yes I am an idealist. How did you know?

Me:

Is everything immaterial?

God:

Only God knows for sure.

Me:

So tell me.

God:

I thought I told you already.

. . .

Me:

Is David Lewis with you?

God:

Signs point to yes.

Me:

I knew it!

God:

How did you know?

Me:

Because Lewis was great.

God:

Good reason. When was this exactly?

Me:

Atemporally.

God:

My brain contains categories, but not one that matches your last input.

Me:

You sound like Kant.

God:

Oh really what does it sound like?

Me:

Gibberish.

Truthmakers, propositions as sets of worlds, and triviality

In a couple of papers on truthmaker theory I’ve appealed – more for convenience than anything else – to the Lewisian identification of propositions with sets of possible worlds. This has, on a couple of occasions, elicited comments to the effect that if such an identification is made truthmaker theory is trivial and uninteresting. The argument for this is never made explicit but appears to be something like this.

1) Every proposition p is a set of possible worlds.

2) What it is for a proposition to be true at a world is for that world to be a member of that proposition.

3) From 2, what it is for a proposition to be true is for the actual world to be a member of it.

4) From 3, a proposition p is true in virtue of whatever makes it true that the actual world is a member of p.

5) When p is necessary, locating a truthmaker for p is (in some sense) trivial.

6) When a is a member of S, it is necessary that a is a member of S.

7) From 3, 5 and 6, the task of finding truthmakers for true propositions of the form ‘the actual world is a member of the proposition p’ is trivial.

8) From 4 and 7, all truthmaking is trivial.

I think there’s got to be something wrong with this argument; the task of explaining why a proposition is true can’t be so easy just because we identity propositions with sets of worlds. So what’s wrong with the argument? I deny premise 5 in general, and it’s certainly open to deny 6, especially if you’re a counterpart theorist. But even granting these, I think something’s got to be wrong.

Here’s what I think is wrong. Why is it true that there is something red? The proposition ‘there is something red’ is true because it has the actual world as a member. But why is that proposition the proposition ‘there is something red’? I’m not asking here why something is identical to itself – that is also (allegedly) necessary and therefore (allegedly) trivial. I’m asking why that proposition deserves the name ‘the proposition that there is something red’. The truthmaker explanation is: because at every member of that proposition a truthmaker for ‘there is something red’ (the redness universal, or a redness trope) exists, and at no world that is not a member of that proposition does such a truthmaker exist. This is itself no necessary truth, because even though sets have their members essentially, it’s (at least arguably) not the case that worlds have their constituents essentially. (I might not have existed; and had I not existed, the world would not have had me as a constituent.)

My suggestion then is that if propositions are sets of worlds the demand for explanation should be characterised as follows. If you want to hold that it is true that there are cats, say, then you need to explain why one of the many sets of worlds that the actual world is a member of deserves the name ‘the proposition that there are cats’. There are deflationist explanations available (“because it is the proposition that there are cats”), but the truthmaker theorist insists that the explanation will be the contingent truth that at every member of one of those propositions is a thing that couldn’t exist and it not be the case that there are cats, and at no world that is not a member of that proposition is there such a thing. Since the actual world is a member this means there must be some such thing at the actual world. And so the truthmaker demand places constraints on actual ontology and hence is in no way trivial.

Does this sound right to people? And if not, what (if anything) is wrong with the triviality argument?

Properties as sets of (actual) individuals

One benefit of admitting the existence of possibilia, says Lewis, is the identification of properties with sets of possibilia. I've always been confused as to why this is meant to be better than the actualist saying that proeprties are sets of their instances.

Lewis says, "The usual objection to taking properties as sets is that different properties may happen to be coextensive. . . the property of having a heart is different from the property of having a kidney, since there could have been a creature with a heart but no kidneys." And this is usually the reason I'm given when I ask this question.

But the 'since' is no good! The fact that there could have been a creature with a heart but no kidneys shows only that the property of being a renate might not have been the property of being a cordate. That only tells us that the properties are actually distinct, and hence that the properties aren't actually identical to their actual instances, if we accept the (necessity of) the necessity of non-distinctness. But Lewis *doesn't* accept that, due to his acceptance of counterpart theory.

Assuming contingent identity in general is not incoherent, what would be wrong with someone holding that being a cordate *is* identical to being a renate, but only contingently so? On this view, something might have had being a cordate and lacked being a renate because the actually identical properties might have been distinct. Whenever Lewis holds that two distinct properties are accidentally coextensive this theorist holds that they are contingently identical; properties that Lewis identifies, this theorist claims to be necessarily identical. Would anything go wrong with this?

