Consider again this curious piece of reasoning:
1. For any x, x = x. Ergo:
2. a = a. Ergo:
3. (Ex)(x = a). Ergo:
4. a exists.
This reasoning is curious because it seems to show that one can deduce the real existence of an individual a from a purely formal principle of logic, the Law of Identity. And yet we know that this cannot be done. We know that the rabbit of real existence cannot be pulled from the empty hat of mere logic. Since the argument cannot be sound, it must be possible to say where it goes wrong. (It is a strange fact of philosophical experience that arguments that almost all philosophers reject nevertheless inspire the wildest controversy when it comes to the proper diagnosis of the error. Think of the arguments of Zeno, Anselm, and McTaggart.)
The move from (1) to (2) appears to be by Universal Instantiation. One will be forgiven for thinking that if everything is self-identical, then a is self-identical. But I say that right here is a (or the) mistake. To move from (1) to (2), the variable 'x' must be replaced by the substituend 'a' which is a constant. Now there are exactly three possibilities:
Either 'a' refers to something that exists, or 'a' refers to something that does not exist or 'a' does not refer at all. On the third possibility it would be impossible validly to move from (2) to (3) by Existential Generalization. The same goes for the second possibility: if 'a' refers to a Meinongian nonexistent object, then one could apply existentially-neutral Particular Generalization to (2), but not Existential Generalization. This leaves the first alternative. But if 'a' refers to something that exists, then right at this point real existence has been smuggled into the argument.
I hope the point is painfully obvious. One cannot move from (1) to (2) by logic alone: one needs an extralogical assumption, namely, that 'a' designates something that exists. To put it another way, one must assume that the domain of quantification is not only nonempty but inhabited by existing individuals. After all, (1) is true for every domain, empty or not. (1) lacks Existential Import. The truth of (1) is consistent with there being no individuals at all.
Let's now consider Peter's supposed counterexample to the principle that if p entails q and p is necessary, then q is also necessary. He thinks that the above argument shows that there are cases in which necessary propositions entail contingent ones. Thus he thinks that the conjunction of (1) and (2) entails (3), but that (3) is contingent.
Well, I agree that if we are quantifying over a domain the members of which are contingent individuals, then (3) is contingent. But surely the conjunction of (1) and (2) is also contingent. For the conjunction of a necessary and a contingent proposition is a contingent proposition. Now of course (1) is necessary. But (2), despite appearances, is contingent. For if 'a' designates a contingent individual, then it designates an individual that exists in some but not all worlds, and in those worlds in which a does not not exist it is not true that a = a.
In the worlds in which a exists, a is essentially a. But a is not necessarily a because there are worlds in which a does not exist.
What accounts for the illusion that if (1) is necessary, then (2) must also be necessary? Could it be the tendency to forget that while 'x' is a variable, 'a' is an arbitrary constant?