Peirce's diagrammatic logic and the opposition between logic as calculus vs. logic as universal language

Abstract

In the last century Jaakko Hintikka tried to determine Peirce’s locus within the framework of the “Logic as Calculus vs. Logic as Universal Language” opposition in the history of mathematical logic, placing it in the former tradition. For this purpose Hintikka reformulated the opposition devised earlier by Jean van Heijenoort in order to investigate not only the development of notations and formal languages in the origins of mathematical logic but also the very original ideas in them. The aim of this paper is to show some difficulties in placing Peirce’s diagrammatic conception of deductive logic inside this opposition. Firstly, Hintikka’s distinction presupposes a linguistic conception of logic by the founders of mathematical logic. However this was not Peirce’s own ultimate conception. Secondly, there is now enough evidence (provided recently by Francesco Bellucci and Ahti-Veikko Pietarinen) that Peirce conceived his diagrammatic system of the Existential Graphs mainly as a tool for logical analysis. This analysis is not of linguistic nature but rather of a semiotic one.