Perspectives and magnets

As Brian Weatherson notes, the new Philosophical Perspectives is now out. This includes a paper of mine called "Illusions of gunk". The paper defends mereological nihlism (the view that no complex objects exist) against a certain type of worry: (1) that mereological nihlism is necessary, if true; and (2) that "gunk-worlds" (worlds apparently containing no non-complex objects) are possible. (See this paper of Ted Sider's for the worry) I advise the merelogical nihilist to reject (2). There are various possibilities that the nihilist can admit, that plausibly explain the illusion that gunk is possible.

The volume looks to be full of interesting papers, but there's one in particular I've read before, so I'll write a little about that right now.

The paper is Brian Weatherson's "Asymmetric Magnets Problem". The puzzle he sets out is based on a well-entrenched link between intrinsicality and duplication: a property is intrinsic iff necessarily, it is shared among duplicate objects. Weatherson examines an application of this principle to a case where some of the features of the objects we consider are vectorial.

In particular, consider an asymmetric magnet M: one which has a pointy-bit at one end, and is such that the north pole of the magnet "points out" of the pointy end. Intuitively, the following is a duplicate of another magnet M*: one with the same shape, but simply rotated by 180 degrees so that both the north pole and the pointy end are both orientated in the opposite direction to M. (Weatherson has some nice pictures, if you want to be clear about the situation).

Though M and M* seem to be duplicates, their vectorial features differ: M has its north pole pointing in one direction, M* has its north pole pointing in the opposite direction. Moral: given the link, we can't take vectorial properties "as a whole" (i.e. building in their directions) as intrinsic, for they differ between duplicates.

What if we think that only the magnitude of a vectorial feature is intrinsic? Then we get a different problem: for their are pointy magnets whose north pole is directed out of the non-pointy end. Call one of these M**. But in shape properties, and so on, it matches M and M*. And ex hypothesi, in all intrinsic respects, their vectorial features are the same. So M, M* and M** all count as duplicates. But that's intuitively wrong (it's claimed).

Such is the asymmetric magnets problem. The challenge is to say something precise about how to think about the duplication of things with vectorial features, that'd preserve both intuitions and the duplication-intrinsicality link.

Weatherson's response is to take a certain relationship between parts of the pointy magnet its vectorial feature, as intrinsic to the magnet. In effect, he takes the relative orientation of the north-pole vector, and a line connecting certain points within the magnet, as intrinsic.

Ok, that's Weatherson's line in super-quick summary, as I read him. Here are some thoughts.

First thing to note: the asymmetric magnets problem looks like a special case of a more general issue. Suppose point particles a, b, c each have two fundamental vectoral features F and G, with the same magnitude in each case. Suppose in a's case they point in different directions, whereas in b and c's cases they point in the same direction (in b's case they both point north, in c's case they both point south). The intuitive verdict is that a and b are not duplicates, but b and c are. But, if you just demand that duplicates preserve the magnitudes of the quantities, you'll get a, b, and c as duplicates of one another; and if you demand that duplicates preserve direction of vectoral quantities, you'll get none of them as duplicates. That sounds just like the asymmetric magnets problem all over again. Let me call it the vector-pair problem.

What's the natural Weathersonian thought about the vector-pair problem? The natural line is to take the relative orientation ("angle") between the instances of F and G as a perfectly natural relation. (I think that Weatherson might go for this line now: see his comment here).

It seemed to me that a natural response to the problem just posed might be this: require that the magnitude of any quantities is invariant under duplication; also that the *relative orientation* of vectoral properties be invariant under duplication. Thus we build into the definition of duplication the requirement that any angles between vectors are preserved. There's thus no easy answer to the question of whether vectorial features of objects are intrinsic: we can only say that their magnitudes and relative orientations are, but their absolute orientation is not.

This leads to a couple of natural questions:

(A) Why do we demand absolute sameness of magnitude, and only relative sameness of direction, when defining what it takes for something to be a duplicate of something else?

I'm tempted to think that there's no deep answer to this question. In particular, consider a possible world with an "objective centre", and where various natural laws are formulated in terms of whether objects have properties "pointing towards" the centre or away from it. E.g. suppose two objects both with instantaneous velocity towards the centre will repel each other with a force proportional to the inverse of their separation; while two objects both with instantaneous velocity away from the centre will attract each other with a similar force (or something like that: I'm sure we can cook something up that’ll make the case work). Anyway, since the behaviour of objects depends on the "direction in which they're pointing", I no longer have strong intuitions that particles like b and c should count as duplicates (with that world considered counteractually).

I find it harder to imagine worlds where only relative magnitudes matter to physical laws, but I suspect that with ingenuity one could describe such a case: and maybe (considering such a scenario counteractually again) we'd be happier to demand only relative sameness of magnitudes, in addition to relative sameness of orientation of vectoral properties, among duplicates.

(B) The above proposal demands invariance of relative orientation of vectoral properties among duplicate entities. But that doesn't straightaway deal with the original asymmetric magnet case. For there we had the orientation of the shape-properties of the object to consider, not just the orientation of the vectoral quantities that the (parts of) the object has.

I'm tempted by the following way of subsuming the original problem under the more general treatment just given: say that some perfectly natural spatial properties are actually vectoral in character. E.g. the spatial property that holds between my hand and my foot is not simply "being separated by 1m" but rather "being separated by 1m downwards" (with, of course, the converse relation holding in the other direction). After all, if in giving the spatial properties that I currently have, we just list the spatial separations of my parts, we leave something out: my orientation. And that is a spatial property that I have (and is coded into the usual representations of location, e.g. Cartesian or polar coordinates. Of course, such representations are all relative to a choice of axes, just as the representation of spatial separation is relative to a choice of unit.)

Now, there might be ways of getting this result without saying that spatial-temporal relations among particulars are fundamentally vectorial. But I'm not seeing exactly how this would work.

(Incidentally, if we do allow fundamentally vectorial spatio-temporal relations, then it's not clear that we need to appeal to spatio-temporal relations among parts of an object to solve the asymmetric magnets problem: appealing to the angle between the "north pole" and the (vectorial) spatio-temporal properties of the pointy magnet may be enough to get the intuitive duplication verdicts. If so, then the Weathersonian solution can be extended to the case where the magnets are extended simples, which is (a) a case he claims not to be able to handle (b) a case he claims to be impossible. But I disagree with (b), so from my perspective (a) looks like a serious worry!)

(x-posted on theories n things)

CMM workshop

This is just a heads-up to the world that there will be a CMM workshop at Leeds on March 10th. The topic is 'Structure in Metaphysics', and Julian Dodd (Manchester), Katherine Hawley (St Andrews), Kris McDaniel (Syracuse) and Leeds' own Robbie Williams are signed up to speak.

Detials of paper titles/registration details etc will follow sooner or later - but for now: keep your diaries free.

The kinds of topic the workshop will deal with are (i) mereology, (ii) grades of being/existence, (iii) ontological dependence, (iv) facts, states of affairs, propositions, etc.

