Credo Ut Intelligam

The Ontological Status of Logic

There two ways of thinking about the ontology of logic.

1. First there is the idea that the rules of reason are the rules of Being. C.S. Lewis defends this idea in “De Futilitate” (in Christian Reflections). He’s arguing against the scientific reductionist. Science, says Lewis, depends on deductive reason. Inductive reason is all well and good, but without deduction it would be impossible to prove anything: Suppose we prove that all masses are attracted to one another by an inverse square law. Does this rule out the possibility that all masses are not attracted by an inverse square law? Only if we assume the law of non-contradiction. Without that, and without deductive logic in general, saying “x is true” won’t tell us that x is not false.

Since our scientific knowledge is capable of describing things in far off galaxies, we must conclude that our deductive logical forms of reasoning are valid just as much for those far off galaxies as for here on earth. Indeed, if our “human reasoning” forbids something, then that thing cannot happen even in a far off galaxy. Which means that our “human reasoning” is not really specifically “human” at all. Rather the rules of logic are written on the face of the universe. Reason is the legislator of the world. So Lewis argues.

But I say, Where is God in all of this? Either 1a) God created logic or 1b) Logic is above God 1c) Logic is God. All three of these are problematic
1a) If God created logic then He Himself is above logic, so logical principles don’t apply to him. For all we know, God could be both A and not A. But this would make theology impossible. The idea that God is omnipotent means nothing unless it rules out the idea that God is not omnipotent. This means that if we read in the Bible that God is almighty, we should not assume that he is not weak. If God is above the law of non-contradiction then God could be both weak and omnipotent at the same time.
1b) If logic is above God, then God is not the ultimate authority in the universe, he must bow before logic. And something other than God is eternal. But God is the ultimate authority, and he created everything that is, except Himself.
1c) If logic is God, then we ought to worship the law of non-contradiction, sing hymns to the principle of excluded middle, fall down at the feet of modus ponens, and offer up praise and thanksgiving to the complex destructive dilemma.

I think the underlying problem with this way of thinking can be best described by way of a metaphor that Lewis uses. In dealing with an objection to his view (the objection says that we can reason about the universe because the universe produced our minds), he points out that the gulf stream produces many things, including the temperature of the Irish Ocean, but it does not produce maps of the gulf stream. My response to Lewis is to point out that the gulf stream does not obey the laws of cartography.

Obeying the laws of cartography allows our maps to be accurate, even maps of distant lands, but this is not because those distant lands obey the same rules as our map-makers. The rules make possible the act of representing things. They don’t order the things represented. The same is true of logic. If we want to speak and think accurately we must obey the rules of logic, but not because the things we talk and think about obey those same rules. Rather, the rules make possible the activity of talking and thinking about things.

2. This brings me to the second way of thinking about the ontology of logic: The idea here is that logic is merely conventional rules of language, or at most a contingent feature of human mentality, not of all mentality as such. God’s mind is not ruled by logical principles. If God speaks, then he’ll take up the conventions of whatever language he uses, including its logical conventions. But he doesn’t need them himself.

According to this view, logically necessary truths are devoid of content. They are no more universal than the rules of chess. If you want to play chess then you need to obey the rules of chess, but no one says you have to play chess. And if you want to think or talk about things, then you have to obey the rules of a certain “language game”, but no one says you have to play that game in the first place. Maybe this particular language game plays an important role in the life of our society; even more than, say, the rules of parliamentary procedure. In fact there are people who don’t obey the rules of reasoning (we call them lunatics). Although most people who are able to play the game will, since it helps them get along in society, nevertheless the rules of the game are merely conventional. Or maybe we are psychologically determined to play this kind of game with each other. Still the rules of this game don’t tell us anything about the world as a whole, only about a contingent feature of human psychology.

On the one hand, I think it is right to see logic as expressing the rules of a certain kind of “game” or activity. What this view misses is how astounding it is that we can play such a game. Why should it be possible to produce sentences that are true about ABSOLUTELY EVERYTHING. Logic, you see, gives us the ability to engage in unrestricted quantification. This is a fancy way of saying that the “game” of speech/thought includes the word “everything”. Not only that, but logic assures us that certain predicates are true of everything. Absolutely everything either is A or is not A. This holds for God as well as for created things. But, why?

There is a passage in Ernst Cassirer’s book, entitled An Essay on Man, in which he recounts the story of how Hellen Keller first learned to use language. Her teacher had often signed out certain words on her hand, but Hellen Keller never really understood the point of those signs, she never saw them as words, until one day, while pumping water, her teacher signed “water” on one hand while Hellen Keller felt the cold water pouring over her other hand. She was startled. Taken aback for a moment. Then, suddenly she became very excited. She asked for what word meant her teacher. She asked how to say grass. She asked and asked and asked, as if she wanted to know what everything was called. A whole world was opened to her. Before, she could only conceive of what was immediately present in her experience. After, she could cognize a universe, and her mind could even pass beyond the universe to the ultimate source of all being. To think. How is it possible? Why is it possible?

When I wonder about the ontological status of logic, I keep coming back to this question: What is it about Being that it should be capable of being represented?