The Aporetics of Existence and Self-Identity

Andrew B. made some powerful objections to a recent existence post.  His remarks suggest the following argument:

Argument A

1. Existence is self-identity
2. My existence is contingent:  (∃x)(x = I) & Poss ~(∃x) (x = I)
Therefore
3. My self-identity is contingent:  I = I & Poss ~ (I = I)

Argument A may be supplemented by the following consideration.  Since I am contingent, there are possible worlds in which I do not exist.  Not being in those worlds, I cannot have properties in them, including the property of self-identity. So it is not the case that I am necessarily self-identical; I am self-identical only in those worlds in which I exist, which is to say: I am contingently self-identical.  I am self-identical in some but not all worlds.

The argument can be rationally resisted. 

Consider a possible world w in which I do not exist.  In w, the proposition expressed by an utterance by me of 'I am not self-identical' is true.  But if it is true in w, then the proposition exists in w.  Now if the proposition exists in w, then so do its constituents.  On a Russellian view of propositions, I am one of the proposition's  constituents.  So for the proposition  *I am not self-identical* to be true in w, I must exist in w.  But if I exist in w, then of course I am self-identical in w, and the proposition is false in w.  But the same goes for every world in which I do not exist.  It follows that I am self-identical in every world and I exist in every world.

Of course, one needn't take a Russellian line on propositions.  One could take a Fregean view according to which propositions about me do not have me as a constituent but an abstract representative of me, a sense or mode of presentation.  But the first-person singular pronoun 'I' has the peculiarity that it cannot be replaced salva significatione by any description; so even if there is an abstract representative of me in the Fregean proposition expressed by my utterance of  'I am not self-identical,' there still has to be a referent of the representative external to the proposition.  So I have to exist in w for the proposition *I am not self-identical* to be true in w.  But if I exist in w then I am self-identical in w.  This in turn implies that the proposition is not true.  

The cognoscenti will appreciate that what I have been doing in a rough and dirty way is reproducing some of the thoughts in Timothy Williamson's paper Necessary Existents.  I am doing so to show that Argument A is not convincing.  Making use of materials from Williamson's paper, we can 'throw Argument A into reverse':

Argument B

1. Existence is self-identity
~3. My self-identity is necessary: Nec (I = I)
Therefore
~2. My existence is necessary.

In point of validity, there is nothing to choose between A and B: both are valid.  And both, I submit, have counterintuitive conclusions.  It seems to me that the arguments cancel each other out.  So I propose that we think very skeptically about the common premise that existence is self-identity, and the Quinean thin theory that commits us to it. 

Comments

[Andrew]

Bill,

If I understood you correctly in previous posts, you agreed with the Quineans that self-identity was co-extensive with existence (something exists iff it is self-identical), but maintained that existence and self-identity were nonetheless distinct. Though existence goes hand-in-hand with self-identity, the thought goes, it is nonetheless *thicker* than mere self-identity. Is that correct?

If so, it would seem that these aporetics create the same puzzles for your view as they do for the Quinean's. For arguments A and B can be reformulated with the weaker premise that existence is co-extensive with self-identity, which premise I thought you accepted. If I'm right about that, then rejecting the common premise between arguments A and B is not, for you, an appealing way out of this puzzle.

Cheers,

-Andrew

[Bill Vallicella]

Andrew,

Excellent comment!

Your first paragraph accurately expresses what I have been maintaining. Necessarily, x exists iff x is self-identical. But I don't take this as sanctioning a reduction of existence to self-identity. (Analogy: necessarily, x is triangular iff x is trilateral. But this equivalence does not underwrite a reduction of one of the properties to the other. Tha analogy limps, however, because existence is not a quidditative property.)

As for your second paragraph, you're right!

What I am trying to do, without succeeding, is to make the 'thickness' of existence intellectually visible while remaining on the plane of the discursive intellect, hence not appealing to intuition (e.g., Wittgenstein's wonder, Sartre's nausea).

My quandary is that the difference between existence and self-identity cannot show up extensionally (given that I have rejected Meinongianism). It is like an intensional difference, except that it is not intensional! Hyper-intensional?