A preliminary webpage is up at

http://www.personal.leeds.ac.uk/~phlrpc/StructureWorkshop.htm

Identity of Indiscernibles and Haecceities

According to the identity of indiscernibles, as a matter of necessity, no two things can share all their properties. If a and b share all their properties then they are not two things, but one: they are numerically identical. You can’t have qualitative identity without thereby having numerical identity.

Why think the identity of indiscernibles is true? Well, suppose it’s false; in that case there is a possible world containing two entities, a and b, which share all their properties. And the uncomfortable thought is meant to be that in that world there is nothing that makes these entities distinct.

This thought proceeds from the idea that, for every object o, something grounds the identity of o: there is a metaphysical explanation for o’s being that very object, and not some other thing. What could do this grounding other than some subset of o’s properties? But if o is the thing it is in virtue of having some subset of its properties, then any thing which had all and only o’s properties would have its identity determined in the same way as o, and hence would be numerically identical to o.

That, I take it, is the intuitive thought behind the identity of indiscernibles. Any defender of that thought has to say something about Max Black’s world consisting solely of the two homogenous iron spheres Castor and Pollux. One thing to say is that the objects have different haecceitistic properties. Castor is distinct from Pollux because one has the property being identical to Castor and the other the property being identical to Pollux. Something seems unsatisfying about that. John Heil describes it somewhere as “the sort of move that gives philosophy a bad name.” But what’s wrong with it?

Firstly, you might not like the admission of such a ‘property’ into your ontology. Our grasp of what properties are seems to be tied to qualitative ways for things to be – such as being red or being round etc; the introduction of mere haecceitistic properties might be thought to have stretched the concept of property beyond breaking point.

But suppose you accept the existence of properties of the form being identical to x; there is a deeper problem. We are told that Castor and Pollux are distinct because Castor has the property being identical to Castor and Pollux has the property being identical to Pollux. But that only serves to ground the distinctness of Castor and Pollux if these properties are themselves distinct. If ‘the property being identical to Castor’ and ‘the property being identical to Pollux’ are two names for the same property then the fact that Castor has the former property and Pollux the latter doesn’t serve to ground their distinctness. So we need to ensure that these haecceitistic properties are distinct if their admission into our ontology is going to help us with Black’s example. But then, by the same reasoning that led us to the identity of indiscernibles in the first place, there must be something that grounds the distinctness of these properties. Now what do we usually think are the individuation conditions for properties? One might try: P and Q are the same property iff they make the same contribution to the qualitative nature of their bearer. But of course, this will only do for qualitative properties; applying it to mere haecceitistic properties would make them all identical, since mere haecceitistic properties don’t make any contribution to the qualitative nature of their bearers (that’s precisely why it rankles to call them ‘properties’). So for mere haecceitistic properties it seems we should have instead: P and Q are the same haecceitistic property iff they belong to the same thing.

But if that’s right then being identical to Castor is distinct from being identical to Pollux in virtue of the bearer of the former being distinct from the bearer of the latter. In which case we can hardly appeal to the distinctness of the properties to ground the distinctness of the bearers.

One who invokes mere haecceitistic properties to deal with Black’s world wants to hold that [Castor is distinct from Pollux] in virtue of the distinctness of being identical to Castor and being identical to Pollux; but it seems that they should be committed to [being identical to Castor is distinct from being identical to Pollux] holding true in virtue of the distinctness of Castor and Pollux. But these ‘in virtue of’ claims can’t both be true, since in-virtue-of is asymmetric. So the introduction of mere haecceitistic properties doesn’t seem to help: to ground the distinctness of Castor and Pollux the distinctness of the properties would apparently need to be taken as brute; and if we’re prepared to do that, why not just accept the distinctness of Castor and Pollux as brute in the first place?

Presentism and Relativity

Familiarly, the presentist faces an objection from special relativity. If presentism is true then only presently existing things exist. What is present is simultaneous with your reading this. So what exists are all and only the things that are simultaneous with your reading this just now. But what is simultaneous with your reading this just now is relative to a frame of reference. Therefore, what exists is relative to a frame of reference. But that’s nuts, so presentism is false.

What does the presentist need to do? Well, they win the game, presumably, if they can give some reason for privileging one reference frame over any other, for in that case they can claim simply that what exists is what is simultaneous with your reading of this according to the privileged reference frame. But how can they have a reason for thinking that one reference frame is privileged (without resorting to claiming that God smiles upon one and not the others)?

What we need is a truthmaker for the claim that some reference frame is privileged. Easy! Remember that to exist is to be present. So consider all the things that exist – they are all and only the present things. So surely the privileged reference frame is just that one according to which exactly these things are simultaneous. In that case the truthmaker for the fact that this is the privileged reference frame is just what makes it true that those things exist – namely, those things.

So the thought is this. Everyone in this debate agrees that there is a unique set, S, which is the set of the existing entities. (If you give up on that you don’t get to say ‘but that’s nuts’ in the original argument against presentism.) This (correct me if I’m wrong – I may be (not for the 1^st time!) misunderstanding the physics) lets us single out a unique reference frame: the unique reference frame according to which exactly the members of S are simultaneous. And so, if we’ve got good reason to think that everything that exists is present then we’ve got good reason to think that this frame is the privileged reference frame. Since everything in S exists then everything in S is present; so they had better be simultaneous; so the reference frame that says they are simultaneous is obviously the privileged one.

Convinced? I imagine not. Nor am I. But what’s wrong? I’m finding it hard to put my finger on it. What more is needed from the presentist? Or what are they doing that’s illegitimate?

A question about relations

Excuse my ignorance on this topic: I might be making either a stupid mistake or an obvious point - pointers to the literature are welcome!

Consider the relational expressions ‘is a child of’ and the relation ‘is a parent of’. It seems that we shouldn’t have to admit relations corresponding to both expressions into our ontology. If we believe in the is a child of relation then it is a constituent of the state of affairs a is b’s child, which is the truthmaker both for [a is a child of b] and [b is a parent of a] – we don’t need a separate relation is a parent of that is a constituent of the state of affairs b is a’s parent which makes the latter proposition true.

So we only need one relation here, not two. And it also seems crazy to think that one of the descriptions is privileged – i.e. to say that there is a relation corresponding to ‘is a child of’ but none corresponding to ‘is a parent of’. If that were the case, how we could know which expression picked out a real relation. Distinguishing between the world where ‘is a child of’ picks out a genuine relation and ‘is a parent of’ doesn’t and the world where ‘is a parent of’ picks out a genuine relation and ‘is a child of’ doesn’t seems like a bad case of distinguishing without a difference. There is just one relation that holds between a and b, and it is appropriate to call it both the ‘being a child of’ relation and the ‘being a parent of’ relation, depending on what order we list the terms.

But if that’s right we need to rethink how we state the properties of relations. Orthodoxy has it that the is a child of relation is non-symmetric: a can bear it to b without b bearing it to a. But if the above is right then this is false: b does bear it back to a – but in the other direction!

Two options then: either we could let symmetry etc apply to descriptions of the relations rather than the relations themselves, or we could ass directionality into our ideology and say that a relation R is symmetric iff if a bears R to b in a particular direction then b bears R to a in the same direction.

