Is it possible to reject the law of non-contradiction?
I had a conversation with my teaching mentor on wednesday. She rejects the law of non-contradiction, or so she claims. She would probably not put it like that, saying instead that the law of non contradiction does not hold in all circumstances, but when I talk about THE law of NC (as opposed to a law of NC) I mean the one that says "X and not-X are never in any circumstances both true at the same time and in the same sense."
I presume she is being honest when she says she rejects that. Since she has a PhD in Philosophy I can assume that she understands what she is saying. So it would seem that she really means what she says.
But is it even possible to reject the law of NC? I can't imagine what it would be like to reject it. I'm not saying it's logically impossible. I can't imagine what it's like to be a bat, but it is logically possible for something to experience bat-life. However, in a weaker sense it is not possible for a human being to experience what it is like to be a bat, just as it is impossible for a human being to swim across the Atlantic Ocean. That's the kind of impossibility I'm talking about.
I can't imagine what it's like to reject the law of NC. I can imagine believing a lot of nonsense: that I am made of glass, that 2+2=579, that I don't exist. I can imagine believing individual contradictions, so long as I don't admit that they are contradictions. I can imagine not understanding the law of NC; I can imagine understanding it, but withholding jundgment; but to actually disbelieve it? It's not just that nothing could convince me that the law is false, I don't even know what it is to hold a belief like that.
So what am I to make of the many educated people who claim to reject the law of NC? Either they have some cognitive faculty that I lack, or else they are deeply mistaken about their own beliefs: they honestly report what they think their belief is: that the law is not true. But they are wrong: as a matter of fact they don't believe that. That's the only way I can make sense of the situation.
If this is correct, a question arises: why do so many people have this misperception of their own minds? I think I can understand why sophomoric relativists think that way: they want to be tolerant and are either too stuborn to think the matter through, or else they just haven't been taught to think clearly. But what about the highly educated thoughtful people--people who are quite capable of rational thought, and who have thought about and seem willing to continue thinking about the law of NC, but still claim to reject it?
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?
Having read some of the discussions on other blogs regarding Clark and VanTil, I take it there's some interest in epistemology among Covenant bloggers. So I thought this might be a good oportunity to say a few things about human knowledge.
Let me start with some questions. Do we need to have an epistemology before we can know things? Clearly not. A child may know that his mother loves him without knowing what knowledge is. Do we need to have an epistemology before we can know that we know things? This is a more vexing question, but I think the answer is still no. Thus I agree with the first part of particularist epistemology: we don't need to have a definition of knowledge before we can distinguish particular instances of knowledge from instances of mere true belief.
The second part of particularist epistemology is a project for coming up with a definition of knowledge. The project works like this: first formulate a definition of knowledge that seems to fit with what we intuitively think knowledge is. Then dream up a situation in which someone has true belief. Then ask, is this instance of true belief also an instance of knowledge? If our intuition gives us an answer different from what our definition gives, then we must change the definition. Once we have a definition such that we can't find any counterexamples, we have our epistemology.
I cannot endorse this project. Let me explain my objection to it by drawing your attention to two proposition:
1) I believe that everything I believe is true
2) Everything I believe is such that I believe it is true.
The first is the height of arrogance, the second is almost a tautology. Probably, a number of my beliefs are false. But I don't know which ones. Now consider the parallel case:
3) I believe that all of my intuitions about whether a particular case of true belief is knowledge are correct
4) For every intuition I have about whether a particular case of true belief is knowledge, I believe that that intuition is correct.
I hold the beliefs described in 4, but this is no reason to think the particularist project will succeed. One would have to hold the belief described in 3 in order to have any confidence in that project. If 3 is wrong then some of my particular intuitions will conflict with the true definition of knowledge. But 3 is wrong. To reject 3 is to claim that I am not infallible when it comes to distinguishing individual cases of knowledge from mere true belief. Indeed, since I reject 1, and since I can see no relevant distinction between my intuitive beliefs about particularist "counterexamples" and all my other beliefs, I must reject 3 as well. This is why I reject particularist epistemology.
If we're going to make any progress in finding a definition of knowledge, we must turn to methodism. The biggest problem with methodism is that all of the various methodist definitions proposed have less intuitive support than our intuitions regarding counterexamples to those definitions. I don't myself have any such definition of knowledge to propose. In that sense I don't have an epistemology. I am not therefore a skeptic. I believe that there is a difference between knowledge and true belief, and I think that there are many things that I know, but I couldn't tell you what the difference is.
Perhaps we will never know what knowledge is.