Classical interpretation: If God makes a rock that heavy, He will be unable to lift it, and thus not omnipotent. If He can't make such a rock, then He is still not omnipotent.
Frankfurt suggests that omnipotence overrides logical consistency. He draws inspiration on this from Descartes, apparently a favorite philosopher of his, who wrote that "it would be presumptuous to think that our imagination extends as far as God's power." Frankfurt's argument: Sure, if God is omnipotent, why couldn't He make a rock so heavy that He cannot lift it? Let's assume that He does. Then, having done that, let's say God now faces the task of lifting a rock designed to be impossible for Him to lift. Why could He not do that too, if He is omnipotent? Problem solved. (All you have to do is consider the tasks separately.)
Of course this does not satisfy me: In order for the first task to be successfully completed, there has to be at least *temporarily* a failure of omnipotence on the part of God. But perhaps so long as God is omnipotent *now* it doesn't matter if He was *always* perfectly omnipotent? And maybe this is one of those cases where the fact that we can cook up an expression in language doesn't necessarily mean that what the expression seems to say must necessarily correspond with anything or have binding force on anything.
But the question this stimulates for me: What is special about non-contradiction? When I read John Haugeland's nifty paper "Truth and Rule-Following" (the last chapter in Having Thought), the otherwise tightly crafted thesis -- which explains how objectivity is possible -- ultimately comes to rest on the principle of non-contradiction. He explains everything else as essentially coming out of a "constitutive" (or "existential") "commitment" by individuals, to keep trying to make consistent sense out of things, even when things are refusing to make sense. But his system depends on the possibility of consistency, which does not seem to be explained by a simple individual commitment. Or is it? Is non-contradiction just something arbitrary like the Gravitational Constant or Avogadro's number, a property of our universe that might not have been that way but made the world possible since it happened to hold? Or is it something non-arbitrary, intrinsic, written into the fabric of existence? Or is it just something that proceeds from our own rational consciousness somehow, and doesn't exist "out there" but only in our subjective, organized experience of the world? (In a way, this uncertainty seems to make Haugeland's theory beg the question. I hope not, because it's otherwise very elegant.)
Incidentally, Harry Frankfurt was recently on The Daily Show, interviewed about his recent book On Bullshit. The segment is online in QT format. More on Harry Frankfurt (and the source of this link) at The Fly Bottle.