I prefer the second route. Can anyone foresee any problems? Or am I missing something in the first place?

Abortion and 'in virtue of'

This is on the ‘values’ side of ‘metaphysical values, rather than the ‘metaphysical’; but I will talk about 'in virtue of', so I don't feel totally ashamed :-)

We are doing a reading group on abortion, and today we were reading Liz Harman’s ‘The potentiality problem’. Harman is interested in how to defend the position that says both that early term abortions are morally permissible and that harms to human babies are worse than harms to, say, cats.

If early term abortions are morally permissible (and not just because not aborting would result in some greater evil, such as the death of the mother) then it seems they are so because the embryo has no moral status. But the baby appears to have moral status, if harming it is worse than harming the cat, so we need an account of what it takes to have moral status that lets the baby in but not the embryo (and it may or may not let the cat it). Harman proposes the following principle:

Conscious: A being has moral status at t just in case it is ever conscious and it is not dead at t.

(She should add ‘and it exists at t’ I think, but let’s not quibble.)

Since I am conscious, the embryo that I was (assuming that I was a embryo) had moral status. But since an embryo which is aborted is not conscious at any time, it does not have moral status at any time, and so it is permissible to abort it.

So I’m permitted to abort this embryo because it lacks moral status, but the reason that it lacks moral status is precisely because I aborted it: had I not aborted it, it would (at least, so we can suppose) have been conscious at some time, and so would have had moral status as an embryo. So I’m permitted to do this action because of something that is only true because I do this action – I don’t like it!

Consider another case. Suppose the moral oracle (completely trustworthy on all moral issues) tells us that it’s really, really bad to utter falsehoods. So bad, in fact, that if someone utters a falsehood, it’s permissible to kill them. Now I ask you what you’re going to do tomorrow and you say ‘I’m going to the cinema’. And then I shoot you. I was perfectly justified, because you spoke falsely: you’re not going to the cinema tomorrow, because tomorrow you will be dead! But intuitively, even in the world in which uttering falsehoods is a bad punishable by death, I shouldn’t be justified in punishing you for something that was only the case because I punished you.

The worry is this. In the ‘falsity is bad’ world, the proposition [it is permissible to kill a] is true in virtue of [a told a falsehood]. But [a told a falsehood] is true in virtue of [I killed a]. So it looks like the ultimate basis for the truth of [it is permissible to kill a] is in [I killed a]. And that looks absurd: my carrying out an action shouldn’t be what makes it the case that I was permitted to carry out that action.

Likewise, for Harman, [it is permitted to abort embryo e] is true in virtue of [e is never conscious] which is in turn true in virtue of [I abort e]. So it looks like the ultimate basis for the truth of [it is permitted to abort embryo e] is in the truth of [I abort e]. And that looks totally wrong to me: my carrying out the abortion shouldn’t make it the case that I was justified in carrying out the abortion.

A leeds-related blog post...

Just a quick post to point to some hot-off-the-press developments here at Leeds (for that is where our current timeslices are located).

Leeds is advertising a new-line professorial chair in philosophy. AOS's are open, but the idea is that the appointment will be related either to areas covered by History and Philosophy of Science, or the Centre for Metaphysics and Mind.

We are also advertising a lecturership/senior lectureship position in philosophy (those grades cover everyone from PhD-ers new on the market this year to senior people). Again no AOS is specified, though philosophy of value and history of philosophy are the areas that the department states it is "keen to appoint in".

Lastly, the recent Gourmet report previews have contained pleasant reading for Leeds. We've among the big movers (upwards!) in both the overall and the local UK rankings. And the mean score has gone up significantly too, by 0.2/0.3 respectively (out of 5). No matter what you think about league tables, there's something strangely addictive about them...

Lowe on necessity of identity

The standard proof of the necessity of identity runs as follows:

1) For all x, necessarily x=x (Premise)
2) a=b (Assumption)
3) Necessarily, a=a (From 1)
4) a has the property of being necessarily identical to a (From 3)
5) b has the property of being necessarily identical to a (From 2,4, and Leibniz’ law)
6) Necessarily, a=b (From 5)

I used to be concerned about Lowe’s objection to this proof. Lowe says (rightly) that we must be careful to distinguish between two properties: the property of being necessarily self-identical, as had by a, and the property of being necessarily identical by a, as had by a. The properties are clearly distinct: everything has the former, but only a has the latter. (3), Lowe said, is ambiguous: it could mean that everything has the property of being necessarily self-identical or it could mean that everything has the property of being necessarily identical to itself (i.e. that for all x, x has the property ‘being necessarily identical to x’). Read in the first way, (3) is uncontroversial, but then (4) doesn’t follow: all that follows is that a is necessarily self-identical and, hence, that b is necessarily self-identical. That is also uncontroversial, and a far cry from the necessity of identity. To get the claim that b is necessarily identical to a we need to get that a is necessarily identical to a, which requires the second reading of (3). But this, says Lowe, is not uncontroversial: to rule out contingent identity, we need to be given an argument for it.

Lowe is definitely right that there are two properties here. But is there any case to be made for the claim that a is necessarily self-identical but is not necessarily identical to a? I don’t think so. We can argue very simply as follows:

1) a is necessarily self-identical (Premise)
2) If is self identical then a is identical to a (Tautology)
3) Necessarily (If a is self identical then a is identical to a) (From (2))
4) Necessarily (a is self-identical) (From 1)
5) If Necessarily (a is self-identical), then Necessarily (a is identical to a) (From (3)
6) Necessarily (a is identical to a) (from (4) and (5))
7) a is necessarily identical to a (From (6))

Where could one resist that? Lowe definitely agrees with (2) because he is happy with the standard proof of the symmetry of identity, which relies on this (this is a point that Bob Hale has emphasised in his discussion of the necessity of identity). And surely (2) is no contingent truth – how could it fail? (Putting aside worries about the contingent existence of a.) (5) follows from (3) in any normal modal logic. Maybe one could resist the moves from (1) to (4) and (6) to (7) if one played silly-buggers with necessity as a predicate modifier – but that looks a bit desperate. The only other step is modus ponens. So the prospects don’t look bright. If you’re going to resist the standard argument, it shouldn’t be on Lowe’s grounds.

presentism fought the law and the law won

There’s loads of stuff I’ve got to get done today. Hence, I am procrastinating and writing more silly blog posts.

Does anyone know that content of the law against denying the Holocaust in countries like Austria? Is it enough to deny the truth of or must one assert the negation of it? I was thinking of a presentist who treats the past like Aristotle treats the future. So you think that only the present exists, and because you’re convinced by the truthmaker objection, you bite the bullet and hold that there’re no truths concerning the past or the future. So isn’t true. Nor is it false: it simply lacks a truth value. If I defend that view in Austria, will I get in trouble?

I heard Ned Markosian defend a presentist view whereby propositions concerning the past or the future are true to a certain degree, depending on how many of the possible (given the present laws of nature and the way things presently are) pasts/futures are the way the proposition says they are. So if every possible past is such that p then it is true that p was the case, but if only some possible pasts are such that p then it is true to some degree n (such that n is between zero and one) that p was the case. If Ned went to Austria and defended that view would he be in trouble to degree n?