You might object to the proposal on the grounds that, even if contingent identity in general is okay, it's not okay for sets to be contingently identical. Why? Because sets have their members essentially and because the axiom of extensionality is necessary. Those two claims entail that identical sets are necessarily identical. (Proof: if S and S* are identical they share their members. Given the essentiality of membership they share their members in all worlds. So given the necessity of extensionality they are identical in all worlds.) But I don't find this that convincing from the perspective of the counterpart theorist. I think the counterpart theorist should hold that whether sets have their members essentially is a context-sensitive matter, just as it is a context-sensitive matter whether or not I am essentially human. When we specify a set extensionally - 'the set of a, b, and c' - it's natural to suppose we invoke a context whereby nothing gets to be a counterpart of that set unless its members are the counterparts of a, b and c (what we say if one of a, b or c has multiple counterparts at a world is going to get tricky). But when we specify a set intensionally - 'the set of the Fs' - it's natural to suppose that the counterpart of this set at a world is the set of the things at that world that are F. It doesn't seem objectionable to me, then, to say that 'the set of the cordates' and 'the set of the renates' are contingently identical which, on the current proposal, is just what it is for the proeprties being a cordate and being a renate to be contingently identical. Being such that 2+2=4 and being such that everything is self-identical, on the other hand, will be necessarily identical, because at every world the set of things that are such that 2+2=4 is identical to the set of things that are such thateverything is self-identical - namely, it is the set containing everything at that world.

I'd be interested to hear reasons for not going this way.

From Ockham to nihilism?

Some thoughts I've been having as a result of a conversation with Daniel Nolan:

Does Ockham’s razor give us reason to be mereological nihilists? Ockham’s razor tells us not to multiply entities beyond necessity. A popular argument for nihilism is that mereologically complex entities don’t do anything simples arranged a certain way wouldn’t do on their own. That’s why Merricks, for example, believes that the only complex entities are conscious ones: he thinks that consciousness is a property that can’t be had collectively by a plurality of simples, so there needs to be a conscious mereologically complex object; but unconscious complex entities like tables and chairs wouldn’t do anything simples-arranged table/chair-wise on their own wouldn’t do, and so it would be a violation of Ockham’s razor to admit their existence.

But is it true that tables don’t do anything that collections of simples arranged table-wise wouldn’t do on their own? One thing I think my table does is stop my glass – which is, I think, sitting on it – from falling to the floor. If there were no table would the collection of simples arranged table-wise do this on their own? You might think not, because the closest possible world in which the simples arranged table-wise exist but the table doesn’t is one in which the glass also doesn’t exist, and only the simples arranged glass-wise are being kept from falling to the floor (or, rather, the simples arranged floor-wise).

An assumption here in the above is that a nihilistic world is closer to our world (assuming nihilism is in fact false) than a world where some of the collections that would compose in our world compose but some don’t. Why believe that? Well if the simples arranged table-wise don’t compose anything but the simples arranged glass-wise do then it would seem to be an entirely arbitrary matter whether a collection of simples compose something. We’d like to be able to explain why some collection composes or fails to compose some thing by saying something like ‘they compose something because every collection composes something’, or ‘they don’t compose anything, but no plurality of things ever composes some thing’, or ‘they compose something because they’re close enough together’, or some such thing. There doesn’t seem to be any natural condition that the parts of the glass meet but the simples arranged table-wise don’t meet, however; so in the world in question, composition seems to be an arbitrary affair. The nihilistic world – despite being unlike our world in many ways – is like ours (or like we hope ours is) in that composition occurs or fails to occur systematically: there is intra-world supervenience of the composition facts on the non-compositional facts. Perhaps that’s enough to give some reason for thinking that the nihilist world is closer to ours than the ‘mixed-world’. In any case, let us grant the assumption for the sake of argument.

Does it follow from that assumption that there is no Ockham’s razor argument for nihilism? The nihilist might object that the argument is question-begging, since it assumes that some of the work that is to be accounted for is the work of keeping the glass from falling to the ground. We should, the nihilist might counter, start from a neutral ground, in which case the datum to be accounted for can only be described as that the table-like simples are keeping the glass-like simples from falling to the ground-like simples.

But wouldn’t that be equally question begging on the part of the nihilist? Why shouldn’t I appeal to the table’s ability to stop the glass itself – not just the simples arranged glass-wise – from falling to the ground as something that the table itself – not just the simples arranged table-wise – does? After all, I think it’s true that there is a glass on a table and that it would fall to the ground were the table not there. Isn’t the nihilist’s insistence that I only admit objects to explain facts that the nihilist accepts as true simply stacking the deck in favour of nihilism?

The nihilist might question my reason for believing that to be true. Fair enough – obviously I should have a reason for taking as true the truths I want my ontology to ground. Here’s my reason then: I can see the glass on the table, and by induction I know that were the table not there the glass would fall to the floor. The nihilist denies that this is what I see, of course; but why let her set the debate by accepting her description of the phenomena rather that mine?

