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#96 Logical Truth and Omnipotence

February 16, 2009

I have a question about omnipotence and necessity. In your writings, debates, and teachings, you follow Flint and Freddoso's definition of omnipotence. Key to their definition is that God cannot actualize logically impossible states of affairs, such as making a round square.

When I used this definition of omnipotence in a discussion with an atheist, he responded with a kind of Euthyphro objection. He said the theist must choose between two options. The first horn is that God decides the fundamental "laws" of logic and math. If this is true, then per Descartes, fundamental truths of logic and math are contingent. That is to say, they could have been different. Thus, 2+2 could have equaled 3. Or "A" could be "not-A" at the same time in the same way. The second horn is that the fundamental laws of logic and math could not have been any different and, thus, are truly necessary because they could not have been different. If this is true, then fundamental truths of mathematics and logic exist in some way (as abstract objects) and God is subject to them.

It seems inconceivable to think the first horn is true because I cannot even think of 2+2=3 of that the law of non-contradiction is not true because I have to assume the law of non-contradiction to deny it. So horn one seems like it should be rejected because it leads to absurdities. If the second horn is true, then God's sovereignty seems impugned because God is forced to comply with something external to himself.

Because this dilemma is so similar to the Euthyphro dilemma in the context of the moral argument, my intuition is to split the horns by appealing to the possibility of some third alternative such as: "God wills that the law of non-contradiction (etc.) obtain because they are consistent with his nature." In this way, the laws aren't contingent or external to God. But this proffered third option seems less plausible to me than it does in the context of the moral argument. Can you shed some light on this for me? Thank you.


United States

Dr. craig’s response


By way of background for those not familiar with the subject matter of this question, the article by Thomas Flint and Alfred Freddoso is "Maximal Power," which is reprinted in my anthology Philosophy of Religion: a Reader and Guide (New Brunswick, N. J.: Rutgers University Press, 2002). It is a brilliant analysis of the concept of omnipotence. (An amusing anecdote: when I was visiting Notre Dame for a conference years ago, I asked Tom and Fred over lunch why they called their article "Maximal Power" instead of the more familiar term "Omnipotence." After explaining to me that they were just trying to add some variety, Fred then asked me what I thought of the title "Great God Almighty." Apparently that was his preferred title, but Tom was concerned lest it sound, as he put it, "impious" (pronounced IMP-ee-us). I had never heard anyone concerned about something's sounding impious before, but I first began to see Tom's sensitive Christian conscience.)

The first horn of your friend's dilemma has been dubbed "universal possibilism" by Alvin Plantinga. It holds that that there are no necessary truths. Though defended by Descartes, it has been rightly rejected by almost every other Christian philosopher. For just ask yourself: is the proposition There are no necessary truths itself necessarily true or not? If so, then the position is self-refuting. If not, then that proposition is possibly false, that is to say, God could have brought it about that there are necessary truths. Using possible worlds semantics, we may say that there is, therefore, a possible world in which God brings it about that there are propositions which are true in every possible world. But if there are such propositions, then there is no world in which it is the case that there are no propositions true in every possible world, that is, it is not possible that there are no necessary truths, which contradicts universal possibilism.

Moreover, Descartes' position is incredible. It asks us to believe, for example, that God could have brought it about that He created all of us without His existing, that is to say, there is a possible world in which both God does not exist and He created all of us. This is simply nonsense.

There must therefore be necessary truths. However, it does not follow from the necessity of the truths of logic and mathematics that "the fundamental truths of mathematics and logic exist in some way (as abstract objects) and God is subject to them," as your friend infers. Rather, as you rightly point out, the Christian should say that the necessary truths of logic (and perhaps math) just are representations of the way God's mind essentially thinks. Theologically, such a doctrine ties in beautifully with the prologue to John's Gospel on Christ's being the Logos of God.

There's no need to introduce considerations of the divine will, however. In ethical theory that's necessary because what constitutes moral obligation is a divine imperative. But with respect to the laws of logic, there is no imperatival aspect. They are simply descriptions of how God necessarily reasons.

- William Lane Craig