Omnipotence?
23 Sep '10 14:17Originally posted by LemonJelloBut that seems like a clearly inadequate result. If, under O3-omnipotence G can create S, then under O3-omnipotence there is some stone that G cannot lift. Then, I do not think O3-omnipotence really survives our common sense intuitions about 'omnipotence'.
I am basically making stuff up as I go along here, so I would start with a similar disclaimer.
[b]So the solution from this way round is that G can create S under O3 and G's inability to lift S does not violate O3, so G remains omnipotent in this sense.
But that seems like a clearly inadequate result. If, under O3-omnipotence G can create S, th ...[text shortened]... t means for G to be "omnipotent". Perhaps I am missing something here.[/b]
Well I'm unsure as to how far we can get by relying on common sense notions of omnipotence in order to judge how successful O3 is, especially given that O3 was introduced precisely to fix problems arising from those very common sense notions. After all, exactly what is it that G cannot lift? The unliftatable. Not just any old stone.
One difficulty I can see is that you could construe the effect of O3 on the stone problem so as to give the result that it is logically impossible for G to create S. To do this, simply reflect that there is nothing logically contradictory about being able to lift stones, hence G ought to be able to lift any stone. Looked at this way, G is unable to create S because S is a stone, which is, in general, liftable by G. So G is faced with creating an unliftable liftable-thing.
So it is not clear whether O3 can decide whether G can create S or not.
You raised this same point in relation to importing some notion of omnipotence. I think O3 does have content though, because it stipulates that G can bring about any state of affairs that is not logically contradictory. We have already identified a potential problem of recursion because of the self referential element in the logical contradiction.
What I mean is that O3 handles G not being able to make a square circle with no difficulty, since the logical contradiction here does not refer to omnipotence under O3 directly.
With the stone case, we have to think whether 'unliftable' can be dealt with under O3 without circularity.
But how does that preserve the question?
The entailment preserves it. If G creates a stone that is unliftable simpliciter then G has created a stone that G cannot lift. However, you could reframe the problem as 'Can G create S such that G cannot lift S but Jones can lift S. So you are right, this fix doesn't really work.
I don't think it is needed though. Suppose S is unliftable-by-G, then can G bring about a state of affairs in which S exists? Yes, so long as there is no logical contradiction in doing so. Well where is the contradiction?
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