Popper’s Theory of Deductive Logic

Abstract

We present Popper’s theory of deductive logic as exhibited in his articles published between 1947 and 1949. After an introduction to Popper’s inferentialist approach and his idea of “inferential definitions” of logical constants, we discuss in more formal detail Popper’s general theory of the deducibility relation (which, using Gentzen’s terminology, might be called his “structural” theory), as well as his special theory of logical constants. We put special emphasis on his inferential notion of duality, which includes his analysis of the “anti-conditional” (today called “co-implication”), his systematic study of various forms of negation including classical, intuitionistic and weaker negations, his system of bi-intuitionistic logic, and his theory of quantification and identity. We also touch on his treatment of modal operators, which is based on Carnap’s Meaning and Necessity.