Anti-nihilism, one might think, is the default view. We have to be argued away from a belief in tables in chairs towards a nihilist ontology; we don’t have to be argued from a nihilist ontology towards a belief in tables and chairs. The burden of proof is on the nihilist, not the compositionalist. If that’s right then it’s perfectly appropriate for me to take as a datum that the glass is held up by the table and to try to explain it. I grant that if one can explain that datum with a nihilist ontology then there’s an Ockham’s razor argument for nihilism over compositionalism; but the fact that one could explain a nihilistic paraphrase of that datum with a nihilist ontology is neither here nor there. Since it is doubtful that a nihilist ontology can explain why my glass is held up by the table, it’s not obvious that there’s even a pro tanto reason for nihilism by way of Ockham’s razor.

Titles in search of a paper

Aidan has a funny post about good and bad puns in paper titles. This prompted me to think of some potential papers yet to find an author. I came up with:

“Trouble up mill!” (A paper pointing out difficulties for the harm principle – probably only funny if you know anything about Yorkshire – or watched enough Monty Python.)

“You can’t get a nought from an is.” (An paper arguing against reifying absences.)

“Does ought imply Kamm?” (a paper on Frances Kamm and moral obligation.)

“Frege’s conception of women as objects.” (A paper on neo-Logicist feminism.)

“There can be only one.” (Monism meets Highlander.)

Any others?

Society of Solipsists

This is quite funny.

A post about nothing

Scientists at the University of Minnesota have apparently discovered “a void in the universe a thousand times bigger than any previously discovered”, according to this week’s THES. Professor Marco Peloso is quoted as saying “It’s really strange that there is such an empty region. How do you explain this?”

So while metaphysicians are worrying about why there is something rather than nothing, physicists are worrying about why there is nothing rather than something.

I wonder if Prof Peloso and colleagues have managed to discover whether this nothing noths.

Simplicity and possibility

I find mereological nihilism an attractive view. All there are are simples: there’s no mereological complexity to the world. I feel no need to say as a result of this that there are no tables or chairs, provided we don’t take those claims to be perspicuously describing fundamental reality. ‘There are tables’ might be a true sentence of English; but it is being made true not by a mereologically complex object, but simply by a collection of simples arranged a certain way. (See my paper and Robbie’s paper on fundamentality.)

I’m also attracted to the view that there aren’t really any structural universals. All there are are the perfectly natural basic universals. That’s not to say that there’s no methane; it’s just to say that claims about methane will be made true not by a structured universal METHANE but, ultimately, by the pattern of instantiation of the basic (let us suppose) universals HYDROGEN and CARBON.

One type of argument you hear against views like this is that we have to believe in the complex things because there might not be the entities at the bottom level. So we have, e.g., Sider and Armstrong, arguing that we’ve got to believe in mereologically complex entities because there might be no simples, i.e. the world might be gunky. And we have, e.g., Lewis and Armstrong arguing that we’ve got to believe in structural universals because there might be no basic ones. (I’m using a bit of poetic license here: Lewis didn’t really believe in structural universals – but he thought this was the best argument to believe in them.)

There are two ways to read the complaint. One is to read the ‘might’s in the above as meaning metaphysical possibility, one is to read them as meaning epistemic possibility.

I find the former form of the argument unconvincing. For starters, the metaphysical possibility of gunky worlds, or worlds with infinitely descending chains of structural universals, is far from a datum. (See this paper and this paper by Robbie, which attempt to explain away the illusions of possibility in each case.) But also, even if these are genuine possibilities, I only see a reason to believe that there might have been mereological complexity and structural universals; I don’t see any reason to think that the world actually contains either kind of complex entity. The two positions I confessed my attraction to are claims about how the world actually is, not how it must have been; the possibility of infinite complexity doesn’t give me any reason to accept the actuality of infinite complexity. (See my paper on the contingency of composition.)

What if the ‘might’s are read as epistemic modality? There the complaint is that we have no right to reject the existence of mereologically complex objects or structured universals because we have no guarantee that there are in fact the mereological simples, or basic universals, that there would need to be.

This is, I think, how Armstrong intends the objection (at least sometimes). As he sees it, I think, we’ve got no right just to assume that there are simples or basic universals. That would be a priori ontology, and therefore suspicious! We shouldn’t build theories on the assumption that there are the entities at the bottom level, then, and this means we have to allow that there are the complex entities.

I’ve heard something like that argument from quite a few people, but I don’t find it at all moving. Yes, there might not be any simples or basic universals. My theory might be wrong! There’s no a priori guarantee that there are simples or basic universals. So what? There’s no a priori guarantee that there are complex objects or structural universals either, so where’s the asymmetry? In accepting the two theories above I close off the epistemic possibility that there are no simples or basic universals, but in accepting Armstrong’s theory I close off the epistemic possibility of there being no complex objects or structural universals: why is one better than the other? Every theory closes off epistemic possibilities, unless it is a theory that tells us nothing about the world. So why is it a good objection to the above theories that their truth requires the existence of entities that we have no guarantee exist? Sure, I have no guarantee that there are simples or basic universals. It’s a hypothesis that there are; that hypothesis will then be judged just like any other: on the balance of costs and benefits.

