London Ed quotes me, then responds. I counterrespond in blue.
1. ‘Island volcanos exist’ is logically equivalent to ‘Some volcano is an island.’
Agree, of course.
2. This equivalence, however, rests on the assumption that the domain of quantification is a domain of existing individuals.
Disagree profoundly. The equivalence, being logical, cannot depend on any contingent assumption. From the logical equivalence of (1), it follows that ‘the domain of quantification is a domain of existing individuals’ is equivalent to ‘some individuals are in the domain’. But the equivalence is true whether or not any individuals are in the domain. E.g. suppose that no islands are volcanoes. Then ‘Some volcano is an island’ is false. And so is ‘island volcanos exist’, by reason of the equivalence. But the equivalence stands, because it is a definition. Thus the move from (1) to (2) is a blatant non sequitur.
Ed says that the move from (1) to (2) is a non sequitur. But the move cannot be a non sequitur since (2) is not a conclusion from (1); it is a separate premise. In any case, Ed thinks that (2) is false while I think it is true. (2) is the bone of contention. To mix metaphors in a manner most atrocious, (2) is the nervus probandi of my circularity objection.
Ed thinks that the assumption that the domain of quantification is a domain of existing individuals is a contingent assumption. But I didn't say that, and it is not. It is a necessary assumption if (1) and sentences of the same form are to hold. Let me explain.
On the thin theory, 'exist(s)' has no extra-logical content. It disappears into the machinery of quantification. It is just a bit of logical syntax: it means exactly what *Some ___ is a ---* means. But quantifiers range over a domain. In first-order logic the domain is a domain of individuals. That is not to say that the domain cannot be empty. It is to say that the domain, whether empty or non-empty is a domain having or lacking individuals as opposed to properties or items of some other category.
Now there is nothing in the nature of logic to stop us from quantifying over nonexistent individuals. So suppose we have a domain populated by nonexistent individuals only. Supppose a golden mountain is one of these individuals. We can then say, relative to this domain, that some mountain is golden. But surely 'Some mountain is golden' does not entail 'A golden mountain exists.' The second sentence entails the first, but the first does not entail the second. Therefore, they are not logically equivalent.
To enforce equivalence you must stipulate that the domain is a domain of existing individuals only. If 'some' ranges over existing individuals, then 'Some mountain is golden' does entail 'A golden mountain exists.' In other words, you must stipulate that the domain be such that, if there are any individuals in it, then they be existent individuals, as opposed to (Meinongian) nonexistent individuals. The stipulation allows for empty domains; what it rules out, however, are domains the occupants of which are nonexistent individuals in Meinong's sense.
I hope it is now clear that a necessary presupposition of the truth of equivalences like (1) is that the domain of quantification be a domain of existing individuals only. Again, such a domain may be empty. But if it is, it is empty of existent individuals -- which is not the same as its harboring nonexistent individuals.
In other words, we can eliminate 'exist(s)' in favor of the particular quantifier 'some,' but only at a price, the price being the stipulation that quantification is over a domain of existing individuals. But then it should be clear that the thin theory is circular. We replace 'exist(s)' with 'some,' but then realize that the particular quantifier must range over a domain of existing individuals. The attempt to eliminate first-level existence backfires. For we end up presupposing the very thing that we set out to eliminate, namely, first-level existence. The circularity is blatant.
Ed's argument against all this is incorrect. We agree that (1), expressing as it does a logical equivalence, is necessarily true. As such, its truth cannot be contingent upon the actual existence of any individuals. If existence reduces to someness, then this is the case whether or not any individuals actually exist. My point, however, was not that (1) presupposes the existence of individuals, but that it presupposes that any individuals in the the domain of quantification be existent individuals as opposed to (Meinongian) nonexistent individuals.
(1) presupposes, not that there are individuals, but that any individuals that there are be existent individuals. If you appreciate this distinction, then you appreciate why Ed's argument fails.
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