It is interesting to sort views of personal identity over time based on the answer to:

- Are the grounds of personal identity over time capable of continuous variation between cases of identity and cases of non-identity?

Theories that answer "Yes" require either vague diachronic identity or an arbitrary transition (something like: it's the same person if and only if at least exactly this number of neurons are had in common between the state now and the state one second ago). Moreover, the transition would have to be metaphysically necessary, since we are talking about the grounds of personal identity: we can't have two worlds with the same grounds but different identity facts.

I do not think an arbitrary metaphysically necessary transition here is plausible. What about vague diachronic personal identity? I think that is impossible. For I think the only sources of vagueness in whether I am suffering a horrific pain are the vagueness in "horrific" and in "pain". But if there was vague diachronic identity, then one could have a token case of definitely horrific pain and still have vagueness as to whether I am suffering it. And that is absurd. Moreover, we have the well-known Leibniz's Law argument against vague identity (*a* does not have the property of being vaguely identical with *a*; if *b* has the property of being vaguely identical with *a*, then by Leibniz's Law, *b* just isn't *a*, plain and simple).

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I am not quite so allergic to vague diachronic identity. Vague identity seems pretty plausible for, say, plants, and for protozoans.

Suppose there is a plan to gradually replace all the parts of my body and brain with silicon and metal. 75% of the way through this process, the creature (me?) will be subjected to a horrible pain. Should I be worried? I’m not sure! If I have power to prevent the pain now, but don’t, will the future creature look back cursing himself for his stupidity, or cursing someone else for their callousness? Still not sure! Maybe, however, this is an epistemic rather than a metaphysical issue.

I am still chewing over the Leibniz’s Law argument, but I am considering variations of the following reply. To say “B is (merely) vaguely identical with A” can be construed two ways. On the first way, it attributes a definite property to B, viz. of merely-vague-identity-with-A. On the second way, it attributes a vague property, viz. identity-with-A, to B (that is, it is a strict identity claim with a vague truth value…or maybe that is a third way). The second (third?) way doesn’t seem (?) to violate LL. I’m not sure that works.

I now think I like the following line of reply better:

If Leibniz’s Law is a criterion for definite identity, then the fact that it is violated in cases of vague diachronic identity is irrelevant, because the whole point is that the identity is vague, not definite.

For cases of vague identity, we need a different Law. The Vague Version of Leibniz’s Law (VVLL):

Necessarily, if x is vaguely identical to y, then for any property P, if Px then at least vaguely Py.

I do not think it is easy to generate violations of VVLL in cases of vague diachronic identity, though I do think it means that VDI will (might) not be transitive.

Vaguely identical as used with Leibniz’s Law may be a vague term. Let's instead define it as "not definitely different from."

Then A may be "not definitely different from" A, and that is transitive.

I now do not like my latter suggestion either. For let P = “is not definitely identical to y.” Then Px but, so far as I can tell, it is not the case that y is at least vaguely not definitely identical to itself. I think “…is at least vaguely not definitely identical to …” means “…is not definitely definitely identical to …” and y IS definitely definitely identical to itself.

This kind of counterexample will also raise problems for William’s suggestion too.

For what it's worth, last I looked at the literature on the Leibniz's Law argument (and it was over a decade ago), it seemed to me that the consensus was that one had to have a non-classical logic to get out of the argument. And it doesn't seem to be a trivial modification.

Heath:

Are you saying this: If you can have cases of vague identity, you can have cases of definitely vague identity. (You might also have cases of vaguely vague identity.) Then:

1. If x is definitely P, and y is definitely not P, then x is definitely not identical with y.

2. Suppose there is vague identity.

3. Then there are cases where x is definitely vaguely identical with y.

4. y is definitely not vaguely identical with y.

5. So, x is definitely not identical with y, a contradiction.

I don’t think that’s exactly what I was saying, though it might be along the same lines. I was generating a counterexample to my proposed VVLL:

Necessarily, if x is vaguely identical to y, then for any property P, if Px then at least vaguely Py.Let x be vaguely, but not definitely, identical to y. Let P be the property “is not definitely identical to y.” Then by hypothesis, Px.

But by VVLL, at least vaguely Py. Which is to say,

1. “y is at least vaguely not definitely identical to y.”

This claim is confusing. How to evaluate it? Two methods: (1) Intuitively, it is false. At any level of definiteness, y=y, and at no level of vagueness is y not identical to y. (2) Treat vagueness and definiteness as duals, so that Vaguely(Qx) = ~Definitely~Qx. Then (ignoring “at least” which is okay) substituting in, we have

2. “y is ~D~ ~D identical to y”

Remove the double negative:

3. y is ~DD = y

Change the notation a bit, to prefix:

4. ~DD=(y,y) but

5. DD=(y,y) contradiction.

For the record, the LL-based argument against vague identity is due to Gareth Evans.

Alexander,

We've been collecting meaningful movie quotes about 'Identity vs Image' for the past 10 years and posting them on the Reel Life Wisdom website. There are just under 200 of them there (Dec. 2015). I'm not sure if they'd be of any interest or use to you, but this message lets you know they are there.

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