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

JAVIER LEGRIS

REVISTA PORTUGUESA DE FILOSOFIA

Axioma - Publicações da Faculdade de Filosofia

Año: 2017 vol. 73 p. 1095 - 1114

0870-5283

Inthe last century Jaakko Hintikka tried to determine Peirce?s locus within the framework of the ?Logicas Calculus vs. Logic as Universal Language? opposition in the history ofmathematical logic, placing it in the former tradition. For this purpose Hintikkareformulated the opposition devised earlier by Jean van Heijenoort in order to investigatenot only the development of notations and formal languages in the origins of mathematicallogic but also the very original ideas in them. The aim of this paper is toshow some difficulties in placing Peirce?s diagrammatic conception of deductivelogic inside this opposition. Firstly, Hintikka?s distinction presupposes a linguistic conception of logic by thefounders of mathematical logic. However this was not Peirce?s own ultimate conception. Secondly, there is nowenough evidence (provided recently by Francesco Bellucci and Ahti-VeikkoPietarinen) that Peirce conceived his diagrammatic system of the ExistentialGraphs mainly as a tool for logical analysis. This analysis is not oflinguistic nature but rather of a semioticone.