Friday, September 03, 2004

Another Round with Richard Chappell

Richard Chappell over at Philosophy, et cetera has a good blog going, and has rendered a great service to philosophy in the blogosphere by organizing the Philosophers' Carnival. I thank him for the following discussion. We post not just out of vanity but to test and clarify our ideas and stimulate inquiry and rational debate.

He writes:

The Maverick Philosopher responds to my charge of question-begging:
Rethinking this, my argument strikes me as logically impeccable. Am I assuming what I need to prove? Not that I can see. What I am arguing, very simply, is that LNC cannot be an empirical generalization since if it were, it would be logically contingent, i.e., logically possible false. But this is absurd since LNC is the criterion of logical possibility. LNC defines what it is to be a logically possible world. Hence a logically possible world in which LNC fails to be true is a world in which a contradiction is true. Hence, by RAA, (1) is false.

To make things clearer, I have emphasised in bold the exact stage which strikes me as question-begging. I could be mistaken here, but as I understand it, to question the necessity of the laws of logic is to question their metaphysical necessity. Surely no-one would doubt that the laws of logic are logically necessary.

BV: I am afraid that RC is not engaging the precise question that I raised in my original post, namely, could LNC be an empirical generalization, as John Stuart Mill thought? RC is mistaken in saying that "no-one would doubt that the laws of logic are logically necessary." J.S. Mill not only doubts, he denies that they are logically necessary by affirming that they are empirical generalizations from the ways in which we as a matter of fact think. Mill questions the necessity of logical laws, period, not their metaphysical necessity as opposed to some other sort of necessity.

Part of the problem here is that RC does not tell us exactly what he means by 'metaphysical necessity.' This is not a term I used in my original post; yet he brings it in to criticize my post.

That's as absurd as doubting that the laws of nature are 'naturally necessary' (by the definition given in my previous post).

BV: RC is saying that it is absurd to doubt that the laws of logic are logically necessary. This is not absurd at all. If LNC, e.g., is an empirical generalization, then it is precisely not logically necessary. Suppose LNC is just a law of human psychology, a generalization from such facts as that "belief and disbelief are two different mental states that exclude one another." (J. S. Mill, quoted from E. Husserl, Logical Investigations, vol. I, p. 112.) Then LNC will be logically contingent.

It's just an empty tautology - as Bill himself noted, "LNC is the criterion of logical possibility". So long as we remain within the framework of classical logic, it is trivially true that the laws of logic could not possibly be false. They are true by definition - by mere stipulation.

BV: RC is saying that 'The laws of logic are logically necessary' is an "empty tautology." This is simply false. The refutation of psychologism cannot be this easy! A statement of the form Every F is a G cannot possibly be a tautology. The easiest way to see this is to consider the negation of 'Every law of logic is logically necessary,' namely, 'Some laws of logic are not logically necessary.' Is this latter statement a contradiction? No, since it is not contradictory in virtue of its logical form. Therefore, the statement of which it is the negation is not a tautology, or more precisely, a logical truth. (Strictly speaking, 'tautology' applies only to logical truths in the propositional as opposed to predicate calculus.)

What RC is failing to consider is the characteristic claim of the psychologistic logicians for whom logical laws are a proper subset of psychological laws. Psychologism took a serious hit from Husserl and Frege, but recently it has resurrected itself -- which is part of the reason I raised the issue in my original post.

Note also that 'The laws of logic are logically necessary' is not itself a law of logic, but is a meta-thesis ABOUT the laws of logic. It belongs to the philosophy of logic. Thus the truth of LNC is logically consistent with the truth of 'LNC is logically contingent.'

It thus seems that RC is involved in a level-confusion.

RC also confuses logically true with stipulatively true. What we stipulate to be true cannot fail to be true for the simple reason that we so stipulate it. Thus I might stipulate that a fred is anything both fat and red. Since there is no 'fact of the matter,' no one can show me to be wrong. But there are all sorts of necessary truths that are not obviously true by stipulation, among them truths of logic. Take LNC. Wouldn't it be absurd to claim that it is true because I stipulate it to be true, when any stipulation I make, including this one, must satisfy LNC to be logically coherent?

But even if RC doesn't buy the little argument I just sketched, he can't just ASSUME that truths of logic are true by stipulation. Too many great philosophers have denied that.

And that is why I consider it question-begging to defend the necessity of logic by merely pointing out that it is "logically necessary".

BV: But that's not what I did. RC is simply ignoring the actual argument I gave and reading into it all sorts of extraneous ideas of your own. For one thing, my argument crucially depends on the meaning of 'empirical generalization.'

For that (I take it) is not in question. Instead, we are asking whether we must be bound by the limits of classical logic.

BV: That's not the question I posed. RC is further confusing the issue by bringing in the question of alternative logics. I didn't mention that. My argument assumes classical logic, with its LNC, and then asks whether its laws could be laws of psychology as Mill and others have maintained. I've read G. Priest on paraconsistent logics, but my post has nothing to with that set of questions. I do suspect, however, that LNC is a sounder principle than any consideration that Priest can muster against it.

The basic problem with RC's attempted critique is that it foists upon my argument extraneous distinctions and questions. In any case, I appreciate RC's comments and interest, and hope my remarks are of some use.