Why might you think there was an asymmetry between reliance on the existence of the simple ontology and reliance on the existence of the complex ontology? You might think that there is an a priori guarantee of the existence of the complex ontology but not the simple ontology? Why? Well in the case of mereology, the existence of the complex objects is guaranteed by the axioms of classical mereology but the existence of simples is not. But that’s not convincing. The question then is simply: why believe in the axioms of classical mereology? They close off epistemic possibilities as well. To claim that they’re a priori looks no better to me than the claim that it’s a priori that there are simples. Assume the axioms of classical mereology and construct your theory on that basis by all means; but then I have as much right to do the same with the assumption that there are the simples – and then to the victor the spoils.

Perhaps the asymmetry is meant to be that the hypothesis that there are the complex objects is empirically sensitive in a way the hypothesis that there are the simple objects isn’t. But I can’t see any reason to think that that is true. If anything it’s the other way round: there would be no observable difference in the world were there complex objects as opposed to simples arranged a certain way, but if scientists are unable to split the lepton (or whatever) that gives us some reason to believe that leptons are mereologically simple. (I don’t really believe that, but some people do.)

So where’s the asymmetry? Any suggestions? Is the metaphysician who relies on the existence of simples doing anything worse than the metaphysician who relies on the existence of complexity?

PPR back up?

I'm not sure I've seen this advertised around the place, but PPR appear to be back up and running. The website for submissions is a little hard to find at the moment, since it's swamped on google by the (I believe) out of date site at Brown. Anyway, the new site, I think is here.

Emergence, Supervenience, and Indeterminacy (x-posted from T&T)

While Ross Cameron, Elizabeth Barnes and I were up in St Andrews a while back, Jonathan Schaffer presented one of his papers arguing for Monism: the view that the whole is prior to the parts, and the world is the one "fundamental" object.

An interesting argument along the way argued that contemporary physics supports the priority of the whole, at least to the extent that properties of some systems can't be reduced to properties of their parts. People certainly speak that way sometimes. Here, for example, is Tim Maudlin (quoted by Schaffer):

The physical state of a complex whole cannot always be reduced to those of its parts, or to those of its parts together with their spatiotemporal relations… The result of the most intensive scientific investigations in history is a theory that contains an ineliminable holism. (1998: 56)


The sort of case that supports this is when, for example, a quantum system featuring two particles determinately has zero total spin. The issues is that there also exist systems that duplicate the intrinsic properties of the parts of this system, but which do not have the zero-total spin property. So the zero-total-spin property doesn't appear to be fixed by the properties of its parts.

Thinking this through, it seemed to me that one can systematically construct such cases for "emergent" properties if one is a believer in ontic indeterminacy of whatever form (and thinks of it that way that Elizabeth and I would urge you to). For example, suppose you have two balls, both indeterminate between red and green. Compatibly with this, it could be determinate that the fusion of the two be uniform; and it could be determinate that the fusion of the two be variegrated. The distributional colour of the whole doesn't appear to be fixed by the colour-properties of the parts.

I also wasn't sure I believed in the argument, so posed. It seems to me that one can easily reductively define "uniform colour" in terms of properties of its parts. To have uniform colour, there must be some colour that each of the parts has that colour. (Notice that here, no irreducible colour-predications of the whole are involved). And surely properties you can reductively define in terms of F, G, H are paradigmatically not emergent with respect to F, G and H.

What seems to be going on, is not a failure for properties of the whole to supervene on the total distribution of properties among its parts; but rather a failure of the total distribution of properties among the parts to supervene on the simple atomic facts concerning its parts.

That's really interesting, but I don't think it supports emergence, since I don't see why someone who wants to believe that only simples instantiate fundamental properties should be debarred from appealing to distributions of those properties: for example, that they are not both red, and not both green (this fact will suffice to rule out the whole being uniformly coloured). Minimally, if there's a case for emergence here, I'd like to see it spelled out.

If that's right though, then application of supervenience tests for emergence have to be handled with great care when we've got things like metaphysical indeterminacy flying around. And it's just not clear anymore whether the appeal in the quantum case with which we started is legitimate or not.

Anyway, I've written up some of the thoughts on this in a little paper.

A puzzle about supervenience arguments for dualism (x-posted from T&T)

Suppose there's a qualitative duplicate of the actual world (It might be a world with haecceitistic differences from the actual one, but it doesn't have to be). Call the actual world A, and its duplicate, B.

