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November 2001 - November 2003 Peirce's logic of continuity: Existential graphs and non-Cantorian continuum
Fernando Zalamea
Rev. Mod. Log. 9(1-2): 115-162 (November 2001 - November 2003).

Abstract

Peirce's systems of existential graphs (Alpha: classical propositional calculus; Beta: first-order purely relational logic; Gamma: modal calculi and second-order logic) are presented both from an historical perspective and succinctly for the modern reader. Peirce's alternative continuum, with its main non-Cantorian properties (genericity, reflexivity, modality), is also presented both historically and synthetically. The blend of Peirce's existential graphs and his non-Cantorian continuum gives rise to a thoroughly original logical approach to the "labyrinth of the continuum". We explain why such an approach was set aside in the main developments of logic in the $\,\hbox{\tiny XX}^{\hbox{\tiny th}}\,$ century, and we hint to a possible renewal of interest for Peirce's continuity logic from the viewpoint of contemporary developments in category theory and geometric logic.

Citation

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Fernando Zalamea. "Peirce's logic of continuity: Existential graphs and non-Cantorian continuum." Rev. Mod. Log. 9 (1-2) 115 - 162, November 2001 - November 2003.

Information

Published: November 2001 - November 2003
First available in Project Euclid: 5 April 2004

zbMATH: 1303.03010
MathSciNet: MR2040860

Rights: Copyright © 2003 The Review of Modern Logic

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Vol.9 • No. 1-2 • November 2001 - November 2003
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