Consider the following theses.
(A) For any person P, P exists iff P is alive.
(B) For any person P, P is alive iff P is not dead.
(C) Whether or not some person is dead is vague.
(D) Whether or not someone exists is not vague.
On the face of it, these four theses seem to be incompatible. If they are then when of them must go, and it’s a little puzzling to me which one it would be. However, there is a background assumption one would need to derive an inconsistency. I’m not quite sure how best to articulate the principle, but it goes something like this:
(E) If two properties A and B are such that A applies iff not-B and it is vague whether or not B applies, then it is vague whether or not A applies.
So here we have 5 principles and it seems that one of them must go.
The Options
Reject A
This would have, what I suspect, is a surprising result to many – namely that whether or not you exist does not depend on whether or not you are alive.
Reject B
This seems like a non-starter, but I invite readers to try and motivate it.
Reject C
You could maintain that it is not a vague matter whether or not someone is dead, but it sure seems like there are border line cases of death. The medical ethics literature is loaded with discussions of how tricky it is to define ‘death’ given that it seems to admit of borderline cases.
Reject D
We could go this route, but it would shake the philosophical community. Metaphysicians have gotten a lot of mileage out of this assumption.
Reject E
I’m not quite sure how to motivate rejecting this, but perhaps this is the one to go.
I’d reject (A). After all, (A) entails, all by itself, the falsehood that there are no dead people.
Andrew,
I wonder if (E) is true.
E. If two properties A and B are such that A applies iff not-B and it is vague whether or not B applies, then it is vague whether or not A applies.
The principle sounds close to a closure principle for vague properties. But it is certainly false that
C0. [](Vx)(Rx -> Ex) -> (InDefRx -> InDefEx)
Necessarily, for all x, x is R only if x is E, then x is indefnitely R only if x is indefinitely E.
Counterexample:
Necessarily, for all x, x is red only if x is colored. Suppose x is indefinitely red. It does not follow that x is indefinitely colored.
Does the biconditional case change things? I don’t think so.
C1. [](Vx)(Rx Ex) -> (InDefRx -> InDefEx)
Seems right that (Vx)(x occupies a smallest spatial region iff x is a material object). But it might be true that x is definitely a material object while x does not definitely occupy a smallest region of space.
Jonathan,
That seems right, however, we might revise things so that instead of focusing on death it could focus on a body.
The principle could be something like:
(A*) For any person P, P exists iff P has a body.
It seems that the predicate is a body is vague. So we might be able to generate the same problem – although I’d be inclined to give up on A* too.
Mike,
This is very good. You have me convinced that (E) is false. I wonder if we could say something strong like:
(E*) If two properties A and B are such that A applies iff (and in virtue of) not-B applying and it is vague whether or not B applies, then it is vague whether or not A applies.
I don’t know if something is red in virtue of its being colored. Somethings being red and being colored would be true in virtue of some other fact. Same thing for being material and occupying a smallest region.
However, the tension is a little more difficult to see if we revise the principle this way. First, it’s not clear that someone exists in virtue of being not-dead. Second, although some metaphysicians readily employ “in virtue of” talk – it’s a little unclear to me what that relation is.
Andrew,
I agree with Jonathan that (A) is false and I believe it is false for the reason he suggests.
But, concerning Mike’s point, I think we can bolster something like (E) without introducing “in virtue of” talk. Here is my suggested modification:
(E**) For any x (Def(Ax –> Bx) –> (InDef Bx –> InDef Ax)
I take it that you think it is definitely true that something is alive just in case it is not dead. so, given (E**) and the claim that it is indefinite whether something is dead or not, you’ll get the conclusion that it is indefinite whether it is alive.
Moreover, I don’t think (E**) falls prey to Mike’s counterexamples.
Enter the layman to muddle through things. Do we need to be rid of any of these? A asserts that, if one is alive, one exists. It seems like this only suggests that the alive are a subset of the existent. This line of thought arrives at the same conclusion that Andrew suggested arises if you discard A, that existence does not depend upon liveliness, without having to discard A.
I suspect that I may be breaking some rule of formal logic, however, not having studied it.