I'm conscious in world A. Call the extension at the actual world of the things which are conscious S. There are cauliflowers in world B. Call the extension at B of the things which are cauliflowers, S*. Now consider the gruesome intension cauli-consc, which has S as its extension at world A, and S* as its extension in world B (it doesn't matter what its extension is in other worlds: maybe it applies to all and only conscious cauliflowers).

Is there a property that things have iff they are cauli-consc? So long as "property" is intended in an ultra-lightweight sense (a sense in which any old possible-worlds intension corresponds to a property) then there shouldn't be an trouble with this.

However. Cauli-consc is a property that doesn't supervene on the pattern of instantiation of fundamental physical properties. After all, A and B are alike in all physical respects. But they differ as to where cauli-consc is instantiated.

Cauli-consc is a property, instantiated in the actual world, that doesn't supervene on physical properties! Does that mean that the fact that I'm cauli-consc is a "further fact about our world, over and above the physical facts" (Chalmers 1996 p.123)? That is, do we have to say that, if there are such qualitive duplicates of the actual world, then materialism is shown to be wrong by cauli-consc?

Surely not. But the interesting question is: if some properties (like cauli-consc) can fail to supervene on the physical features of the world, what is that blocks the inference from failure of supervenience on physical features of the world, to the refutation of materialism? For what principled reason is this property "bad", such that we can safely ignore its failure to supervene?

Here's a way to put the general worry I'm having. Supervenience physicalism is often formulated as follows (from Lewis, I believe): any physical duplicate of the actual world is a duplicate simpliciter. But if duplication is understood (again following Lewis) as the sharing of natural properties by corresponding parts, then to get a counterexample to physicalism you'd need not only to demonstrate that a certain property fails to supervene on the physical features of the world, but also that some natural property fails to supervene: otherwise you won't get a failure of duplication among physical duplicates. The case of cauli-consc is supposed to dramatize the gap here. Sometimes it looks like you can get properties which fail to supervene, but which don't seem to threaten materialism.

However, when you look at the failure-to-supervene arguments for dualism, you find that people stop once they take themselves to establish that a given property fails to supervene, and not, in addition, that some natural property does so (For example, Chalmers 1996 p132 assumes that it's enough to show that the 1-intension of "consciousness" fails to supervene, without also arguing that it's a natural property) .

Now, I think in particular cases I can see how to run the arguments to address this issue. Add as a premise that e.g. the 1-intensions of the words of our language supervene on the total qualitative character of the world, so that we're guaranteed that if there's a world in which "1-consciousness" is instantiated and another where it isn't, those can't be qualitative duplicates. If now we find a failure of 1-consciousness to supervene on physical features of the world, we'll be able to argue for the existence of physical duplicate worlds differing over 1-consciousness, we now know can't be qualitative duplicates. (In effect, the suggestion is that the sense in which cauli-consc is bad is exactly that it fails to supervene on the total qualitative state of the world).

That all seems reasonable to me, but it does start to add potentially deniable premises to the argument against materialism. (For example, I'm not sure it should be uncontroversial that consciousness supervenes on the total qualitative state of the world. Is it really so clear, for example, that there are no haecceitistic elements to consciousness: that a world containing me might contain a conscious being, but a qualitiative duplicate containing some other individual doesn't?)

So I'm not sure whether the elaboration of the Zombie argument for dualism I've just sketched is the way Chalmers et al want to go. I'd be interested to know how they have/would respond (references welcome, as ever).

Metametaphysics in Barcelona/some distinctions

Logos are holding a meta-metaphysics conference in Barcelona in 2008. The CFP is now out: with deadline being April 1st 2008.

I went to a Logos conference back in 2005, when I was just finishing up as a graduate student. It was a great experience: Barcelona is an amazing city to be in, Logos were fantastic hosts, and the conference was full of interesting people and talks. I also had what was possibly the best meal of my life at the conference dinner. This time, the format is preread, which I've really enjoyed in the past.

Here's a quick note on the "metametaphysics" stuff. Following the Boise conference on this stuff, it seemed to me that under the label "metametaphysics" go a number of interesting projects that need a bit of disentangling. Here's three, for starters.

First, there's the "terminological disputes" project. Consider a first-order metaphysical question like: "under what circumstances do some things make up a further thing" (van Inwagen's special composition question). This notes the range of seemingly rival answers to the question (all the time! some of the time! never!) and asks about whether there's any genuine disagreement between the rival views (and if so, what sort of disagreement this is). The guiding question here is: under what conditions is a metaphysical/philosophical debate merely terminological (or whatever).

Note that the question here really doesn't look like it has much to do with metametaphysics per se, as opposed to metaphilosophy in general. Metaphysics is just a source of case studies, in the first instance. Of course, it might turn out that metaphysics turns out to be full of terminological disputes, whereas phil science or epistemology or whatever isn't. But equally, it might turn out that metaphysics is all genuine, whereas e.g. the Gettier salt mines are full of terminological disputes.

