Here's yet another version, probably unoriginal, version of the Gareth Evans argument against vague identity. Say that two properties P and Q are definitely incompatible if it is definitely true that it is impossible for an object to satisfy both of them.
- (Premise) For any property R, being definitely R and being vaguely R are definitely incompatible.
- (Premise) If P and Q are definitely incompatible, and x has P while y has Q, then x is definitely distinct from y.
- For any x, being definitely identical with x is definitely incompatible with being vaguely identical with x. (By 1)
- (Premise) For any x, x is definitely identical with x.
- So, if y is vaguely identical with x, then y is definitely distinct from x. (By 2 and 3)
- So, there are no cases of vague identity.
One might want to weaken (1) to say that being definitely definitely R and being definitely vaguely R are definitely incompatible. We then need to strengthen (4) to say that x is definitely definitely identical with x, and our conclusion becomes the weaker conclusion that there is no definitely vague identity. But I suspect that if there is vague identity, there is definitely vague identity, so we can get the stronger conclusion as well.
