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.
| 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 |
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.
Chateaubriand, Oswaldo. Logical Forms. Part I: Truth and Description. Campinas: UNICAMP, Centro de Lógica, Epistemologia e História da Ciência, 2001.
Couturat, Louis. L´Algebre de la logique. Paris: Gauthier-Villars, 1905.
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.
Hilpinen, Risto. ‘Peirce’s Logic’. In Handbook of the History of Logic, vol. 3: The Rise of Modern Logic: From Leibniz to Frege, edited by Dov M. Gabbay and John Woods, 623-670, Amsterdam et al.: Elsevier - North Holland, 2004.
Hintikka, Jaakko. ‘On the Development of the Model-Theoretic Viewpoint in Logical Theory’ Synthese 77, no. 1 (1988): 1-36. doi: 10.1007/BF00869545.
Hintikka, Jaakko. “Quine as a Member of The Tradition of The Universality of Language”. In Perspectives on Quine edited by R. Barrett and R. Gibson, 159-175. Oxford: Basil Blackwell, 1990.
Hintikka, Jaakko. “The Place of C. S. Peirce in the History of Logical Theory”. In The Rule of Reason: The Philosophy of Charles Sanders Peirce, edited by Jacqueline Brunning and Paul Forster, 13–33. Toronto: University of Toronto Press, 1996.
Jourdain, Philip E. “Preface”. In The Algebra of Logic by Louis Couturat, pp. iii-x: Chicago and London: Open Court, 1914.
Legris, Javier. “Between Calculus and Semantic Analysis. Symbolic Knowledge in the Origins of Mathematical Logic”. In Symbolic Knowledge from Leibniz to Husserl, edited by Abel Lassalle Casanave, 79-113. London: College Publications, 2012.
Peckhaus, Volker. Logik, Mathesis universalis und allgemeine Wissenschaft. Leibniz und die Wiederentdeckung der formalen Logik im 19. Jahrhundert. Berlin: Akademie Verlag, 1997.
Peckhaus, Volker. ‘Calculus Ratiocinator vs. Characteristica Universalis? The Two Traditions in Logic, Revisted’, History and Philosophy of Logic (Special Issue in Honor of Ivor Grattan-Guinness, ed. by John W. Dawson, Jr.) 25 (2004): 3-14. doi: 10.1080/01445340310001609315.
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.
Quine, Willard Van Orman. Methods of Logic, 2nd. ed. Cambridge (Mass.): Harvard University Press, 1956.
Roberts, Don. The Existential Graphs of Charles. S. Peirce. La Haya: Mouton, 1973.
Stjernfelt, Frederik. ‘Two Iconicity Notions in Peirce’s Diagrammatology’. In Conceptual Structures: Inspiration and Application. ICCS-ConceptStruct 2006, edited by H. Schärfe , P. Hitzler and P. Øhrstrøm P. Lecture Notes in Computer Science, vol 4068, 70 - 86. Berlin and Heidelberg: Springer, 2006. doi: https://doi.org/10.1007/11787181_6
van Heijenoort, Jean. 1967. ‘Logic as Calculus And Logic As Language’. Synthese 24 (1967): 324-330. doi: 10.1007/BF00485036. Reprinted in Selected Essays, 11-16. Naples by Bibliopolis.