This is a flippant point, of course; but behind it lies a more serious one: just what do laws that impose a limit on freedom of speech make illegal? If they infringe on academic freedom, that doesn’t appear to me to be a very good thing.

There are sets . . . (not really!)

I’ve been thinking a lot recently about relations of fundamentality. There are, I think, three relations here: a relation of ontological dependence that holds between entities, a relation of grounding/truth-in-virtue-of that holds between propositions, and the truth-making relation, that holds between an entity and a proposition.

One thing I am interested in is the connection between the relations. One potential connection is the following: if A makes p true and if p grounds q (i.e. if q is true in virtue of p) then A makes q true. This seems pretty plausible. If p grounds q then it doesn’t take anything more for the world to be a q-world than for it to be a p-world: so to make the world a p-world is to make it a q-world.

I’m currently intrigued by the potential of this to allow us to make sense of Fine’s distinction between what there is and what there really is. It would be nice to be allowed to make such a distinction. In particular, I’d like to be able to say that there are abstracta, but that there aren’t really any abstracta. I’d like to say that there are sets, for example, because it’s really useful to be able to talk about such things; but I’d like to deny that there are really any sets because an ontology without sets is, other things’ being equal, preferable to one with.

Now, it’s natural to think that a set is ontologically dependent on its members. Socrates’ singleton depends for its existence on Socrates, and not vice-versa. You might be tempted as well (perhaps as a consequence) to the claim that the proposition the singleton of Socrates exists is true in virtue of Socrates exists. Since Socrates is the truthmaker for Socrates exists the above principle will then imply that Socrates is the truthmaker for the singleton of Socrates exists.

First thought then: we don’t need there to actually be a singleton of Socrates. We only need Socrates, and he makes true all the truths talking about his singleton. Generalising, all we need are the ordinary concrete objects, and we get all the truths about sets for free. (Pure sets will be a bit trickier – but there are any number of stories we might tell here.) So we can secure all the truths we want – we get the benefit of talking about sets – without admitting sets into our ontology.

But that can’t be quite right. We can’t deny the existence of sets and affirm the truth of the proposition the singleton of Socrates exists. But what we can do is accept that there are sets and deny that there are really any sets. The thought is that the singleton of Socrates exists is true (and hence there are sets), and is made true by Socrates; but the singleton of Socrates really exists is not made true by Socrates; in fact, it’s not made true by anything, and so it’s false.

Armstrong says that a exists is always made true by a. I am denying that: I claim that the singleton of Socrates exists is made true not by the singleton of Socrates (since the truthmakers are what there really is, and there aren’t really any sets) but by Socrates. But I can accept a variant of the Armstrong position: that a really exists is always made true by a, which is a fundamental being.

So the thought is that we have a bunch of fundamental entities that do all our truthmaking. Some of the things they make true is that they really exist. Other things that they make true is that some non-fundamental entities exist (but not that they really exist – they don’t!). This is meant to secure all the benefits without the cost. We get the benefit of talking about sets, since all we need to secure that is that we can presuppose that sets exist – we couldn’t care less whether or not they really exist. And we secure a parsimonious ontology: since what we care about here is what there really is – what exists in reality – and sets don’t really exist.

I have no idea whether that is in line with Fine’s thinking on the distinction, but it seems to me not wholly crazy, and worthy of pursuit.

On other news, I’ve been invited to respond to Jonathan Schaffer (UMass) at the Pacific APA in San Francisco next April. I’ve never been to SF, and am looking forward to it. Schaffer is defending the view that, necessarily, every true proposition is made true by the world, which is the only fundamental entity that there is. We’ve already had some correspondence over his paper, after meeting at Bellingham, and it’s been lots of fun – so this should be a good time. San Francisco was the home of the one and only Emperor of the United States, which is reason enough to visit.

Eliminating cross-level universals

I've just come back from a CMM discussion of Lewis on Quantities (built around John Hawthorne's paper of that title).

One thing that came up was the issue of what you might call potentially "cross level" fundamental properties. These are properties that you might expect to find instantiated at the "bottommost" microphysical level, but also instantiated "further up". For example, electrons have negative charge; but so do ions. But ions are composite entities, which (from what I remember of A-level chemistry) are charged in virtue of the charges of their parts.
Clearly in some sense, electrons and ions can have the same determinate property: e.g. "charge -1". But, when giving e.g. a theory of universals, I'm wondering whether we have to say that they share the same Universal.

On Armstrong's theory of quantities, it looks to me that we won't say that the ion and the electron both instantiate the same Universal. The "charge -1" we find instantiated by the ion will be a structural universal, composed of the various charge Universals instantiated by the basic parts of the ion. The "charge -1" we find instantiated by an electron, on the other hand, looks like it'll be a basic, non-structural universal. So, it seems to me, it'll then be a challenge to Armstrong's account to say why these two universals resemble each other in a tight enough way that we apply to them the same preicate. (To avoid confusion, let's call the former "ur-charge -1" and leave "charge -1" as a predicate that applies to both ions and electrons, though not, on this view, in virtue of them instantiating the same Universal).

Let's suppose we're looking at a theory of universals (such as the one Lewis seems to contemplate at various points) which is just like Armstrong's except for ditching all the structural universals. Electrons get to instantiate the Universal "ur-charge -1". But ions, as actual-worldly complex objects, instantiate no Universals at all. Of course, again there's the challenge to spell out exactly what the conditions are under which we'll apply the predicate "charge -1" to things (roughly: when the various ur-charges instantiated by their parts "balance out"---though the details get tricksy).

What goes for charge can go for various other types of property. So we may find it useful to distinguish ur-mass 1kg (which will be a genuine basic universal) from the set of things "having mass 1kg".


A last thought. What is the relation between mass properties and ur-masses? In particular, is it the case that things can only ever have masses when their basic parts have ur-masses? I don't see any immediate reason to think so. Perhaps the actual world is one where things have mass in virtue of their parts having ur-mass. But why shouldn't we think that "having parts that have ur-masses" is but one *realization* of mass: and that at other worlds quite different ur-properties may underlie mass (say, ur-mass-densities, rather than ur-masses). That's potentially significant for discussions of modality and quantities: for two worlds that intially seem to be share the same stock of fundamental properties (spin, charge, mass, etc) may turn out to actual contain alien properties from each others point of view: if one contains ur-masses underlying the (non-fundamental) mass properties, while the other contains ur-mass-densities underlying those same properties.

(Thanks to all those at CMM for the discussion that led to this. This is x-posted at Theories n Things. And thanks to an anonymous commentator, who pointed out in an early version of this post that by "free radicals" I meant "ions"!))

Hawthorne on Lewis on Quantity

Just a quick reminder to metaphysicians in the Leeds area: the CMM seminar today is going to be on Hawthorne's paper "Lewis on Quantity" from his Metaphysical Essays.

A quick puzzle I'm having over Lewis-interpretation. Suppose that in the actual world, a fundamental property P is instantiated by pointy things. Can that very same fundamental property be instantiated in another world by non-pointy things?

