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)