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.