C.S.Peirce and the Early Phases of Model-theoretic Logic

Abstract

This paper focuses on C. S. Peirce's philosophy of logic and mathematics pertinent to the so-called model-theoretic tradition in formal logic. While it is common to trace the development of model-theoretic logic back to Peirce, closer textual study tends to reveal that there is a gap between the work of Peirce and what was later achieved by, among others, Lowenheim and Skolem. As Peirce's nonstandard model of the theory of reals suggests, however, Peirce does belong to the model-theoretic tradition at least in a broad sense. This paper thus makes efforts to better situate Peirce in the model-theoretic movement by considering Cantor's influence on Peirce, which most probably motivated Peirce to develop his nonstandard model of the reals. The paper also endeavors to shed light on Peirce's highly original ideas regarding the logic of mathematics seen in this particular context.