From the Mail: To Be Is to Be the Value of a Variable
I enjoyed, and generally agreed with your papers about "existence". I think you are right that the Fregean account of existential statements is blatantly circular. To be is to be the value of a variable. But (if you take that seriously) Pegasus is such a value.
I touch on this in a review here. Read from the bit "Asserting "John is happy" ...".
Thanks for writing, Mr. Buckner. You apparently take me to be rejecting the Fregean account of existence in favor of the Quinean. But I reject both. See "A Tension in Quine's Theory of Existence," PHILO, vol. 6, no. 2 (Fall-Winter 2003), pp. 193-204. Available here. Suppose we briefly revisit Quine's famous explication (as he calls it) of 'a exists,' to wit:
1. a exists =df (Ex)(x = a).
In something more like English, an arbitrary individual a exists if and only if there exists something to which it is identical. This too is blatantly circular if (1) is evaluated relative to a domain of existing items. For then what it boils down to is that a exists iff a is identical to something that exists. And that makes for a circle the diameter of which is embarrassingly short.
If, on the other hand, (1) is evaluated relative to a domain of nonexistent objects, then (1) comes out obviously false. Pegasus is the value of the bound variable 'x' in '(Ex)(x = Pegasus),' but Pegasus does not exist.
There is not much to choose as between vicious circularity and falsehood.
Of course, one could take '= a' as an unanalyzable unit, and thus as the haecceity-property, identity-with-a, or a-ness, if you will, in which case (1) becomes
1.' a exists =df (Ex)Ax,
where 'A' denotes the haecceity-property, a-ness. This avoids the circularity of saying that a exists iff a is identical to something that exists. But this move brings us back to something like Frege's instantiation account with its attendant circularity. Besides, there are no haecceity-properties as I argue in A Paradigm Theory of Existence (Kluwer 2002), pp. 99-103.
There is a lot more to be said, but there is no point in repeating what I have said in my published papers.