The point is that in characterizing Humean supervenience, Lewis mentions ways it might fail e.g. there being "emergent natural properties of more-than-point sized things". He insists that, though such properties are possible, they would have to occur in worlds featuring properties "altogether alien to this world". But that wouldn't be the case if it were a contingent feature of the properties we found lying around this world, that they hold of pointy things rather than more-than-point-sized things.

Maybe the moral is that the mereological structure of the instantiators of a property is *not* a matter that can vary from world to world, for Lewis. If so, it seems a pretty strange claimed of necessity.

Just me ranting . . .

Companies can be really annoying. I doubt anyone needs convincing of that, but my current gripe is rather amusing, so I’ll share it.

When I moved into my new flat I phoned Power Company (I won’t use the real name) to let them know to start my account from my move in date, and that the old occupiers had moved. After a month I duly got my first bill, addressed to me. I also got a bill addressed to ‘the occupier’, for the account of the previous occupiers. It started:

Dear occupier,

We notice you have now moved from this address: please settle your account . . . etc

I phoned Power Company to explain to them that ‘the occupier’ was an indexical, and that while it used to refer to the people who had the unpaid account, it now refers to me. I also tried to explain that ‘the occupier of flat X no longer lives in flat X’ can never express a truth, but without much success.

I thought that was the end of it until I received a letter from their solicitors (again, addressed to the occupier) demanding payment. And the funniest thing is, when I phoned them up to politely explain again, they chastised me for opening someone else’s mail! Again, I tried to explain that if you write ‘to the occupier of flat X’ on the envelope, then that is to address it to me, but they didn’t seem to be getting this.

On another totally frivolous note. I’m interested in whether particular issues of religious faith can be reconciled with science. The current hot topic here, I guess, is creationism. Some Christians appear to think they’ve got reason to hold that the Earth is only six thousand years old, and that humans were created in close to their present form. This seems straightforwardly incompatible with the scientific view that we evolved over rather a longer period. But perhaps not. Consider the eternalist/presentist debate. The eternalist thinks there is a past time with dinosaurs, the presentist thinks there is only the present time, but that it is true at the present time that there were dinosaurs nevertheless. I think the creationist should hold that there are past times only six thousand years into the past, but that it is nevertheless true that prior to this such-and-such was going on. It’s true that there were apes who would evolve into humans; but nevertheless, there are no past apes who are our ancestors. That seems like a perfectly consistent view. I wonder if I can get a grant to put this view across to US high-schools. Would that count as knowledge transfer?

Sorry this post has been a bit frivolous. That’s what we get for working in something like philosophy. Oh for the rigour and intellectual honesty of science, where they’ve just discovered that having a cup of tea can relax you. Well, no one could have told you that! – I’m glad the research money is being put to good use.

Ontic vagueness: the shape of the debate.

(cross-posted on theories n things)

One of my projects at the moment is writing a survey article on ontic vagueness. I've been working on this stuff for a while now, but it's time to pull things together. (And writing up comments on Hugh Mellor's paper "Micro-composition" at the RIP Being conference got me puzzling about some of these issues all over again.)

One thing I'd like to achieve is to separate out different types of ontic vagueness. The "big three", for me, are vague identity, vague existence, vague instantition. But there also might be: vagueness in the parthood relation, vague locations, vague composition, vagueness in "supervening" levels (it being ontically vague whether x is bald); vagueness at the fundamental level (it being ontically vague whether that elementary particle is charged). These all seem prima facie different, to me. And (as Elizabeth Barnes told me time and again until I started listening) it's just not obvious that e.g. rejecting vague identity for Evansian reasons puts in peril any other sort of ontic vagueness, since it's not obvious that any other form of ontic vagueness requires vague identity.

[Digression: It's really not very surprising that ontic vagueness comes in many types, when you think about it. For topic T in metaphysics (theory of properties, theory of parts, theory of persistence, theory of identity, theory of location etc etc), we could in principle consider the thesis that the facts discussed by T are vague. End Digression]

Distinguish (a) the positive project of giving a theory of ontic vagueness; and (b) the negative project of defending it against its many detractors. The negative project I guess has the lion's share of the attention in the literature. I think it helps to see the issues here as a matter of (i) developing arguments against particular types of ontic vagueness (ii) arguing that this or that form of ontic vagueness entails some other one.

Regarding (i), Evans' argument is the most famous case, specifically against vague identity. But it won't do what Evans claimed it did (provide an argument against vagueness in the world per se) unless we can argue that other kinds of ontic vagueness give rise to vague identity (and Evans, of course, doesn't say anything about this). Vague existence is another point at which people are apt to stick directly. I think some of Ted Sider's recent arguments against semantically or epistemically vague existence transfer directly to the case of ontically vague existence. And we shouldn't forget the "incredulous stare" maneuver, often deployed at this point.

Given these kind of answers to (i), I think the name of the game in the second part of the negative project is to figure out exactly which forms of ontic vagueness commit one to vague existence or vague identity. So, for example, one of the things Elizabeth does in her recent analysis paper is to argue that vague instantiation entails vague existence (at least for a states-of-affairs theorist). Implicit in an argument due to Katherine Hawley are considerations seemingly showing that vague existence entails vague identity (at least if you have sets, or unrestricted mereological composition, around). (I set both of these out briefly and give references in this paper).
Again, you can think of Ted Sider's argument against vague composition as supporting the following entailment: vague composition entails vague existence. And so on and so forth.

[A side note. Generally, all these arguments will have the form:

Ontic vagueness of type 1
Substantive metaphysical principles
Therefore:
Ontic vagueness of type 2.

What this means is that these debates over ontic vagueness are potentially extemely metaphysically illuminating. For, suppose that you think that ontic vagueness of type 2 occurs, but that ontic vagueness of type 1 is impossible (say because it entails vague identity). Then, you are going to have to reject the substantive metaphysical principles that provide the bridge from one to the other. For example, if you want vague instantiation, but think vague existence is, directly or indirectly, incoherent, then you have an argument against states-of-affairs-theorists. The argument from vague existence to vague identity won't worry someone who doesn't believe in or in unrestricted mereological fusion. Hence, if cogent, it can be turned into an argument against sets and arbitrary fusions (actually, it's in that form --- as an argument against the standard set theoretic axioms --- that Katherine Hawley first presented it). And so forth.]

So that's my view on what the debate on ontic vagueness is, or should be. It has the advantage of unifying what at first glance appear to be a load of disparate discussions in the literature. It does impose a methodology that's not in keeping with much of the literature by defenders of ontic vagueness: in particular, the way I'm thinking of things, classical logic will be the last thing we give up: though non-classical logics are often the first tool reached for by defenders of ontic vagueness (notable exceptions are the modal-ish/supervaluation-ish characterizations of ontic vagueness favoured in various forms by Ken Akiba, Elizabeth Barnes and, erm, me). I'll have to be up front about this.

Still, I'd like to use the above as a way of setting up the paper. It can only be 5000 or so words long, and it has to be comprehensible to advanced undergraduates, so I may not be able to include everything, particularly if the issues allude to complex areas of metaphysics. But I'd like to have an as-exhaustive-as-possible taxonomy, of which I can extract a suitable sample for the paper. I'd be really interested in collecting any discussions of ontic vagueness that can fit into the project as I've sketched it. And I'd also be really grateful to hear about other parts of the literature that I'm in danger of missing out or ignoring if I go this route, and any comments on the strategy I'm adopting.

