Friday, January 07, 2005

Am I Illogical? An Excursus on the Syllogism

My correspondent R. L. has a friend (whose name shall go unmentioned to save him embarrassment) who writes the following about an argument I presented here.

There is a major fallacy in the logical construction of your friend's
syllogism below. he's broken certain rules of elementary argumentation.

I won't waste my time on this one.

Here is my syllogism:

Every belief is either true or false
No brain state is either true or false
So, No belief is a brain state.

1. Note first that this is indeed a syllogism. A syllogism is a deductive argument possessing exactly two premises. It is a mistake to refer to any old argument as a syllogism. First, no inductive argument is a syllogism. Second, no argument having less than or more than two premises is a syllogism. Ordinary usage is looser than this, but on this philosophical weblog strict use of terms rules.

2. With respect to any deductive argument, syllogistic or not, it is crucial to distinguish the validity/invalidity of the argument from the truth/falsity of its constituent propositions. This is a Logic 101 distinction that gets covered on the first day of class. To say that an argument is valid is to say that the reasoning it embodies is correct. But that is not to say that the premises are true or that the conclusion is true. One can reason correctly from false premises, just as one can reason incorrectly from true premises. The ideal, of course, is to reason correctly from true premises. Correct deductive reasoning from true premises will always bring one to a true conclusion. An argument that embodies such reasoning is said to be sound. A sound argument, then, is a valid deductive argument all of whose premises are true. It goes without saying that sound, like valid, is a terminus technicus. That implies that people are not entitled to read their own idiosyncratic meanings into them.

3. Is the syllogism I gave above valid? In other words, is the reasoning embodied therein correct? Anyone with the merest acquaintance with logic can see that it is, and that no fallacy has been committed. Check it against the rules of the syllogism. The logical form of my argument is this:

Every P is M
No S is M
So, No P is S.

To prove this form invalid, you would have to find substitutions for 'P,' 'M,' and 'S' that make the premises true and the conclusion false. Anyone who can do this will receive from me the most expensive Mexican dinner in Apache Junction, Arizona, and that includes cerveza and tequila.

If my computer skills weren't so miserable, I would slap a Venn diagram onto this page that would constitute proof positive that my argument is valid in point of logical form. (Note that 'valid in point of logical form' is, strictly speaking, a redundant expression: validity by its very nature is a formal property of deductive arguments. But as I always say, redundancy in the pursuit of precision is no pecadillo, indeed, it is no sin at all, but mere inelegance.)

4. Is the syllogism I gave above sound? That depends on whether or not the premises are true. Surely the major is true. But so is the minor. So in my book the argument is sound and constitutes a very powerful objection to naturalism (physicalism, materialism). (There are distinctions among these three that can be made, but they would not be to the point at present.)

5. The point of my previous post, however, is that a sophisticated naturalist will not allow himself to be bowled over by this argument. His 'faith-commitment' will not allow it. What he will do is try to show how one or the other of the premises is false. He might argue that the major is false by arguing that it is not beliefs (occurrent episodes of believing, acts of believing) that are true or false but the objects or accusatives of these acts, namely, Fregean propositions. Etc. Of course, I would counterargue against this argument, and the dialectic would be up and running.

6. Finally, it is churlish to say to someone, "You're wrong!" unless one is prepared to explain the mistake the person is supposed to have made. It is uncharitable, and R.L.'s friend, given his public persona and faith commitments, ought to behave charitably. And if he had tried to specify the fallacy, he would have seen that there isn't one.