Tuesday, July 26, 2005

Argument from the Psychological Relevance of Logical (and mathematical) Laws

IV. Argument from the Psychological Relevance of Logical Laws
My fourth argument concerned the role of logical laws in mental causation. In order for mental causation to be what we ordinarily suppose it to be, it is not only necessary that mental states be causally efficacious in virtue of their content, it is also necessary that the laws of logic be relevant to the production of the conclusion. That is, if we conclude “Socrates is mortal” from “All men are mortal” and “Socrates is a man, then no only must we understand the meanings of those expressions, and these meanings must play a central role in the performance of these inferences, but what Lewis call the ground-and-consequent relationship between the propositions must also play a central role in these rational inferences. We must know that the argument is structured in such a way that in arguments of that form the conclusion always follows from the premises. We do not simply know something that is the case at one moment in time, but we know something that must be true in all moments of time, in every possible world. But how could a physical brain, which stands in physical relations to other objects and whose activities are determined, insofar as they are determined at all, by the laws of physics and not the laws of logic, come to know, not merely that something was true, but could not fail to be true regardless of whatever else is true in the world.
We can certainly imagine, for example, a possible world in which the laws of physics are different from the way they are in the actual world. We can imagine, for example, that instead of living in a universe in which dead people tend to stay dead, we find them rising out of their graves on a regular basis on the third day after they are buried. But we cannot imagine a world in which, once we know which cat and which mat, it can possibly be the case that the cat is both on the mat and not on the mat. Now can we imagine there being a world in which 2 + 2 is really 5 and not 4? I think not.
It is one thing to suggest that brains might be able to “track” states of affairs in the physical world. It is another thing to suggest that a physical system can be aware, not only that something is the case, but that it must be the case; that not only it is the case but that it could not fail to be the case. Brain states stand in physical relations to the rest of the world, and are related to that world through cause and effect, responding to changes in the world around us. How can these brain states be knowings of what must be true in all possible worlds?
Consider the difficulty of going from what is to what ought to be in ethics. Many philosophers have agreed that you can pile up the physical truths, and all other descriptive truths from chemistry, biology, psychology, and sociology, as high as you like about, say, the killings of Nicole Brown Simpson and Ronald Goldman, and you could never, by any examination of these, come to the conclusion that these acts we really morally wrong (as opposed to being merely widely disapproved of and criminalized by the legal system). Even the atheist philosopher J. L. Mackie argued that if there were truths of moral necessity, these truths, and our ability to know those truths, are do not fit well into the naturalistic world-view, and if they existed, they would support a theistic world-view. Mackie could and did, of course, deny moral objectivity, but my claim is that objective logical truths present an even more serious problem for naturalism, because the naturalist cannot simply say they don’t exist on pain of undermining the very natural science on which his world-view rests.
Arguing that such knowledge is trivial because it merely constitutes the “relations of ideas” and does not tell anything about the world outside our minds seems to me to be an inadequate response. If, for example, the laws of logic are about the relations of ideas, then not only are they about ideas that I have thought already, but also they are true of thoughts I haven’t even had yet. If contradictions can’t be true because this is how my ideas relate to one another, and it is a contingent fact that my ideas relate to one another in this way, then it is impossible to say that they won’t relate differently tomorrow.
Carrier responds somewhat differently. He says:
For logical laws are just like physical laws, because physical laws describe the way the universe works, and logical laws describe the way reason works—or, to avoid begging the question, logical laws describe the way a truth-finding machine works, in the very same way that the laws of aerodynamics describe the way a flying-machine works, or the laws of ballistics describe the way guns shoot their targets. The only difference between logical laws and physical laws is that the fact that physical laws describe physics and logical laws describe logic. But that is a difference both trivial and obvious.
What this amounts to, it seems to me, is a denial of the absolute necessity of logic. If the laws of logic just tell us how truth-finding machines work, then if the world were different a truth-finding machine would work differently. I would insist on a critical distinction between the truths of mathematics, which are true regardless of whether anybody thinks them or not, and laws governing how either a person or a computer ought to perform computations. I would ask “What is it about reality that makes one set of computations correct and another set of computations incorrect?”
William Vallicella provides an argument against the claim that the laws of logic are empirical generalizations:
1. The laws of logic are empirical generalizations. (Assumption for reductio).
2. Empirical generalizations, if true, are merely contingently true. (By definition of ‘empirical generalization’: empirical generalizations record what happens to be the case, but might have not been the case.)
3. The laws of logic, if true, are merely contingently true. (1 and 2)
4. If proposition p is contingently true, then it is possible the p be false. (True by definition)
5. The laws of logic, if true, are possibly false. (From 3 and 4)
6. LNC is possibly false: there are logically possible worlds in which p & ~p is true.
7. But (6) is absurd (self-contradictory): it amounts to saying that it is logically possible that the very criterion of logical possibility, namely LNC, be false. Therefore 1 is false, and its contradictory, the clam that the laws of logic are not empirical generalizations, is true.
Logic, I maintain, picks out features of reality that must exist in any possible world. We know, and have insight into these realities, and this is what permits us to think. A naturalistic view of the universe, according to which there is nothing in existence that is not in a particular time and a particular place, is hard-pressed to reconcile their theory of the world with the idea that we as humans can access not only what is, but also what must be.