Some examples to get us started:

If composition is identity, then it looks like vague parthood entails vague identity. For if it's vague whether the a is part of b, then it'll be vague whether the a's are identical to b.

Indeed, if classical mereology holds, then it looks like vague parthood entails vague identity. For if it's vague whether the aa's are all and only the parts of b, then mereology will give us that that object which is the fusion of the aa's is identical to b iff the aa's are all and only the parts of b. Since the RHS here is ex hypothesi vague, the LHS will be too.

If the Wigginsean "individuation criteria" for Fs are vague, it looks like vague existence will follow when it's vague whether the conditions are met.

An argument for conditional excluded middle

(cross-posted from Theories n Things)

Conditional excluded middle is the following schema:

if A, then C; or if A, then not C.

It's disputed whether everyday conditionals do or should support this schema. Extant formal treatments of conditionals differ on this issue: the material conditional supports CEM; the strict conditional doesn't; Stalnaker's logic of conditionals does, Lewis's logic of conditionals doesn't.

Here's one consideration in favour of CEM (inspired by Rosen's "incompleteness puzzle" for modal fictionalism, which I was chatting to Richard Woodward about at the Lewis graduate conference that was held in Leeds yesterday).

Here's the quick version:

Fictionalisms in metaphysics should be cashed out via the indicative conditional. But if fictionalism is true about any domain, then it's true about some domain that suffers from "incompleteness" phenomena. Unless the indicative conditional in general is governed in general by CEM, then there's no way to resist the claim that we get sentences which are neither hold nor fail to hold according to the fiction. But any such "local" instance of a failure of CEM will lead to a contradiction. So the indicative conditional in general is governed by CEM

Here it is in more detail:

(A) Fictionalism is the right analysis about at least some areas of discourse.

Suppose fictionalism is the right account of blurg-talk. So there is the blurg fiction (call it B). And something like the following is true: when I appear to utter , say "blurgs exist" what I've said is correct iff according to B, "blurgs exist". A natural, though disputable, principle is the following.

(B) If fictionalism is the correct theory of blurg-talk, then the following schema holds for any sentence S within blurg-talk:

"S iff According to B, S"

(NB: read "iff" as material equivalence, in this case).

(C) The right way to understand "according to B, S" (at least in this context) is as the indicative conditional "if B, then S".

Now suppose we had a failure of CEM for an indicative conditional featuring "B" in the antecedent and a sentence of blurg-talk, S, in the consequent. Then we'd have the following:

(1) ~(B>S)&~(B>~S) (supposition)

By (C), this means we have:

(2) ~(According to B, S) & ~(According to B, ~S).

By (B), ~(According to B, S) is materially equivalent to ~S. Hence we get:

(3) ~S&~~S

Contradiction. This is a reductio of (1), so we conclude that

(intermediate conclusion):
No matter which fictionalism we're considering, CEM has no counterinstances with the relevant fiction as antecedent and a sentence of the discourse in question as consequent.

Moreover:

(D) the best explanation of (intermediate conclusion) is that CEM holds in general.

Why is this? Well, I can't think of any other reason we'd get this result. The issue is that fictions are often apparently incomplete. Anna Karenina doesn't explicitly tell us the exact population of Russia at the moment of Anna's conception. Plurality of worlds is notoriously silent on what is the upper bound for the number of objects there could possibly be. Zermelo Fraenkel set-theory doesn't prove or disprove the Generalized Continuum Hypothesis. I'm going to assume:

(E) whatever domain fictionalism is true of, it will suffer from incompleteness phenomena of the kind familiar from fictionalisms about possibilia, arithmetic etc.

Whenever we get such incompleteness phenomena, many have assumed, we get results such as the following:

~(According to AK, the population of Russia at Anna's conception is n)
&~(According to AK, the population of Russia at Anna's conception is ~n)

~(According to PW, there at most k many things in a world)
&~(According to PW, there are more than k many things in some world)

~(According to ZF, the GCH holds)
&~(According to ZF, the GCH fails to hold)

The only reason for resisting these very natural claims, especially when "According to" in the relevant cases is understood as an indicative conditional, is to endorse in those instances a general story about putative counterexamples to CEM. That's why (D) seems true to me.

(The general story is due to Stalnaker; and in the instances at hand it will say that it is indeterminate whether or not e.g. "if PW is true, then there at most k many things in the world" is true; and also indeterminate whether its negation is true (explaining why we are compelled to reject both this sentence and its negation). Familiar logics for indeterminacy allow that p and q being indeterminate is compatible with "p or q" being determinately true. So the indeterminacy of "if B, S" and "if B, ~S" is compatible with the relevant instance of CEM "if B, S or if B, ~S" holding.)

Given (A-E), then, I think inference to the best explanation gives us CEM for the indicative conditional.

[Update: I cross-posted this both at Theories and Things and Metaphysical Values. Comment threads have been active so far at both places; so those interested might want to check out both threads. (Haven't yet figured out whether this cross-posting is a good idea or not.)]

The necessity of identity and essentialism

Here's one argument for the necessity of identity. Assume a=b. a has the property of being essentially identical to a. By Leibniz's law, b also has this property. So in every world in which b exists, b is identical to a, so there's no world in which a and b are distinct.

Will that convince the anti-essentialist? No, because it relies on an essentialist assumption: that every thing x has the property of being essentially identical to x. (This is not the premise that every thing x has the property of being essentially self-identical, which the anti-essentialist may well grant.)

Can the necessity of identity be established without relying on essentialist assumptions? I don't think so. But there is a tradition of thinking it can be established solely by considerations concerning rigid designation. I thought this tradition had died and been buried, but it has arisen in a recent article in the Philosophical Quarterly by Sören Häggqvist. (Häggqvist, Sören, (2006), ‘Essentialism and Rigidity’, The Philosophical Quarterly 56:223, p275-283.)

He argues as follows. If ‘a’ and ‘b’ are rigid designators then they designate in every possible world that which they designate in the actual world. Since they designate the same thing in the actual world (let us suppose) they therefore designate the same thing in every possible world, and so ‘a=b’ is a necessary truth.

I don't think this argument works, and want to bury it for good. The argument moves from (1) ‘a’ and ‘b’ designate the same thing in the actual world and (2) in any world, both ‘a’ and ‘b’ designate what they designate in the actual world to (3) in any world ‘a’ and ‘b’ designate the same thing. But (3), pretty obviously, only follows from (1) and (2) if the necessity of identity is true, and so to rely on this move is just to beg the question. Suppose ‘a’ and ‘b’ actually co-designate but that there is a world, w, in which ‘a’ designates something distinct from ‘b’. Does it follow that one or other of ‘a’ and ‘b’ designate in w something that they do not designate in the actual world? Not if a and b are identical in the actual world but distinct in w. If a and b are merely contingently identical then of course the rigid designators ‘a’ and ‘b’ will not necessarily co-designate; in a world in which a and b are distinct then, since ‘a’ must still designate a and ‘b’ still designate ‘b’ in this world, ‘a’ and ‘b’ will designate distinct things in this world. And so to conclude that the rigid designators ‘a’ and ‘b’ necessarily co-designate because they actually do begs the question against the contingent-identity theorist.

