Review of Symbolic Logic 13 (3):509-540 (2020)
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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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DOI | 10.1017/s1755020318000187 |
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References found in this work BETA
Gamma Graph Calculi for Modal Logics.Minghui Ma & Ahti-Veikko Pietarinen - 2018 - Synthese 195 (8):3621-3650.
Existential Graphs as an Instrument of Logical Analysis: Part I. Alpha.Francesco Bellucci & Ahti-Veikko Pietarinen - 2016 - Review of Symbolic Logic 9 (2):209-237.
New Light on Peirce's Conceptions of Retroduction, Deduction, and Scientific Reasoning.Ahti-Veikko Pietarinen & Francesco Bellucci - 2014 - International Studies in the Philosophy of Science 28 (4):353-373.
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Citations of this work BETA
Notational Differences.Francesco Bellucci & Ahti-Veikko Pietarinen - 2020 - Acta Analytica 35 (2):289-314.
Semeiotic Completeness in the Theory of Signs.Ahti-Veikko Pietarinen - 2019 - Semiotica 2019 (228):237-257.
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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