Article ID: CBB001210993

Peirce's Truth-Functional Analysis and the Origin of the Truth Table (2012)

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We explore the technical details and historical evolution of Charles Peirce's articulation of a truth table in 1893, against the background of his investigation into the truth-functional analysis of propositions involving implication. In 1997, John Shosky discovered, on the verso of a page of the typed transcript of Bertrand Russell's 1912 lecture on `The Philosophy of Logical Atomism' truth table matrices. The matrix for negation is Russell's, alongside of which is the matrix for material implication in the hand of Ludwig Wittgenstein. It is shown that an unpublished manuscript identified as composed by Peirce in 1893 includes a truth table matrix that is equivalent to the matrix for material implication discovered by John Shosky. An unpublished manuscript by Peirce identified as having been composed in 1883--1884 in connection with the composition of Peirce's `On the Algebra of Logic: A Contribution to the Philosophy of Notation' that appeared in the American Journal of Mathematics in 1885 includes an example of an indirect truth table for the conditional.

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Authors & Contributors
Campos, Daniel G.
Bellucci, Francesco
Shin, Sun-Joo
Brady, Geraldine
Ferriani, Maurizio
Dea, Shannon
Journals
History and Philosophy of Logic
Transactions of the Charles S. Peirce Society
Synthese
Dianoia: Annali di storia della filosofia
Journal Electronique d'Histoire des Probabilités et de la Statistique
Journal of the History of Ideas
Publishers
Elsevier/North-Holland
MIT Press
Cambridge University Press
Princeton University
Concepts
Logic
Philosophy
Mathematics
Philosophy of science
Philosophy of mathematics
Explanation; hypotheses; theories
People
Peirce, Charles Sanders
Frege, Gottlob
Löwenheim, Leopold
Skolem, Thoralf Albert
Venn, John
Spinoza, Baruch
Time Periods
19th century
20th century, early
20th century
Places
United States
North America
Europe
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