Peirce’s calculi for classical propositional logic

Review of Symbolic Logic 13 (3):509-540 (2020)


This article investigates Charles Peirce’s development of logical calculi for classical propositional logic in 1880–1896. Peirce’s 1880 work on the algebra of logic resulted in a successful calculus for Boolean algebra. This calculus, denoted byPC, is here presented as a sequent calculus and not as a natural deduction system. It is shown that Peirce’s aim was to presentPCas a sequent calculus. The law of distributivity, which Peirce states in 1880, is proved using Peirce’s Rule, which is a residuation, inPC. The transitional systems of the algebra of the copula that Peirce develops since 1880 paved the way to the 1896 graphical system of the alpha graphs. It is shown how the rules of the alpha system reinterpret Boolean algebras, answering Peirce’s statement that logical graphs supply a new system of fundamental assumptions to logical algebra. A proof-theoretic analysis is given for the connection betweenPCand the alpha system.

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Minghui Ma
Sun Yat-Sen University

Citations of this work

Abduction and Diagrams.Ahti-Veikko Pietarinen - forthcoming - Logic Journal of the IGPL.
To Peirce Hintikka’s Thoughts.Ahti-Veikko Pietarinen - 2019 - Logica Universalis 13 (2):241-262.
Notational Differences.Francesco Bellucci & Ahti-Veikko Pietarinen - 2020 - Acta Analytica 35 (2):289-314.
Peirce’s Dragon-Head Logic.Minghui Ma & Ahti-Veikko Pietarinen - 2022 - Archive for History of Exact Sciences 76 (3):261-317.

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