Here is London Ed's most recent version of his argument in his own words except for one word I added in brackets:
1. There is no such thing as Caesar any more.
2. The predicate 'there is no such thing as -- any more' is satisfied by
3. If a relation obtains [between] x and y, then there is such a thing as y.
4. (From 2) the relation 'is satisfied by' obtains between the predicate '--
is not a thing any more' and Caesar.
5. (3, 4) There is such a thing as Caesar.
6. (1, 5) contradiction.
Premiss (1) is Moorean. There is no longer any such thing or person as Caesar. (Or if you dispute that for reason of immortality of Caesar, choose some mortal or perishable object). (2) is a theoretical. (3) is a logical truth, and the rest is also logic. You must choose between (1) and (2), i.e. choose between
a Moorean truth, and a dubious theoretical assumption.
(1) is indeed 'Moorean,' i.e., beyond the reach of reasonable controversy. (2) is indeed theoretical inasmuch as it involves an optional albeit plausible parsing in the Fregean manner of the Moorean sentence.
Ed tells us that (3) is a logical truth. I deny that it is. A logical truth is a proposition true in virtue of its logical form alone. 'Every cat is a cat' is an example of a logical truth as are 'No cat is a non-cat' and 'Either Max is a cat or Max is not a cat.' One can test for logical truth by negating the proposition to be tested. If the result is a logical contradiction, then the proposition is a logical truth. For example, if we negate 'Every cat is a cat' we get 'Some cat is not a cat.' The latter sentence is a logical contradiction, so the former sentence is a logical truth. The latter is a logical contradiction because its logical form -- Some F is not an F -- has only false substitution-instances.
Negating (3) yields 'A relation obtains between x and y, but there is no such thing as y.' But this is not a logical contradiction in the strict and narrow sense defined above. Suppose I am thinking about the Boston Common which, unbeknownst to me, ceases to exist while I am thinking about it. I stand in the 'thinking about' relation to the Common during the whole period of my thinking despite the fact that at the end of the period there is no such thing as the Boston Common. There are philosophers who hold that the intentional relation is a genuine relation and not merely relation-like as Brentano thought, and that in some cases it relates an existing thinker to a nonexisting object.
Now there are good reasons to reject this view as false, but surely it is not false as a matter of formal logic. If it is false, it is false as a matter of metaphysics. A philosopher such as Reinhardt Grossmann who holds that the intentional relation is a genuine relation that sometimes relates an existent thinker to a nonexistent object is not contradicting himself.
Since (3) is not a logical truth, one way to solve Ed's problem is by rejecting (3) and holding that there are genuine relations that relate the existent to the nonexistent. One could hold that the relation of satisfaction is such a genuine relation: it relates the existing predicate to the nonexistent emperor: Caesar satisfies the predicate despite his nonexistence.
Note that I am not advocating this solution to the puzzle; I am dismissing Ed's dismissal of this putative solution. I am rejecting Ed's claim that one is forced to choose between (1) and (2). One can avoid the contradiction by denying (3), and one is not barred from doing so by logic alone.
Ed claims that (1) and (5) are logical contradictories. But they are not. Just look carefully at both propositions and you will see. Ed thinks they are contradictories because he assumes that 'There is no such thing as y any more' is logically equivalent to 'There is no such thing as y.' But to make that assumption is to to assume the substantive metaphysical thesis known in the trade as
Presentism: Necessarily, only temporally present concrete objects exist.
Given Presentism, (1) and (5) are indeed contradictory. This is why I said earlier that Ed's argument cannot get off the ground without Presentism. For suppose we reject Presentism in favor of the plausible view that both past and present concreta exist, i.e., are within the range of our unrestricted quantifiers. Then Ed's puzzle dissolves. For then there is such a thing as Caesar, it is just that he is past. The relation of satisfaction connects a present item with a past item both of which exist. Or, since Ed is allergic to 'exist': both of which are such that there such things as them.
So a second way to solves Ed's puzzle is by rejecting the Presentism that he presupposes.
So I count at least three ways of solving Ed's puzzle: reject (2), reject (3), reject the tacit assumption of Presentism which is needed for (1) and (5) to be contradictory.
My inclination is to say that the puzzle is genuine, but insoluble. And this because the putative solutions sire puzzles as bad as the one we started with. Of course, I haven't proven this. But this is what my metaphilosophy tells me must be the case.