Bill argues here that we cannot have univocity of 'exists' over singular and general existential statements without the monstrosity of haecceities. I'm not convinced.
Consider the cubic polynomial p(x)=x**3-7x+6 over the real numbers. p(3)=12 and p(-4)=-30 so by the intermediate value theorem p has a real root: ∃x.p(x)=0. Denote this root by 'a'. Now 'a exists' is surely true. But this, despite the proper name 'a', has to be understood as a general existential claim---the concept 'real root of p' is instantiated---since this is all we know about a. So we have univocity of 'exists'. Yet we don't pay the price of a haecceity property that uniquely captures a-ness. There can be no such haecceity because a could be any of -3, 1, or 2.
Bill persists in seeing things in terms of theories of existence. I have increasingly come to see it as a question of how proper names are introduced into discourse, and how they subsequently work. I'm much influenced here, of course, by Ed Ockham's story-relative theory of reference. See here, and especially here.
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