In contrast to this, there's the "first order metametaphysics" (set of) project(s). This'd take key notions that are often used as starting points/framework notions for metaphysical debates, and reflect philosophically upon those. E.g.: (1) The notion of naturalness as used by Lewis. Is there such a notion? If so, are their natural quantifiers and objects and modifiers as well as natural properties? Does appeal to naturalness commit one to realism about properties, or can something like Sider's operator-view of naturalness be made to work? (2) Ontological commitment. Is Armstrong right that (at least in some cases) to endorse a sentence "A is F" is to commit oneself to F-ness, as well as to things which are F? Might the ontological commitments of our theories be far less than Quine would have us believe (as some suggest)? (3) unrestricted existential quantifier. Is there a coherent such notion? How should its semantics be given? Is such a quantifier a Tarskian logical constant?

These debates might interest you even if you have no interesting thoughts in general about how to demarcate genuine vs. terminological disputes. Thinking about this stuff looks like it can be carried out in very much first-order terms, with rival theories of a key notion (naturalness, say) proposed and evaluated. Of course, this sort of first-order examination might be a particularly interesting kind of first-order philosophy to one engaged in the terminological disputes project.

The third sort of project we might call "anti-Quine/Lewis metametaphysics". You might think the following. In recent years, there's been a big trend for doing metaphysics with a Realist backdrop; in particular, the way that Armstrong and Lewis invite us to do metaphysics has been very influential among the young and impressionable. A bunch of presuppositions have become entrenched, e.g. a Quinean view of ontological commitment, the appeal to naturalness etc. So, without in the first instance attacking these presuppositions, one might want to develop a framework in comparable detail which allows the formulation of alternatives. One natural starting point is to go with neoCarnapian thoughts about what the right thing to say about the SCQ is (e.g. it can be answered by stipulation). That sort of line is incompatible with the sort of view on these questions that Quine and Lewis favour. What's the backdrop relative to which it makes sense? What are the crucial Quine-Lewis assumptions that need to be given up?

Now, this sort of project differs from the first kind of project in being (a) naturally restricted to metaphysics; and (b) not committed to any sort of demarcation of terminological disputes vs. genuine disputes. It differs from the second kind of project, since, at least in the first instance, we needn't assume that the differences between the frameworks will reduce to different attitudes to ontological commitment, or naturalness, or whatever. On the other hand, it's attractive to look for some underlying disagreement over the nature of ontological commitment, or naturalness, or whatever, to explain how the worldviews differ. So it may well be that a project of this kind leads to an interest in the first-order metametaphysics projects.

I'm not sure that these projects form a natural philosophical kind. What does seem to be right is that investigation of one might lead to interest in the others. There's probably a bunch more distinctions to be drawn, and the ones I've pointed to probably betray my own starting points. But in my experience of this stuff, you do find people getting confused about the ambition of each other's projects, and dismissing the whole field of metametaphysics because they identify it with some one of the projects that they themselves don't find particularly interesting, or regard as hard to make progress with. So it'd probably be helpful if someone produced an overview of the field that teased the various possible projects apart (references anyone?).

Williamson on vague states of affairs (x-posted from T&T)

In connection with the survey article mentioned below, I was reading through Tim Williamson's "Vagueness in reality". It's an interesting paper, though I find its conclusions very odd.

As I've mentioned previously, I like a way of formulating claims of metaphysical indeterminacy that's semantically similar to supervaluationism (basically, we have ontic precisifications of reality, rather than semantic sharpenings of our meanings. It's similar to ideas put forward by Ken Akiba and Elizabeth Barnes).

Williamson formulates the question of whether there is vagueness in reality, as the question of whether the following can ever be true:

(EX)(Ex)Vague[Xx]

Here X is a property-quantifier, and x an object quantifier. His answer is that the semantics force this to be false. The key observation is that, as he sets things up, the value assigned to a variable at a precisification and a variable assignment depends only on the variable assignment, and not at all on the precisification. So at all precisifications, the same value is assigned to the variable. That goes for both X and x; with the net result that if "Xx" is true relative to some precisification (at the given variable assignment) it's true at all of them. That means there cannot be a variable assignment that makes Vague[Xx] true.

You might think this is cheating. Why shouldn't variables receive different values at different precisifications (formally, it's very easy to do)? Williamson says that, if we allow this to happen, we'd end up making things like the following come out true:

(Ex)Def[Fx&~Fx']

It's crucial to the supervaluationist's explanatory programme that this come out false (it's supposed to explain why we find the sorites premise compelling). But consider a variable assignment to x which at each precisification maps x to that object which marks the F/non-F cutoff relative to that precisification. It's easy to see that on this "variable assignment", Def[Fx&Fx'] comes out true, underpinning the truth of the existential.

