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, the 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 everything 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.