ours actually reason, psychologism misses logic’s normative force; as he explains in “Thought”:
Error and superstition have causes just as much as correct cognition. Whether what you take for true is false or true, your so taking it comes about in accordance with psychological laws. A derivation from these laws, an explanation of a mental process that ends in taking something to be true, can never take the place of proving what is taken to be true.12
And again in his Fundamental Laws of Arithmetic:
Anyone who understands logical laws as prescribing how one should think, as laws of being true, not as natural laws of human beings’ holding as true, will ask: who is right? Whose laws of holding as true are in accord with the laws of being true? The psychological logician cannot ask this, since he would thereby be recognizing laws of being true, which would not be psychological.13
The normativity of logic is inextricably linked with the truth-preserving character of inferences made in accordance with it; but descriptive laws of human thought can hardly be truth-preserving (since people, unlike logic, can make mistakes), and mutually incompatible sets of rules likewise cannot all be equally truth-preserving. Hence normative polylogism makes no sense.
But Frege’s critique of normative polylogism does not rule out descriptive polylogism. Admittedly, Frege sometimes writes as though logic sets out the standards for mindedness as such – for what is so much as to count as a mind – as when, for example, he writes:
Neither logic nor mathematics has the task of investigating minds and contents of consciousness owned by individual men. Their task could perhaps be represented rather as the investigation of the mind; of the mind, not of minds.14
12 Michael Beaney, ed., The Frege Reader (Blackwell, 1997) 325-6.
13 Cited in Beaney, op. cit., p. 203.
14 Ibid., p. 342.
R. T. Long – Wittgenstein, Praxeology, and Frege’s Three Realms – p. 8