Naturalism and First Philosophy: Logic & Usefulness

From what I can currently understand, naturalism is dominant among current philosophers. Naturalism excludes any consideration of first philosophy. First philosophy is the philosophy that we engage in prior to any scientific or generally empirical understanding. It is sometimes, perhaps usually, associated with justifying the scientific method or science in general. My first reaction to this is that there is nothing wrong with first philosophy, and it looks to be necessary. A consideration of the logical principle of non-contradiction and it justification by usefulness contributes towards showing that this is true.

Consider the realm of logic. Aside from various formal logics, and the standard treatment of fallacies, there are basic principles of logic. One of these is the principle of non-contradiction: it is not the case that P & not-P. For example, it is not the case that I exist and I do not exist. This principle was first formalized by Aristotle. It is part of first philosophy for two reasons: no empirical evidence supports this, and no empirical evidence can defeat it (contra Quine). Therefore, there is a first philosophy because certain logical principles are a part of it. Since these logical principles are also necessary for any kind of thinking, first philosophy is also necessary.

The naturalist could claim that our belief in logic is justified by its usefulness. Without it, we would be unable to think correctly or behave well. This principle was useful in our survival. Let's suppose that we grant this. We can understand the usefulness claim in two ways. One is a justifiying way: I am justified in believing the principle of non-contradiction because it is justified by my experiences of the world. The other is historical: I came to believe in the principle because of its survival value. The historical reading does not justify my belief. All it does is explain why I have it. So I can still ask what justifies my belief in it. If we use the justifying reading, then we are left with a question: just how are my experiences of the world supposed to justify the principle of non-contradiction?

When I come to the world I do not take any experience as being a possible defeater for the principle of non-contradiction. If went outside and saw that the moon was bright green, I would not conclude that the moon is both white and not-white (green). I would conclude that the appearance of the moon is now green, but was previously white. Those who believe in the doctrines of the Trinity or Incarnation do not believe that there is no sense to be had in the doctrine. They believe that they do not understand all of it, and cannot. Neither case is a violation of the law of non-contradiction. Therefore, as far as I know, there is no experience that either defeats or supports my belief in the principle. I am highly attached to the claim and would give up anything else to preserve it.

Now we move into the territory of Quine. He claimed that our web of beliefs were all revisable in principle - including our logical beliefs. However, we must revise as little as possible, and make the changes as simple as possible in order to preserve coherence. It is fairly easy to point out given Quine's principles of belief revision, the principle of non-contradiction is not revisable. First, the very principles he gives assume that the principle is true. What determines how much revision and how many changes are necessary is found by determining what set of beliefs can be held without contradiction. Second, no possible change could ever be sufficient to alter this principle. Let's suppose that you denied the principle. By doing this, you are adding the contradictory of every belief in your web to your web. You also add every other belief and its contradictory to your web. So now your web of belief contains every possible belief and its contradictory. It is as large as possible. But that violates Quine's first principle - make as little revision as possible. Any other set of beliefs would be smaller, therefore, one should never reject this belief. Therefore, the principle of non-contradiction is not revisable - even in principle - on Quine's system. Since Quine's system is the only one to provide a way to revise our logical beliefs, there are no systems that successfully show that belief in the principle of non-contradiction is revisable by anything at all.

These considerations defeat the naturalist who attempts justify the principle of non-contradiction using its usefulness as the reason. The naturalist does have other options. She could attempt to justify it by rationality, or could deny that the principle is a belief. I will examine these options some other time. Apart from the success of those other options, the naturalist will be unable to reject at least some of the traditional first philosophy.