Frege on Knowing the Third Realm

Abstract

Anyone who reads Frege with moderate care is struck by a puzzle about the central objective of his work. His main project is to explain the foundations of arithmetic in such a way as to enable us to understand the nature of our knowledge of arithmetic. But he says very little about our knowledge of the foundations. A full treatment of this and associated puzzles would require more room than I have here.2 I want to give a short solution to the puzzle, and then discuss one aspect of it that I find interesting. The short solution is that Frege accepted the traditional rationalist account of knowledge of the relevant primitive truths, truths of logic. This account, which he associated with the Euclidean tradition, maintained that basic truths of geometry and logic are Frege says on several occasions that such primitive truths-as well as basic rules of inference and certain relevant definitionsare He did not develop these remarks because he thought they admitted little development. The interesting problems for him were finding and understanding the primitive truths, and showing how they, together with inference rules and definitions, could be used to derive the truths of arithmetic. This short solution seems to me correct-as far as it goes. It does, however, leave out a lot. Frege thought that knowledge of the axioms of geometry required intuition-an imaginative or broadly perceptual capacity (1968, pp. 19-21). Knowledge of the basic truths of logic simply required reason. He regarded both types of basic truths as self-evident, but the differences between the two types of knowledge are significant. That is one complication. Another is that Frege uses a variety of terms that are translated self-evident. His sophisticated understanding of the notion is neither psychologistic nor purely proof-theoretic. He does not mean by it what most contemporary philosophers would mean by it. His uses of it relate in interesting ways to his basic philosophical views. A third complication is that there are complex relations between Frege's appeals to self-evidence and an appeal he makes to pragmatic epistemological considerations. This appeal