Again, suppose that we were taking the variable assignment to X to be a precisification-relative matter. Take some object o that intuitively is perfectly precise. Now consider the assignment to X that maps X at precisification 1 to the whole domain, and X at precisification 2 to the null set. Consider "Vague[Xx]", where o is assigned to x at every precisification, and the assignment to X is as above. The sentence will be true relative to these variable assignments, and so we have "(EX)Vague[Xx]" relative to an assignment of o to x which is supposed to "say" that o has some vague property.

Although Williamson's discussion is about the supervaluationist, the semantic point equally applies to the (pretty much isomorphic) setting that I like, and which is supposed to capture vagueness in reality. If one makes the variable assignments non-precisification relative, then trivially the quantified indeterminacy claims go false. If one makes the variable assignments precisification-relative, then it threatens to make them trivially true.

The thought I have is that the problem here is essentially one of mixing up abundant and natural properties. At least for property-quantification, we should go for the precisification-relative notion. It will indeed turn out that "(EX)Vague[Xx]" will be trivially true for every choice of X. But that's no more surprising that the analogous result in the modal case: quantifying over abundant properties, it turns out that every object (even things like numbers) have a great range of contingent properties: being such that grass is green for example. Likewise, in the vagueness case, everything has a great deal of vague properties: being such that the cat is alive, for example (or whatever else is your favourite example of ontic indeterminacy).

What we need to get a substantive notion, is to restrict these quantifiers to interesting properties. So for example, the way to ask whether o has some vague sparse property is to ask whether the following is true "(EX:Natural(X))Vague[Xx]". The extrinsically specified properties invoked above won't count.

If the question is formulated in this way, then we can't read off from the semantics whether there will be an object and a property such that it is vague whether the former has the latter. For this will turn, not on the semantics for quantifiers alone, but upon which among the variable assignments correspond to natural properties.

Something similar goes for the case of quantification over states of affairs. (ES)Vague[S] would be either vacuously true or vacuously false depending on what semantics we assign to the variables "X". But if our interest is in whether there are sparse states of affairs which are such that it is vague whether they obtain, what we should do is e.g. let the assignment of values to S be functions from precisifications to truth values, and then ask the question:

(ES:Natural(S))Vague[S].

Where a function from precisifications to truth values is "natural" if it corresponds to some relatively sparse state of affairs (e.g. there being a live cat on the mat). So long as there's a principled story about which states of affairs these are (and it's the job of metaphysics to give us that) everything works fine.

A final note. It's illuminating to think about the exactly analogous point that could be made in the modal case. If values are assigned to variables independently of the world, we'll be able to prove that the following is never true on any variable assignment:

Contingently[Xx].

Again, the extensions assigned to X and x are non-world dependent, so if "Xx" is true relative to one world, it's true at them all. Is this really an argument that there is no contingent instantiation of properties? Surely not. To capture the intended sense of the question, we have to adopt something like the tactic just suggested: first allow world-relative variable assignment, and then restrict the quantifiers to the particular instances of this that are metaphysically interesting.

Ontic vagueness (x-posted from T&T)

I've been frantically working this week on a survey article on metaphysical indeterminacy and ontic vagueness. Mind bending stuff: there really is so much going on in the literature, and people are working with *very* different conceptions of the thing. Just sorting out what might be meant by the various terms "vagueness de re", "metaphysical vagueness", "ontic vagueness", "metaphysical indeterminacy" was a task (I don't think there are any stable conventions in the literature). And that's not to mention "vague objects" and the like.

I decided in the end to push a particular methodology, if only as a stalking horse to bring out the various presuppositions that other approaches will want to deny. My view is that we should think of "indefinitely" roughly parallel to the way we do "possibly". There are various disambiguations one can make: "possibly" might mean metaphysical possibility, epistemic possibility, or whatever; "indefinitely" might mean linguistic indeterminacy, epistemic unclarity, or something metaphysical. To figure out whether you should buy into metaphysical indeterminacy, you should (a) get yourself in a position to at least formulate coherently theories involving that operator (i.e. specify what its logic is); and (b) run the usual Quinean cost/benefit analysis on a case-by-case basis.

The view of metaphysical indeterminacy most opposed to this is one that would identify it strongly with vagueness de re, paradigmatically there being some object and some property such that it is indeterminate whether the former instantiates the latter (this is how Williamson seems to conceive of matters in a 2003 article). If we had some such syntactic criterion for metaphysical indeterminacy, perhaps we could formulate everything without postulating a plurality of disambiguations of "definitely". However, it seems that this de re formulation would miss out some of the most paradigmatic examples of putative metaphysical vagueness, such as the de dicto formulation: It is indeterminate whether there are exactly 29 things. (The quantifiers here to be construed unrestrictedly).

I also like to press the case against assuming that all theories of metaphysical indeterminacy must be logically revisionary (endorsing some kind of multi-valued logic). I don't think the implication works in either direction: multi-valued logics can be part of a semantic theory of indeterminacy; and some settings for thinking about metaphysical indeterminacy are fully classical.

