@emagalha,
Quote:Fortunately, I didn't say Statue and Piece lack "identical definitions." I said "Statue is not identical with Piece."
I know. This "philosophical dilemma" only works if one keeps the concept of "identity" as ambiguous as possible. That is why I used the term "definitions": since the dilemma depends on our mapping the ambiguity of X and Y's identity onto physical objecthood, it doesn't matter how one defines "identity," as long as we believe that X not equaling Y is the same as X being a different object than Y, which doesn't follow.
Quote:And if X is not identical with Y it does appear to follow that X and Y are "two different objects."
It may appear so to you, but it doesn't to me. It follows only if X and Y are defined in reference to specific physical objects rather than properties of physical objects or names we give to physical objects, which they needn't necessarily be.
X = a green copper statue
Y = The Statue of Liberty
X and Y are not identical, but there is no philosophical dilemma in claiming that both X and Y exist in the same place in New York, right off the tip of Manhattan. Like the Clay Statue Paradox, this statement is "paradoxical" only if we keep silent about the terms of "identity" between X and Y and hope that the reader will assume that this identity is contingent upon specific physical objecthood.