Frege’s Basic Logics (without Wertverläufe)

Abstract

In 1879 Frege set forth a monograph: Begsriffsschrift: a formal language, modeled on that of arithmetic, for pure thought. This concept-writing and its proof theory is very unusual compared to modern symbolic logic. The notational and axiomatic changes he made to the system in subsequent years — in his Die Grundlagen der Arithmetik and later in Grundgesetze der Arithmetik — have a central role to play in current debates about Frege’s philosophy of arithmetic. In this chapter, we set out the basic logics involved in these systems.