But at other times Frege seems to regard logic as only normative for, not descriptive of, human minds, as when he raises the question: “what if beings were even found whose laws of thought directly contradicted our own ...?” Here he replies that while the “psychological logician could only simply acknowledge this and say: those laws are valid for them, these for us” (thereby embracing normative polylogism), Frege’s own response would be that “here we have a hitherto unknown kind of madness.”15 Calling deviant logics “madness” is clearly a rejection only of normative and not of descriptive polylogism: Frege does not deny that alternative ways of thinking can exist, he only denies that they would be valid forms of logic if they did.
Perhaps Frege’s project does not require the rejection of descriptive polylogism, but Mises’ project does, since praxeology – the body of conceptual truths about action – is supposed to be descriptive of all human action. Mises writes:
No facts provided by ethnology or history contradict the assertion that the logical structure of mind is uniform with all men of all races, ages, and countries. ... He who addresses fellow men, who wants to inform and convince them ... can proceed in this way only because he can appeal to something common to all men – namely, the logical structure of human reason. The idea that A could at the same time be non-A or that to prefer A to B could at the same time be to prefer B to A is simply inconceivable and absurd to a human mind.16
It is crucial to Mises’ project that the laws of praxeology be not just normative but descriptive of human behaviour – since otherwise they would merely tell us what it would be reasonable for people to do, but would offer no insight into what people actually do, and so would be of little use in grounding economic science. But for Frege, neither the discovery of tribes who contra-logically regard A as non-A nor the discovery of tribes who contra-praxeologically prefer both A to B and B to A is ruled out a priori.
15 Ibid., p. 203.
16 Ludwig von Mises, Human Action: A Treatise on Economics, 4th ed. (Foundation for Economic Education, 1996), pp. 36-38.
R. T. Long – Wittgenstein, Praxeology, and Frege’s Three Realms – p. 9