Thursday, January 13, 2011

The problem of the stone

I like to use the stone argument as a warm-up in a philosophy of religion class. But it's actually kind of tricky to use. Here's a natural way to put it:

  1. Either God can or cannot make a stone he can't lift.
  2. If God cannot make such a stone, then there is something God can't do.
  3. If God can make such a stone, then there is something God can't do, namely lift the stone.
  4. So, there is something God can't do.

But in this formulation, (3) can be easily rejected. It does not follow follow from God's merely being able to make such a stone that there is something God can't do, just as it doesn't follow from God's being able to make a unicorn that there is a unicorn. The correct conditional is:

  1. If God does make such a stone, then there is something God can't do, namely lift the stone.
But if we replace (3) by (5) in the argument, the argument ceases to be valid.

This means that the stone argument isn't actually an argument against omnipotence. If all that was in view was omnipotence, one could say: "Sure, God can create such a stone. Were he to create it, he wouldn't be omnipotent. But he hasn't created such a stone and he is omnipotent." Rather, we should take the stone argument as an argument against essential omnipotence. And that makes the argument a little less suited for warm-up classroom use, because one has to introduce the notion of an essential property.

What I actually did in class today is I gave the argument in the invalid form. Alas, nobody caught the invalidity. Though, interestingly, one student was unsure of disjunction-elimination in general.

I also emphasized that the stone wasn't really a problem for omnipotence, but for particular attempts to define omnipotence. I think it's important to to distinguish those atheological arguments that are problems for theism from those that are problems for particular ways of defining theism. The inductive problem of evil is an argument against theism; the stone argument is only an argument against particular formulations.

13 comments:

David Parker said...

I've confused myself somehow:

1. Either God can or cannot make a stone he can't lift.
2. God has unlimited making powers
3. God has unlimited lifting powers
4. No intersection? (1 is false?)

Heath White said...

I've long (and perhaps simplistically) been convinced by Savage's treatment of this problem. God has unlimited stone-making powers and unlimited stone-lifting powers. It follows that there is no stone he cannot lift (nothing could fit that description) but that is not a limitation on his power.

Is there a problem with that answer?

David Parker said...

Where does Savage discuss this? Sounds like what I've been thinking about.

Heath White said...

Wade Savage, "The Paradox of the Stone," Phil Review 76.1 (1967)

Alexander R Pruss said...

It's interesting that one point Savage himself is guilty of the fallacy of running the argument using (5). He says "'x can create a stone that x cannot lift' does indeed entail that there is a task which x cannot perform". But that seems false. All it entails is that there can be a task that x cannot perform.

Unless, maybe, one assumes that to create a stone that x can't lift is to create a stone that has the essential property of being such that x can't lift it. If S is a particular such stone, then it does follow that there is a task x can't do--the task of lifting S. But then it becomes unclear why we should think it is possible for there to be a stone with the essential property of being such that x can't lift it. This is not even obvious in the case where I am x. Sure, I can't lift a 200kg stone, but perhaps no stone could have the essential property of weighing 200kg. Stones can gain and lose weight.

Alexander R Pruss said...

Savage ends his paper with: "And 'God can create stones of any poundage, and God can lift stones of any poundage' entails 'God cannot create a stone that He cannot lift.'"

Well, that inference is dubious. Imagine a being that can create stones of any poundage and shape and can lift stones of any poundage, but can only lift stones that aren't too slick. Such a being can create a stone that it can't lift.

OK, so charitably modify. Maybe instead of quantifying over weight, one should quantify over weight, size and shape. But it still doesn't follow from 'for any weight, size and shape, x can create a stone with those specifications, and x can lift a stone with those specifications' that x can't create a stone that x can't lift. Imagine that x can't lift stones that are very hot, but x can create stones that are very hot.

So, maybe, we should now quantify not just over size, shape and weight, but also over temperature. But the game goes on. Maybe the coefficient of friction matters. And so on. We don't want to just keep on adding parameters to quantify over.

This suggests that the way to make Savage's claim come out is something like this. For any stone specification S, God can make a stone satisfying S, and God can lift a stone satisfying S.

But now the question is what counts as a stone specification. If "cannot be lifted by x" counts as a stone specification, then it may be false that God can make a stone satisfying every stone specification.

