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Peirce’s Diagrammatic Logic and the Opposition between Logic as Calculus vs. Logic as Universal Language

Peirce’s Diagrammatic Logic and the Opposition between Logic as Calculus vs. Logic as Universal Language

Javier Legris, “Peirce’s Diagrammatic Logic and the Opposition between Logic as Calculus vs. Logic as Universal Language,” Revista Portuguesa de Filosofia 73, no. 3–4 (2017): 1095–1114, DOI 10.17990/RPF/2017_73_3_1095.

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Peirce’s Diagrammatic Logic and the Opposition between Logic as Calculus vs. Logic as Universal Language

Type Journal Article
Author Javier Legris
Rights © 2018 Aletheia - Associação Científica e Cultural | © 2018 Revista Portuguesa de Filosofia
Volume 73
Issue 3-4
Pages 1095-1114
Publication Revista Portuguesa de Filosofia
ISSN 0870-5283; 2183-461X
Date 2017
DOI 10.17990/RPF/2017_73_3_1095
Language English
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.
Date Added 17/01/2018, 17:50:07
Modified 17/01/2018, 19:27:34

Tags:

  • Charles S. Peirce,
  • diagrammatic reasoning,
  • history of logic,
  • philosophy of logic

Notes:

  • Bellucci, Francesco and Ahti-Veiko Pietarinen. ‘Existential Graphs as an Instrument for Logical Analysis’. Part 1: Alpha’. Review of Symbolic Logic 9, no. 2 (2016): 209-237. doi: 10.1017/S1755020315000362.
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    Frege, Gottlob. ‘Über den Zweck der Begriffsschrift’ (original from 1883), translated as ‘On The Aim of The Conceptual Notation’. In Gottlob Frege, Conceptual Notation and related articles, edited by Terrel Ward Bynum, 90-100. Oxford: Oxford University Press, 1972, 
    Grattan-Guinness, Ivor. ‘Living together and living apart. On the interactions between mathematics and logics from the French Revolution to the First World War’. South African Journal of Philosophy 7, no. 2 (1988): 73-82.
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    Peckhaus, Volker. Logik, Mathesis universalis und allgemeine Wissenschaft. Leibniz und die Wiederentdeckung der formalen Logik im 19. Jahrhundert. Berlin: Akademie Verlag, 1997.
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    Peirce, Charles Sanders. Collected Papers. 8 vols., vols. 1 – 6 ed. by Charles Hartshorne & Paul Weiss, vols. 7-8 ed. by Arthur W. Burks. Cambridge (Mass.): Harvard University Press, 1931-1958.
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