What if logic is simply wrong?
At the fine institute of higher learning I attend, all philosophy majors are required to take a course in basic logic. It's a simple course, really - basic laws of logic, truth tables, lots of Ps and Qs, that sort of thing. The first and most basic law of logic we learned was the Law of Identity: A = A. Essentially, all this says is that a thing is identical to itself. This seems self-evidently true, right? A rock is a rock, a carrot is a carrot, a key is a key - so obvious we needn't even worry about it, right?
It's also profoundly important to logic, and, I think, it's fairly obvious why: without the certainty of the Law of Identity, everything else, it seems, would fall apart. Take this basic logical inference: P > Q, P, || Q (in English, "If P, therefore Q; P; therefore Q.") That makes sense. But what if the Law of identity is false, and P does not equal P? Then, even if P > Q is true, asserting P doesn't guarantee Q. That's a big problem!
In his book All Things are Possible, the philosopher Lev Shestov makes this same point:
A = A. —They say that logic does not need this postulate, and could easily develop it by deduction. I think not. On the contrary, in my opinion, logic could not exist without this premise. Meanwhile it has a purely empirical origin. In the realm of fact, A is always more or less equal to A. But it might be otherwise. The universe might be so constituted as to admit of the most fantastic metamorphoses. That which now equals A would successively equal B and then C, and so on. At present a stone remains long enough a stone, a plant a plant, an animal an animal. But it might be that a stone changed into a plant before our eyes, and the plant into an animal. That there is nothing unthinkable in such a supposition is proved by the theory of evolution. This theory only puts centuries in place of seconds. So that, in spite of the risk to which I expose myself from the admirers of the famous Epicurean system, I am compelled to repeat once more that anything you please may come from anything you please, that A may not equal A, and that consequently logic is dependent, for its soundness, on the empirically-derived law of the unchangeableness of the external world. Admit the possibility of supernatural interference - and logic will lose that certitude and inevitability of its conclusions which at present is so attractive to us.
What if Shestov is right? What if the Law of Identity is not self-evidently true, but is merely an assumption based on observations? All of our rational argument would be called into question. One could no longer attack another's argument by saying "your logic is flawed;" one would have to say flatly, "logic is flawed." Rational discourse suddenly wouldn't be so highly valued!
Finally - and this is the most important thing - if Shestov is right, why did I have to bother taking a course on logic?