So for Savage's story to work, we need a way of excluding "cannot be lifted by x" from the stone specifications. One way to do this is to say that stone specifications can only make use of intrinsic properties. That'll take care of this problem, but introduces others. A stone might be unliftable for extrinsic reasons, such as that it's glued to a heavy log, or that it's in a strong magnetic field. So the quantification over stone specifications had better include specifications like "is glued to a heavy log" or "is in a strong magnetic field", but not "cannot be lifted by x". The intrinsicness restriction doesn't do the job. (I also think shape and size are relational properties, but that's controversial.)

So, in the end, I don't think Savage's solution works. But the intuition behind it does.

So what works? I think the following, which I'm writing up with Kenneth Pearce:

1. x is omnipotent iff x is perfectly free and x is perfectly efficacious.
2. x is perfectly efficacious iff for all p, if x were to will that p, then p would hold.

Then we add: it is compatible with perfect freedom that one have autonomous rational constraints on one's will. A restriction on the will not to will there to be a stone that one can't lift is compatible with perfect freedom. Perfect efficacy implies that if God were to will there to be such a stone, there would be such a stone. But he wouldn't will it.

Heath White said...

2. x is perfectly efficacious iff for all p, if x were to will that p, then p would hold.

Alex,

I think you're going to get into wierd Cartesian territory here. If God were to will that 2+2=5, would it be? And is the fact that God does not will this merely a matter of autonomous rational constraint (he holds himself back, as it were) or that it's just not willable? If the latter, I think you're relying on a prior notion of possibility/necessity that you're trying to explain. I.e. if I can have logical necessity, then omnipotence is more like, "If x wills a _logically possible_ p, then p."

[I want to continue by saying, but am not sure about:]

But then the stone paradox can be handled by saying that there is no logically possible stone such that God cannot lift it, precisely because if God willed to lift it, he would.

Alexander R Pruss said...

Heath:

It's not rational to will the impossible. So it doesn't limit God's perfect freedom that he can't will the impossible. But if he were to will it, then it would happen, on this view.

"But then the stone paradox can be handled by saying that there is no logically possible stone such that God cannot lift it, precisely because if God willed to lift it, he would."

This requires an account of omnipotence where the quantification is over non de se propositions to be brought about rather than action types. If we quantify over action types, then the action type make a stone that one can't lift is possibly exemplified, and so we can't exclude it.

David Parker said...

Those distinctions make sense, but what is the problem with simply saying God has unlimited making and lifting powers?

A necessary being with accidental omnipotence? I didn't even know that was in play...yowsers. Back to the books...

Alexander R Pruss said...

There is a sense in which God can restrict his omnipotence. He can promise not do A, and then he can't will to do A any more. I don't want to say that this is really giving up omnipotence (for one, if God promises not to do A, there is still a sense in which he can do A: were he to will to do A, he would do A).

Some folks think that when the second person of the Trinity became man, he gave up his omnipotence. I myself think this is not orthodox.

Heath White said...

It's not rational to will the impossible. So it doesn't limit God's perfect freedom that he can't will the impossible. But if he were to will it, then it would happen, on this view.

I would have thought it is irrational to will the impossible because doing so is futile ... what you're willing CAN'T BE DONE. But since God COULD do it, I don't see why it would be irrational on his part.

For example, consider Plantinga's free will defense, which relies on the claim (roughly) that it is impossible for God to create a universe of agents who all make correct decisions. But hey, if God wills it, it is done, so why doesn't God will that, even if it impossible?

Alexander R Pruss said...

Good point.

Maybe it's irrational or even immoral to will what's not in consonance with one's nature. But the impossible is identical with what is incompatible with God's nature. And maybe logical incompatibility is the strongest sort of inconsonance? I am not sure I find this line convincing. I'll see if my coauthor has something good to say here.

Kenny said...

Willing to bring about and not bring about the same thing (at the same time, in the same respect, etc.) seems to me to be irrational completely independent of futility concerns.

If we want God to have counterpossible power of the sort we've suggested (and we're drawing on Aquinas here, though he only makes the claim about doing evil, not about doing the impossible), then we need God to deeply identify with the laws of logic (and ethics). I, at least, would not want to go voluntarist and say that these laws depend on his will; I would want to place them in the divine intellect or character. As long as they are necessary features of God (and God's willings are not supposed to be necessary in this strong sense), it seems to me that we get a robust distinction between possibility and impossibility, and as long as they are internal to God in the right sort of way, we preserve omnipotence, including counterpossible power.

Does that solve (or mitigate) the problem?