The author concludes:
The consequence for philosophy of religion is quite simple--that if God is an agent, his hands must be bound by logic. To many, this might seem to be a conclusion which is so trivial as to be scarcely worth stating--apart from Descartes, and a few other exceptions, have not most philosophers of religion always held that God's omnipotence does not include the ability to do illogical things?
I don't want to question this conclusion, but I do want to give it a bit of a shake. It strikes me that there's a much more general point lurking around here somewhere, that it says little interesting about God (after all, we're "bound by logic" just as much as God is), and, maybe more surprisingly, it says little interesting about logic either.
The idea is this: how do we conclude that God's hands are tied by logic? We conclude that it's logically impossible for God to do something which is prohibited by logic. God can't square a circle, or make a tautology untrue, or do anything else like that. Why is this? It's because it's logically necessary that if something is logically necessary, it's true.
In other words, logical necessity (which I'll represent by 'L') satisfies the following condition:
L(Lp → p)
But this is not distinctively true of logical necessity. Lots of other operators satisfy this condition too. (1) It's quite plausible to think that it's physically necessary that what's physically necessary is true. (2) When you think about it, it's obvious that it's always true that what's always true is true. (3) I have even convinced myself that it would be nice that (if it would be nice that p then p)! And there are more where they came from. (If you like possible worlds semantics, let the accessibility relation governing L satisfy the condition that if a world y is accessed by a world x then y accesses itself too. Then L(Lp → p) is always satisfied).
So, what's the upshot? For any modality L satisfying this condition, it's L necessary that what is L necessary is true. That is, in particular it's L-necessary that God not do things that are L-impossible.
What's the upshot of this conclusion? Consider the case of a trivial modality like the temporal always. Even though God will never for do something which doesn't at some time, that doesn't mean that there's no broader sense of possible for which it's possible that God to do something which doesn't actually happen. Now consider physical possibility. Even though it is physically impossible for God to do something which breaks the laws of physics (whatever the actual laws might be, thinking of them as universally true regularities, not things with actual exceptions), there can still be a broader sense of possibility, according to which it is possible that the laws of physics be different.
The interesting issue is whether there's any reason to think that the modality of logical necessity is any different to the others, or whether we could consider yet broader senses of possibility. That's the place to look for something distinctive about the nature of the grip of logical necessity.
I’m Greg Restall, and this is my personal website. I teach philosophy and logic as Professor of Philosophy at the University of Melbourne. ¶ Start at the home page of this site—a compendium of recent additions around here—and go from there to learn more about who I am and what I do. ¶ This is my personal site on the web. Nothing here is in any way endorsed by the University of Melbourne.