Defining presentism: the real problem

At the CMM event Robbie mentions below, Jonathan Tallant discussed a problem for defining presentism. The problem didn't seem to me to problematic, since it assumed the only existential quantifiers the presentism has in her toolbox are one equivalent to 'exists now' and one equivalent to 'existed, exists now, or will exist'. Since this is patently false, that problem seems to vanish.

But there did seem to me to be a problem in the vicinity; namely, that all obvious attemtps at a definition require us to reify times.

Intuitively I can refuse to admit the existence of times and there still be an eternalism/presentism question. Two theorists should be able to have a debate concerning the nature of time and existence without quantifying over times. But I couldn't think how to define the terms without reifying times, and certainly the familiar definitions fail.

Consider 'the only time is the present time'. If there are no times, this is true. So if there can be a presentist/eternalist debate between those who don't reify times, this doesn't capture presentism.

What about 'only present things exist' (where 'exists' here is atemporal)? Nope, that won't do if there are no times. Consider two endurentists who believe that the world started with A, B and C coming into existence. Those three objects proceed to endure through some changes, and then the world ends (taking A, B and C with it of course). So nothing comes into or goes out of existence in this world. At any time it is true that only the things that are present at that time exist atemporally, since A, B and C are the only things that exist at any time, and are the only things that exist atemporally. But that doesn't mean presentism is true at this world: intuitively, there is still a debate to be had between the two endurentists as to whether presentism or eternalism is true.

Any thoughts?

CMM event

Just a quick note to remind those in the Leeds area of today's internal workshop, featuring CMM-ers Tallant, Shalkowski, McGonigal and Keiran (and of course pertinent and witty interventions from the rest of us). Schedule:

9.30-11.00 Matthew Kieran. "Aesthetic Judgement and snobbery"
11.30-1.00 Andrew McGonigal "Truth, relativism and serial fiction"
1-2 lunch
2-3.30 Scott Shalkowski. "A Short Argument for Essentialism"
4-5.30 Jonathan Tallant "Presentism vs. Eternalism and the Problem of Tense"

6+ meal and pub.

We have a seminar room + a coffee room booked at the IDEA CETL for the day. No specific arrangements for lunch and dinner have been made, but I conjecture Opposite Café will be involved.

bestriding the blogosphere...

Five posts in, and we're up at the latest Philosopher's carnival! The kids go wild for a good bit of truthmaking...

Why hold truthmaker necessitarianism?

It is orthodoxy amongst truthmaker theorists that the existence of a truthmaker necessitates the truth of that which it makes true: if a thing A is a truthmaker for the proposition that p, then there is no possible world in which A exists and p is false. Is there any good argument for this claim?

The only argument I know of for truthmaker necessitarianism is that given by David Armstrong. Armstrong says[1]:

If it is said that the truthmaker for a truth could have failed to make the truth true, then we will surely think that the alleged truthmaker was insufficient by itself and requires to be supplemented in some way. A contingently sufficient truthmaker will be true only in circumstances that obtain in this world. But then these circumstances, whatever they are, must be added to give the full truthmaker.

His thought, I take it, is this. Suppose that A makes p true but doesn’t necessitate the truth of p. In that case there are some possible worlds in which A exists and p is false: some set of circumstances in which the existence of A does not suffice for the truth of p. But then isn’t it overwhelmingly intuitive that the truthmaker for p is not simply A but rather A together with whatever makes it true that those circumstances do not in fact obtain?

Let’s spell this argument out in a little more detail, making explicit Armstrong’s implicit assumptions. A first shot is:

1) A makes p true. (Assumption)

2) The existence of A does not necessitate the truth of p. (Assumption for reductio)

3) There is a possible world in which A exists and p is false. (From 2)

4) There is a (probably highly disjunctive) proposition q which is true in exactly those worlds in which A exists and p is false. (q is the proposition that describes the circumstances in which the existence of A does not suffice for the truth of p.) (This assumption follows from the general assumption that for any set of possible worlds, there is a proposition that is true at exactly those worlds.)

5) What makes p true is A together with what makes not-q true. I.e. if not-q is made true by B, then p is made true by the sum of A and B. (Assumption)

6) p is not made true by both A and the sum of A and B. (Assumption)

7) p is not made true by A. (From 5 and 6)

8) Contradiction. (From 1 and 7)

But what right does Armstrong have for premise (6)? A proposition can have more than one truthmaker – you and I both make it true that there are humans – so there is no contradiction in holding that p is made true both by A and by the sum of A and B. I guess Armstrong’s thought is that the sum of A and B jointly necessitate the truth of p, and that if there is a necessitating truthmaker for a proposition, nothing which did not necessitate the truth of that proposition deserves to be called its truthmaker. That is, it would only be reasonable to think that p had a non-necessitating truthmaker if p had no necessitating truthmaker. (That is, I think, what is behind his comment that “the alleged truthmaker was insufficient by itself”.) That is a fairly plausible thought, so let us amend Armstrong’s argument as follows:

1) A makes p true. (Assumption)

2) The existence of A does not necessitate the truth of p. (Assumption for reductio)

3) There is a possible world in which A exists and p is false. (From 2)

4) There is a (probably highly disjunctive) proposition q which is true in exactly those worlds in which A exists and p is false. (q is the proposition that describes the circumstances in which the existence of A does not suffice for the truth of p.) (This assumption follows from the general assumption that for any set of possible worlds, there is a proposition that is true at exactly those worlds.)

5) The truth of p is necessitated by A together with what makes not-q true (call it B). A and B together are a necessitating truthmaker for p. (Assumption)

6) There is no non-necessitating truthmaker for p. (From 5)

7) Contradiction. (From 1, 2 and 6)

I used to think the best point of resistance for the denier of necessitarianism was the assumption, presupposed by premise (5), that every truth has a truthmaker. [2] If we deny that negative facts such as not-q require a truthmaker then the argument doesn’t go through. But, I thought, one who upholds truthmaker maximalism is committed, by this argument, to truthmaker necessitarianism. Now I think that is wrong. No one, maximalist or non-maximalist, should be persuaded by this argument to accept truthmaker necessitarianism.

Ask yourself first: what right does Armstrong have to premise (5)? Why should we think that A together with whatever makes it true that not-q is a necessitating truthmaker for p? The only reason I can see is as follows. q is a complete specification of the possible circumstances in which A exists and p is false. So if not-q is made true then those circumstances do not obtain. So if not-q is made true then we are in a world in which the existence of A suffices for the truth of p. So, necessarily, if both the truthmaker for not-q and A exist, then p is true.

