The famous Stone Paradox asks, 'can an omnipotent being make a stone so heavy he can't lift it?' A simpler question, and one which I think makes the issues clearer, is, 'can an omnipotent being fail?'
If a being can fail, then there is something that being doesn't have the power to do, namely, whatever it is it can fail to do. If a being can't fail, then there is something it doesn't have the power to do, namely, to fail.
Now, we sometimes have chancy powers/abilities, as, for instance, in J. L. Austin's famous example, the power to sink a putt from a certain distance. The possibility of failure is compatible with this sort of power. However, surely when we ascribe omnipotence to God, we don't mean to say that he has chancy powers of this sort; we mean that he has infallible powers. In fact, I would claim, in ascribing omnipotence to God, part of what we mean is precisely that he can't fail to do anything he tries to do. (This isn't all we mean; to avoid some counterexamples, we need some conditions about what he can try to do. In an as-yet-unpublished paper, Alexander Pruss and I argue that this additional condition is perfect freedom of will.)
Call the following property 'act-omnipotence':
S is act-omnipotent =df. S can perform a token of any logically possible action-type
We can turn the above reasoning into an argument that act-omnipotence is inconsistent with omnipotence:
- If a being can fail, that being is not omnipotent.
- If a being cannot fail, that being is not act-omnipotent.
- Every being either can fail or cannot fail.
- No being is both omnipotent and act-omnipotent.
Now, of course, if omnipotence implies act-omnipotence, then this is just another way of saying that omnipotence is self-inconsistent. But why think that omnipotence implies act-omnipotence?
As far as I can see, act-omnipotence is self-consistent. 'Causing oneself to cease to be act-omnipotent' appears to be a logically possible action, and if the act-omnipotent being can do this, then it seems that it can fail, and that it can create a stone it can't lift. It can do these things by ceasing to be act-omnipotent. But act-omnipotence is inconsistent with omnipotence and, therefore, should not be ascribed to God.
[cross-posted at blog.kennypearce.net]