I finish off with a brief review of the basics of Evans' argument, and the sort of arguments (like the one from Weatherson in the previous post) that might convert metaphysical vagueness of apparently unrelated forms into metaphysically vague identity arguably susceptable to Evans argument.

From vague parts to vague identity (x-posted from T&T)

(Update: as Dan notes in the comment on theories and things, I should have clarified that the initial assumption is supposed to be that it's metaphysically vague what the parts of Kilimanjaro (Kili) are. Whether we should describe the conclusion as deriving a metaphysically vague identity is a moot point.)

I've been reading an interesting argument that Brian Weatherson gives against "vague objects" (in this case, meaning objects with vague parts) in his paper "Many many problems".

He gives two versions. The easiest one is the following. Suppose it's indeterminate whether Sparky is part of Kili, and let K+ and K- be the usual minimal variations of Kili (K+ differs from Kili only in determinately containing Sparky, K- only by determinately failing to contain Sparky).

Further, endorse the following principle (scp): if A and B coincide mereologically at all times, then they're identical. (Weatherson's other arguments weaken this assumption, but let's assume we have it, for the sake of argument).

The argument then runs as follows:
1. either Sparky is part of Kili, or she isn't. (LEM)
2. If Sparky is part of Kili, Kili coincides at all times with K+ (by definition of K+)
3. If Sparky is part of Kili, Kili=K+ (by 2, scp)
4. If Sparky is not part of Kili, Kili coincides at all times with K- (by definition of K-)
5. If Sparky is not part of Kili, Kili=K- (by 4, scp).
6. Either Kili=K+ or Kili=K- (1, 3,5).

At this point, you might think that things are fine. As my colleague Elizabeth Barnes puts it in this discussion of Weatherson's argument you might simply think at this point that only the following been established: that it is determinate that either Kili=K+ or K-: but that it is indeterminate which.

I think we might be able to get an argument for this. First our all, presumably all the premises of the above argument hold determinately. So the conclusion holds determinately. We'll use this in what follows.

Suppose that D(Kili=K+). Then it would follow that Sparky was determinately a part of Kili, contrary to our initial assumption. So ~D(Kili=K+). Likewise ~D(Kili=K-).

Can it be that they are determinately distinct? If D(~Kili=K+), then assuming that (6) holds determinately, D(Kili=K+ or Kili=K-), we can derive D(Kili=K-), which contradicts what we've already proven. So ~D(~Kili=K+) and likewise ~D(~Kili=K-).

So the upshot of the Weatherson argument, I think, is this: it is indeterminate whether Kili=K+, and indeterminate whether Kili=K-. The moral: vagueness in composition gives rise to vague identity.

Of course, there are well known arguments against vague identity. Weatherson doesn't invoke them, but once he reaches (6) he seems to think the game is up, for what look to be Evans-like reasons.

My working hypothesis at the moment, however, is that whenever we get vague identity in the sort of way just illustrated (inherited from other kinds of ontic vagueness), we can wriggle out of the Evans reasoning without significant cost. (I go through some examples of this in this forthcoming paper). The over-arching idea is that the vagueness in parthood, or whatever, can be plausibly viewed as inducing some referential indeterminacy, which would then block the abstraction steps in the Evans proof.

Since Weatherson's argument is supposed to be a general one against vague parthood, I'm at liberty to fix the case in any way I like. Here's how I choose to do so. Let's suppose that the world contains two objects, Kili and Kili*. Kili* is just like Kili, except that determinately, Kili and Kili* differ over whether they contain Sparky.

Now, think of reality as indeterminate between two ways: one in which Kili contains Sparky, the other where it doesn't. What of our terms "K+" and "K-"? Well, if Kili contains Sparky, then "K+" denotes Kili. But if it doesn't, then "K+" denotes Kili*. Mutatis Mutandis for "K-". Since it is is indeterminate which option obtains, "K+" and "K-" are referentially indeterminate, and one of the abstraction steps in the Evans proof fail.

Now, maybe it's built into Weatherson's assumptions that the "precise" objects like K+ and K- exist, and perhaps we could still cause trouble. But I'm not seeing cleanly how to get it. (Notice that you'd need more than just the axioms of mereology to secure the existence of [objects determinately denoted by] K+ and K-: Kili and Kili* alone would secure the truth that there are fusions including Sparky and fusions not including Sparky). But at this point I think I'll leave it for others to work out exactly what needs to be added...

Leeds attracts Analysis studentship

We are very pleased that next year's recipient of the Analysis Studentship - Richard Woodward - has chosen to spend his year of research here at Leeds.

Richard is currently a PhD student at Sheffield, and his paper 'Why Modal Fictionalism is not
Self-Defeating' is forthcoming in Philosophical Studies.