For Cyrus
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A reader is skeptical of my solubility skepticism. He adduces the problem of psychologism in logic which, he suggests, has been definitively settled in favor of the anti-psychologizers. Here, then, is a problem that supposedly has been solved. There is progress in philosophy after all. My reader is joined by Robert Spaemann who, in his Persons, tr. O'Donovan, Oxford 2006, writes:
The refutation of psychologism in logic, with which Husserl and Frege are associated, is among the very few philosophical achievements that have brought an existing debate to a decisive close. (54)
Would that it were so! But alas it is not. The existing debate rages on. Having been brought up on Husserl, and influenced by Frege, I was for a long time an opponent of psychologism in logic, and thought the issue resolved. Time to revaluate! Here is a post from August 2004 from my first blog:
ARE THE LAWS OF LOGIC EMPIRICAL GENERALIZATIONS?
Someone on a discussion list recently resurrected the old idea of John Stuart Mill and others that the laws of logic are empirical generalizations from what we do and do not perceive. Thus we never perceive rain and its absence in the same place and at the same time. The temptation is to construe such logic laws as the Law of Non-Contradiction — ~(p & ~p) — as generalizations from psychological facts like these. If this is right, then logical laws lack the a priori character and epistemic ‘dignity’ that some of us are wont to see in them. They rest on psychological facts that might have been otherwise.
But now consider this reductio ad absurdum:
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 not have been the case.) Therefore,
3. The laws of logic, if true, are merely contingently true. (From 1 and 2)
4. If proposition p is contingently true, then it is possible that p be false. (Def. of ‘contingently true.’)Therefore,
5. The laws of logic, if true, are possibly false. (From 3 and 4)Therefore,
6. LNC is possibly false: there are logically possible worlds in which ‘p&~p’ is true. (From 5 and the fact that LNC is a law of logic.)
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. Corollary: if laws of logic were empirical generalizations, we would be incapable of defining ‘empirical generalization’: this definition requires the notion of what is the case but (logically) might not have been the case.
The above is a good, but not a compelling, argument. For it presupposes the distinction between necessary and contingent propositions. Is that distinction objectively self-evident? Martin Kusch, Psychologism, Stanford Encyclopedia of Philosophy:
Massey also invokes the stronger form of the claim that logical truths are not necessary (1991, 188). According to this criticism, the very notion of necessity which is presupposed in calling logical laws ‘necessary truths’, is beset with difficulties. The argument leading to this conclusion was developed in a series of well-known papers by Quine. Quine argued that the notions of analyticity, necessity and aprioricity stand or fall together and that the traditional distinction between analytic and synthetic truths is relative rather than absolute. But once this distinction becomes relative, necessity and aprioricity go by the board (Quine 1951, Engel 1991, 268–70). Massey summarises the implications of Quine’s arguments succinctly:
If we reject the concept of necessity … we also forego the concept of contingency. If it makes no sense to say that the truths of mathematics are necessary, it makes no better sense to say that those of psychology or any other so-called empirical science are contingent. But if we may not employ necessity and contingency to demarcate the deliverances of the empirical sciences from those of the formal sciences, how are we to distinguish them in any philosophically interesting way? (1991, 188).
Now I don't much cotton to Quine, but he is no slouch of a logician! And he is certainly a looming presence in 20th century American philosophy. So on the basis of his dissent alone, we ought to agree that the psychologism problem has not been solved. I am assuming that a problem hasn't been solved unless it has been solved to the satisfaction of all competent practitioners. It hasn't been solved until the debate about it has been brought to a decisive close. Kusch gives several reasons in addition to the one cited above why this is not the case with respect to the psychologism debate.
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