Unfortunately, this last step is no good. It is true that every world in which not-q is true is a world in which the existence of A suffices for the truth of p. There is no possible world in which not-q is true and A exists and p is false. But it only follows that the truthmaker for not-q cannot exist in a world in which A exists and p is false if we add the assumption that the truthmaker for not-q cannot exist in a world in which not-q is false (i.e. a world in which q is true). But of course we can’t assume that, for that would simply beg the question. Our only reason for thinking that the truthmaker for not-q couldn’t exist in a world in which q is true is if truthmakers must necessitate the truth of the propositions they are truthmakers of, and that is exactly what the argument is trying to establish.

If Armstrong is to avoid begging the question he must leave it open that B, the truthmaker for not-q, can exist in a world in which q is true. That is a world in which the existence of A does not suffice for the truth of p, so we have been given no reason to rule out the possibility of worlds in which A and B both exist and p is false. So we have no reason to think that A and B together are a necessitating truthmaker for p, and hence no reason to think that A is not an adequate truthmaker for p.

To focus discussion, let us consider a particular account of truthmakers according to which a truthmaker for p need not necessitate the truth of p: Josh Parsons’ theory that the truthmaker for p is that which is intrinsically such that p.[3] Since an object needn’t have its intrinsic properties essentially, Parsons denies necessitarianism. A can make p true and exist in worlds in which p is false provided that, in each of those worlds, A differs intrinsically from how it actually is.

How should Parsons respond to Armstrong’s argument? Well, what should Parsons think the truthmaker for not-q is? q is the proposition that describes exactly the circumstances in which A exists and p is false. What are those circumstances on Parsons’ theory? They are the circumstances in which A differs intrinsically from how it actually exists. So not-q is the proposition that is true exactly when A is as it actually is intrinsically. So what makes this true? That which is intrinsically such that A has the intrinsic properties it actually has – namely, A.

So for Parsons, A is the truthmaker for not-q. What makes it true that we are not in the circumstances in which A can exist and p be false is just the truthmaker for p. A can exist in worlds in which not-q is false, of course – the existence of A does not necessitate that A is intrinsically as it actually is. But that is no objection; it is part of the theory that the existence of the truthmaker need not necessitate the truth of that which it makes true. All that is required is that in the worlds in which A exists and not-q is false, A differs intrinsically from how it actually is. And that is obviously guaranteed: A cannot be as it actually is intrinsically and q be true, since q just is the proposition that A differs intrinsically from how it actually is.

It is clear then that Armstrong’s argument has no pull against someone who accepts a theory like Parsons’. The argument only works if the truthmaker for not-q must be a necessitating truthmaker, but to assume this would beg the question.

---

[1] D.M. Armstrong, A World of States of Affairs, Cambridge: Cambridge University Press, 1997, p116

[2] Ross Cameron, ‘Truthmaker Necessitarianism and Maximalism’, Logique et Analyse 48(189-192), p43-56, 2005

[3] Josh Parsons, ‘There is no truthmaker argument against nominalism’, Australasian Journal of Philosophy 77(3), p325-334, 1999

Semantics for nihilists

Microphysical mereological nihilists believe that only simples exist---things like leptons and quarks, perhaps. You can be a mereological nihilist without being a microphysical mereological nihilist (e.g. you can believe that ordinary objects are simples, or that the whole world is one great lumpy simple. Elsewhere I use this observation to respond to some objections to microphysical mereological nihilism). But it's not so much fun.

If you're a microphysical mereological nihilist, you're likely to start getting worried that you're committed to an almost universal error-theory of ordinary discourse. (Even if you're not worried by that, your friends and readers are likely to be). So the MMN-ists tend to find ways of sweetening the pill. Van Inwagen paraphrases ordinary statements like "the cat is on the mat" into plural talk (the things arranged cat-wise are located above the things arranged mat-wise"). Dorr wants us to go fictionalist: "According to the fiction of composition, the cat is on the mat"). There'll be some dispute at this point about the status of these substitutes. I don't want to get into that here though.

I want to push for a different strategy. The way to do semantics is to do possible world semantics. And to do possible world semantics, you don't merely talk about things and sets of things drawn from the actual world: you assign possible-worlds intensions as semantic values. For example, the possible-worlds semantic value of "is a cordate" is going to be something like a function from possible worlds to the things which have hearts in those worlds. And (I assume, contra e.g. Williamson) that there could be something that doesn't exist in the actual world, but nevertheless has a heart. I'm assuming that this function is a set, and sets that have merely possible objects in their transitive closure are at least as dubious, ontologically speaking, as merely possible objects themselves.

Philosophers prepared to do pw-semantics, therefore, owe some account of this talk about stuff that doesn't actually exist, but might have done. And so they give some theories. The one that I like best is Ted Sider's "ersatz pluriverse" idea. You can think of this as a kind of fictionalism about possiblia-talk. You construct a big sentence that accurately describes all the possibilities. Statements about possibilia will be ok so long as they follow from the pluriverse sentence. (I know this is pretty sketchy: best to look at Sider's version for the details).

Let's call the possibilia talk vindicated by the construction Sider describes, the "initial" possibila talk. Sider mentions various things you might want to add into the pluriverse sentence. If you want to talk about sets containing possible objects drawn from different worlds (e.g. to do possible world semantics) then you'll want to put some set-existence principles into your pluriverse sentence. If you want to talk about transworld fusions, you need to put some mereological principles into the pluriverse sentence. If you add a principle of universal composition into the pluriverse sentence, your pluriverse sentence will allow you to go along with David Lewis's talk of arbitrary fusions of possibilia.

Now Sider himself believes that, in reality, universal composition holds. The microphysical mereological nihilist does not believe this. The pluriverse sentence we are considering says that in the actual world, there are lots of composite objects. Sider thinks this is a respect in which it describes reality aright; the MMN-ist will think that this is a respect in which it misdescribes reality.

I think the MMN-ist should use the pluriverse sentence we've just described to introduce possibilia talk. They will have to bear in mind that in some respects, it misdescribes reality: but after all, *everyone* has to agree with that. Sider thinks it misdescribes reality in saying that merely possible objects, and transworld fusions and sets thereof, exist---the MMN-ist simply thinks that it's inaccuracy extends to the actual world. Both sides, of course, can specify exactly which bits they think accurately describe reality, and which are artefactual.

The MMN-ist, along with everyone else, already has the burden of vindicating possibilia-talk (and sets of possibilia, etc) in order to get the ontology required for pw-semantics. But when the MMN-ist follows the pluriverse route (and includes composition priniciples within the pluriverse sentence), they get a welcome side-benefit. Not only do they gain the required "virtual" other-worldly objects; they also get "virtual" actual-worldy objects.

The upshot is that when it comes to doing possible-world semantics, the MMN-ist can happily assign to "cordate" an intension that (at the actual world) contains macroscopic objects, just as Sider and other assign to "cordate" an intension that (at other worlds) contain merely possible objects. And sentences such as "there exist cordates" will be true in exactly the same sense as it is for Sider: the intension maps the actual world to a non-empty set of entities.

So we've no need for special paraphrases, or special-purpose fictionalizing constructions, in pursuit of some novel sense in which "there are cordates" is true for the MMN-ist. The flipside is that we can't read off metaphysical commitments from such true existential sentences. Hey ho.

(cross posted on theories 'n things)