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I take it you agree with van Inwagen's conditional that IF "exist" is a number word, then it is a univocal term. But can you elaborate on your defense of why "exist" is not to be applied to individuals as a number word? I agree that at first blush it sounds absurd to say "How many Max are there in BV's house?" However, what if we alter two aspects of that statement. What if we change "How many" to "Is there at least one," and what if for "Max" we substitute a description that picks out only Max and picks him out necessarily. (I take it that accidental descriptions of Max -- "The cat who drank milk in BV's house at time t" -- might pick out only Max in the actual world but not in every possible world, i.e. might not be essential definitions.) So, what if instead we say, "Is there at least one cat with (say) DNA structure X in BV's house?" Having thought about this issue for quite some time, I'm very curious as to your view on whether, for individuals as opposed to kinds, there even are any descriptions that essentially pick out an individual and only that individual. You may not think so -- I'm not sure I do, I'm not sure I think Max's DNA (or anything else) is Max's essence, if he has an essence (though it also doesn't sit easy with me thinking that we can change his properties as much as we like, all the while leaving his Max-hood intact. Then individual existence can begin to seem quite untethered and elusive -- Plato's basic intuition?). But if there were, ex hypothesi, descriptions that gave the essences of individuals, could not "exist" be used as a number word when applied to individuals? If we could make "There is at least one Max in BV's house" sensible (via supplying an adequate description of Max), wouldn't "exist" be a number word? Along these lines, might van Inwagen's argument be salvaged by our finding the description that picks out only Max? Perhaps such a description is an El Dorado or a Fountain of Youth.
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Jul 13, 2012