Omnipotence and Possibility

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This is the the thirty-third post in my Theories of Knowledge and Reality series. Follow the link for more on the series and for links to other entries as they appear. In the last post, I finished up the final post on the problem of evil. This post begins what I expect to be a four-part series on philosophical theology.

[Note: The next few posts on philosophical theology are derived in part from discussions in Gregory E. Ganssle, Thinking About God (2004) InterVarsity Press.]

Philosophical theology is just philosopher-speak for thinking about what God might be like if God exists. Three philosophically important features traditionally have been omnipotence, omniscience, and complete goodness, and some interesting issues come up in the Ganssle book related to these three. The issue I'm dealing with in this post has come up before in relation to the problem of evil, but I thought it was worth a more extended discussion in light of its relevance for the issues that I think are much more interesting that will come in the next few posts.

The puzzle is sometimes given about whether God could make a rock so big that God could not move it. If omnipotence is the ability to do anything, then it seems God could. But then there would be a rock that God could not move, and that could never be true if God is omnipotent. So God must be unable to make such a rock. But then there is a limit to God’s ability, and does that mean God is not omnipotent? So either way God is not omnipotent. If God can make the rock, then God is not omnipotent. If God cannot make the rock, then God is not omnipotent.

The most common solution to the puzzle is to reexamine the definition of omnipotence. Some people consider omnipotence to be the ability to do anything. Most theists do not agree. They prefer to think of it as the ability to do anything possible. Maybe we can call the ability to do anything by the term ‘super-omnipotence’. But omnipotence itself is just the ability to do anything possible, not the ability to do anything you can put words to. You can put words to the action of making a rock God cannot move, but that does not mean such an action is possible. Some things are not possible. An omnipotent being could not make a square circle, could not make 2+2 be 5, and could not make something both red and not red at the same time in the same way. These are logical and mathematical limits. The actions so described are not real actions, since they are not possible in any sense. So it is not a big limit on God to say that God cannot do things that are not real actions to begin with.

So God is not super-omnipotent, since such a description leads to incoherence. But that does not mean that omnipotence is impossible. There could still be an omnipotent being even if super-omnipotence leads to contradictions.

I should mention the minority position. One famous philosopher, Rene Descartes, did at least at one point think that God is super-omnipotent. He said that God could make square circles. God could make a rock too big even for God to move. Of course, God could then move it. If God can make contradictions true, why couldn’t God move a rock too big even for an omnipotent being to move? Some medieval Christian philosophers attributed a similar position to some of the medieval Islamic philosophers, who said that God is above reason in some sense, and thus reason (and therefore logic) does not control God. I am not 100% sure that these philosophers held this position, but some of the philosophers in the middle ages did take some of them to be saying these things.

Next: Omniscience and Time


That's similar to the disadvantage of omniscience. Where if you were, for example, to play chicken racing cars toward each other with an omniscient, being you can be confident that he knows your intention (even prior to you) so you can just choose to drive straight. The omniscient individual then must swerve, knowing that you will not. So you can then win then all the time, by counting on this.

I'm not sure that's a disadvantage. The omniscient being knows what you will do, which means the omniscient being knows if it's necessary to turn. On the other hand, you don't know if the omniscient being will act on that knowledge or will deliberately not turn or not turn enough, just to spite you. I suppose it also depends on what you think constitutes winning and whether you think it's a good thing to win.

Well, typically both lose (big) if you crash and you lose (not so big, you lose "face"?) if you turn away first. If you know the other is omniscient then the 'non-omniscient' has the advantage. The point is, from a game theoretic standpoint, omniscience is seen as a disadvantage in a game where both know of the omniscience of the one player.

So much for game theory, then. I don't see why the value of saving face is supposed to be more than the value of omniscience.

Well, mostly its a demonstration that an advantage in a game (like omniscience) can be a disadvantage in counterintuitive ways.

It seems to me that the problem with this sort of reasoning about the omniscient game of Chicken is that it assumes that I know my intention as well as the omniscient opponent does and that I know, for instance, that I'll actually be able to maintain my resolve to keep driving straight. One could just as well reason that, since the omniscient opponent keeps driving straight, he knows that I'll lose nerve. It's not enough to know that the other player is omniscient; one must know what the omniscient player knows about oneself. That's what would give the advantage -- knowing about yourself and knowing that your opponent knows it. On the assumption that we both know that I won't swerve, the omniscient opponent is guaranteed to crash or swerve. But we don't know that; only the omniscient opponent does. So I can't guarantee that either we'll crash or the opponent will swerve. Think of it in terms of putting up bets before the match. If we crash, we both give up a lot of money; if one of us swerves first, he gives up a little money to the one who doesn't. My betting position is not improved by my knowledge that my opponent is omniscient, even if we assume that I know (as Jeremy pointed out we'd have to assume) that my opponent will minimize how much money he'll lose. It's only improved if I also know for certain that I won't swerve first.

Perhaps the omniscient one would know that the game of chicken was a no win situatiomn and would therefore refuse to particiate.

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