## Thursday, March 5, 2015

### Definitely incompatible properties and vague identity

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.

1. (Premise) For any property R, being definitely R and being vaguely R are definitely incompatible.
2. (Premise) If P and Q are definitely incompatible, and x has P while y has Q, then x is definitely distinct from y.
3. For any x, being definitely identical with x is definitely incompatible with being vaguely identical with x. (By 1)
4. (Premise) For any x, x is definitely identical with x.
5. So, if y is vaguely identical with x, then y is definitely distinct from x. (By 2 and 3)
6. 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.

Mike Almeida said...

Alex,

Doesn't (4) beg the question. If some y is vaguely identical to x, then no z is definitely identical to x. Or is (4) just a datum?

Alexander R Pruss said...

I don't think it begs the question, but I think it needs some more defense, and I'm grateful for your pointing me to it.

I could see someone saying that if it's vague whether x exists, then it's vague whether x=x. (After all, that x=x entails that x exists.)

For instance, maybe it's vague whether Santa Claus exists. (Why? Because maybe it's vague whether Santa Claus = St. Nicholas, and Santa Clause exists iff Santa Clause = St. Nicholas.)

So maybe for 4, I need to assume that it's definite that x exists. This weakens the argument. I only get to conclude that if it's definite that x exists, then nothing can be vaguely identical with x. But that weaker conclusion is still incompatible with most views on which there is vague identity, since on those views there can be vague identity even when there is definite existence.

For instance, the kinds of alleged cases of vague identity that arise from weird personal identity thought experiments are typically ones where it's definite that the pre-experiment person exists and it's definite that the post-experiment person exists but allegedly vague whether the pre-experiment person = the post-experiment person.

Brandon said...

What is the motivation for (2)? Consider some case that someone might consider best understood as a case of vague identity -- perhaps something like the relation between Brandon-ten-years-ago and Brandon-now, or pre-experiment and post-experiment person. Brandon-ten-years-ago and Brandon-now have definitely incompatible properties, but anyone who saw this as a possible candidate for vague identity would surely already resist the idea that the bare fact that they have definitely incompatible properties means that they are definitely non-identical, because vague identity would mean that we could not take for granted that they would definitely have them in the same respect.

Alexander R Pruss said...

Brandon:

Very good!

Maybe I should weaken the conclusion.

Replace 2 with:

2'. If P and Q are definitely incompatible, and x definitely has P while y definitely has Q, then x is definitely distinct from y.

Then replace 4-6 with:
4'. (Premise) For any x, x is definitely definitely identical with x.
5'. So, if y is definitely vaguely identical with x, then y is definitely distinct from x. (By 2' and 3)
6'. So, there are no cases of definitely vague identity.

But, plausibly, if there is vague identity, there is definitely vague identity.