EPISTEMOLOGY he was concerned to set out the relationship between epistemology and other related disciplines In the tradition of Descartes, Frege believed, epistemology had been given a fundamental role in philosophy that should really be assigned to logic On the other hand, philosophers in the empiricist tradition had confused logic with psychology In working out his logical system Frege was anxious to show the difference in nature and role between logic and these two other branches of study Frege took over, and adapted for his own purposes, Kant’s distinction between a priori and a posteriori knowledge To ensure that talk of a priori knowledge involves no confusion between psychology and logic, he reminds us that it is possible to discover the content of a proposition before we hit on a proof of it We must distinguish, therefore, between how we first come to believe a proposition, and how we would eventually justify it There must be a justification, if we are to talk of knowledge at all, for knowledge is belief that is both true and justified It is absurd to talk of an a priori mistake, because one can only know what is true When a proposition is called a posteriori or analytic in my sense, this is not a judgement about the conditions, psychological, physiological and physical, which have made it possible to represent the content of the proposition in consciousness Nor is it a judgement about the possibly defective method by which some other person has come to believe it true Rather, it is a judgement about the fundamental ground which provides the justification for believing it to be true (FA 3) If the proposition is a mathematical one, its justification must be mathematical; it cannot be a psychological matter of processes in the mathematician’s mind To be sure, mathematicians have sensations and mental images, and these may play a part in the thoughts of someone who is calculating But these images and thoughts are not what arithmetic is about Different mathematicians associate different images with the same number: in operating with the number one hundred, one person may think of ‘100’ and another of ‘C’ Even if psychology could give a causal explanation of the occurrence of the thought that ten squared is one hundred, it would still be totally different from arithmetic, for arithmetic is concerned with the truth of such propositions, psychology with their occurrence in thought A proposition may be thought of without being true, and a proposition may be true without being thought of 156