A short essay on God and Four Sided Triangles
One of the problems that exercised theologians during the middle ages was the question of whether God could envision or, indeed, make a four sided triangle or a three sided square or some such monstrosity. At first sight the problem seems trivial or foolish, but it really is an instance of a more fundamental problem: Is God bound and limited by the laws of reason and logic or can She overcome them or alter them as She chooses. On one hand God is omnipotent; She may do anything She pleases, logic and reason notwithstanding. On the other hand it seems inconceivable that anyone, even God Herself, can maintain that 1=2.
At first sight it would seem that there is no theological problem here. It is a well founded principle of theology that revelation is superior to reason; that God may work miracles if She so chooses; that the universe is an artifact of Hers that She may alter without regard as to its internal logic or laws. The trouble is that logic and reason, truth and beauty, are not in the universe per se. That is, there is not thing that is truth, no object that is reason. They are absolutes, ideals, outside the universe, affecting and shaping the character of the universe but unaffected by it. In fact, their existential character is much like that of God Herself, and it widely held that these ideals are aspects of God. That is the crux of the problem; for if God is Truth and Truth is God, then how could God conceive of that which is not truth. On the other hand, it is held that God is omnipotent and therefore may do as She chooses, including thinking untruths. So you see, the four sided triangle is an aspect of a fundamental theological problem.
Now it seems to me that the answer must be in the affirmative; that God can make four sided triangles if She so chooses. My answer is based on the observation that it is in fact possible to conceive of four sided triangles and defend their existence. I suspect that She has chosen not to do so, but I argue that it is within Her powers, Let us consider for a moment a conversation between those redoubtable and hoary combatents, Sage and Simp:
I think we can leave them here. It is clear that their dispute can go on indefinitely. Sage is going to say, in one way or another, that three and four are the same. Simp is going to catch him at his trick and point out that Sage is, in effect, saying that three and four are the same. Sage is going to deny that he is saying any such thing. Simp is going to go back and ask what he did say if it wasn't sayiing that three and four are the same. Sage is going to assert the same thing in a different form. Round the mulberry bush they go again. Simp can never establish that Sage is being inconsistent because Sage always changes his position to avoid the immediate inconsistency while retaining the basic inconsistency by returning to it whenever he gets the chance.
Sage's rather heavy handed little game with Simplicitus is based on a principle well known to mathematicians; it is perfectly possible to be consistent within a formally inconsistent system provided you never carry inconsistent lines of reasoning to the point of inconsistency. This is done in the foundations of Mathematics wherein traditional Mathematics, which is consistent and not totally rigorous, is based on Set Theory, which is rigorous and inconsistent.
Now it is presumed, at least by Mathematicians, that Mathematicians know what they are doing when they are skirting the edge of inconsistency. However we have many instances of people who engage in inconsistent conceptual frames of thinking and don't know that they are doing so. Such people are called psychotics, or, sometimes, politicians.
Now surely god, if she chose to, could engage in such modes of thought if She wished. However She would have great advantages for She could shape the universe to Her will. Not only could She create a formally inconsistent universe, but She could also rig things so that the thinking beings in Her universe could not detect it.
For all we know that's exactly what She did. Maybe triangles "really" do have four side and we have been tricked into incorrectly perceiving them as having three sides. Certainly we would have no way of ever knowing. I kind of like to think that She did. To me it seems like the sort of trick that a God that could create a universe having theologians and politicians would pull.
This page was last updated February 1, 2006.