What, if anything, is wrong with the following argument:
1. (x)(x = x) (Principle of Identity)
2. John McCain = John McCain (From 1 by Universal Instantiation)
3. (Ex)(x = John McCain) (From 2 by Existential Generalization)
4. John McCain exists. (From 3 by translation into ordinary idiom)
The initial premise states that everything is identical to itself, that nothing is self-diverse. Surely this is a necessary truth, one true no matter what, or in the jargon of possible worlds: true in every (broadly logically) possible world.
(2) follows from (1) by the intuitively clear inference rule of Universal Istantiation. Surely, if everything is self-identical, then John McCain is self-identical. The inferential move from (2) to (3) is also quite obvious: if McCain is self-identical, then something is identical to McCain. But (3) is just a complicated way of saying that John McCain exists. So we get the surprising result that the existence of John McCain is validly deducible from an a priori knowable necessary truth of logic!
You understand, of course, that the argument is not about John McCain: it is about any nameable entity. Supposedly, Wilhelm Traugott Krug (1770-1842) once demanded of Hegel that he deduce Herr Krug's pen. If we name that pen 'Skip,' we can then put that name in the place of 'John McCain' and run the argument as before.
There is one premise and three inferences. Does anyone have the chutzpah to deny the premise? Will anyone make bold to question inference rules U.I. and E.G.? And yet surely something has gone wrong. Intuitively, the existence of a contingent being such as McCain cannot be deduced from an a priori knowable necessary truth of logic. For that matter, the existence of a necessary being such as God cannot be deduced from an a priori knowable necessary truth of logic. Surely nothing concrete, not even God, is such that its existence can be derived from the Law of Identity.
So what we have above is an ontological argument gone wild whereby the rabbit of real existence is pulled from the empty hat of mere logic!
St. Bonaventura said that if God is God, then God exists. If such reasoning does not work in the case of God, then a fortiori it does not work in the case of McCain or Herr Krug's pen.
Note that (1) is necessarily true. (It doesn't just happen to be the case that each thing is self-identical.) If (2) follows immediately from (1), (2) is also necessarily true. And if (2) is necessarily true, then (3) is necessarily true. And the same holds for (4). But surely it is not the case that, necessarily, John McCain exists. He cannot be shown to exist by the above reasoning, and he certainly cannot be shown to necessarily exist by it.
So what went wrong? By my count there are three essentially equivalent ways of diagnosing the misstep.
A. One idea is that the argument leaves the rails in the transition from (3) to (4). All that (3) says is that something is identical to John McCain. But from (3) it does not follow that John McCain exists. For the something in question might be a nonexistent something. After all, if something is identical to Vulcan, you won't conclude that Vulcan exists. To move validly from (3) to (4), one needs the auxiliary premise:
3.5 The domain of quantification is a domain of existents only.
Without (3.5), John McCain might be a Meinongian nonexistent object. If he were, then everything would be logically in order up to (3). But to get from (3) to (4) one must assume that one is quantifying over existents only.
But then a point I have been hammering away at all my philosophical life is once again thrown into relief: The misnamed 'existential' quantifier, pace Quine, does not express existence, it presupposes existence!
B. Or one might argue that the move from (1) to (2) is invalid. Although (1) is necessarily true, (2) is not necessarily true, but contingently true: it is not true in possible worlds in which McCain does not exist. There are such worlds since he is a contingent being. To move validly from (1) to (2) a supplementary premise is needed:
1.5 'John McCain' refers to something that exists.
(1.5) is true in some but not all worlds. With this supplementary premise on board, the argument is sound. It also loses the 'rabbit-out-of-the-hat' quality. The original argument appeared to be deducing McCain from a logical axiom. But now we see that the argument made explicit does no such thing. It deduces the existence of McCain from a logical axiom plus a contingent premise which is indeed equivalent to the conclusion.
C. Finally, one might locate the error in the move from (2) to (3). No doubt McCain = McCain, and no doubt one can infer therefrom that something is identical to McCain. But this inferential move is not existential generalization, if we are to speak accurately and nontendentiously, but particular generalization. On this diagnosis, the mistake is to think that the particular quantifier has anything to do with existence. It does not. It does not express existence, pace Quine, it expresses the logical quantity someness.
In sum, one cannot deduce the actual existence of a contingent being from a truth of logic alone. One needs existential 'input.' It follows that there has to be more to existence than someness, more than what the 'existential' quantifier expresses. The thin conception of existence, therefore, cannot be right.
Now let me apply these results to what Peter Lupu has lately been arguing. Here he argues:
(ii) a=a, for any arbitrarily chosen object a; (from (i))
(iii) (Ex)(x=a); (from (ii) by existential generalization);
Now, (i) is necessary, but (iii) is contingent. Yet (i) entails (iii) via (ii), which is also necessary. So I simply do not see how the principle (1*) which you and Jan seem to accept applies in modal logics that include quantification plus identity.
Peter thinks he has a counterexample to the principle that if p entails q, and p is necessary, then q is also necessary. For he thinks that *(x)( x = x)*, which is necessary, entails *(Ex)(x = a)*, which is contingent.
But surely if *a = a* is necessary, i.e. true in all worlds, then *(Ex)(x = a)* is necessary as well.
The mistake in Peter's reasoning comes in with the move from *Necessarily, (x) (x = x)* to *Necessarily, a = a*. For surely it is false that in every possible world, a = a. After all, there are worlds in which a does not exist, and an individual cannot have a property in a world in which it doesn't exist. One must distinguish between essential and necessary self-identity. Every individual is essentially (as opposed to accidentally) self-identical: no individual can exist without being self-identical. But only some individuals are necessarily self-identical, i.e, self-identical in every world. Socrates, for example, is essentially but not necessarily self-identical: he is self-identical in every world in which he exists (but, being contingent, he doesn't exist in every world). By contrast, God is both essentially and necessarily self-identical: he is self-identical in every world, period (because he is a necessary being).