Peirce's Truth-functiona Analysis and the Origin of Truth Tables

TL;DR

This paper investigates Charles Peirce's early work on truth tables, revealing historical developments and unpublished manuscripts that contributed to the foundation of truth-functional analysis in logic.

Contribution

It uncovers previously unknown manuscripts by Peirce from 1883-1893 that contain early truth table matrices, linking his work to later developments in logic.

Findings

Peirce's 1893 manuscript includes a truth table for implication.

Unpublished 1883-84 manuscript contains an indirect truth table for the conditional.

Historical evidence connects Peirce's work to Russell and Wittgenstein's matrices.

Abstract

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 It is shown that an unpublished manuscript identified as composed by Peirce in 1893 includes a truth table matrix that is equivalent to the matrix for material implication discovered by John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 An unpublished manuscript by Peirce identified as having been composed in 1883-84 in connection with the composition of Peirce's "On the Algebra of Logic: A Contribution to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.