The Journal of Symbolic Logic: A Completeness Theorem in Modal Logic.

KRIPKE, Saul A.

$6,000.00

Item Number: 88076

New Haven, New Jersey: Association for Symbolic Logic, Inc, March 1959.

First edition of Volume 24 of The Journal of Symbolic which includes the first appearance of Kripke’s landmark paper, A Completeness Theorem in Modal Logic. Presentation copy, inscribed by Saul A. Kripke on the first page of his theorem, “For Thorild Dahlquist, Saul Kripke.” In this paper, Kripke both proves the formal completeness of modal logic (supplemented by first-order quantifiers and the sign of equality) and “create[s] a semantics, now called Kripke semantics” (Hurley, Logic: The Essentials, 217). “Of great importance is the paper “Semantical Analysis of Modal Logic I” where normal systems are treated. It is here that Kripke fully develops the analogy with the algebraic results of Jónsson and Tarski and proves completeness and decidability for propositional systems T, S4, S5, and B (the Brouwersche system), which is here introduced It is in this paper that two crucial generalizations of the model theory are introduced” (Stanford Encyclopedia of Philosophy). Octavo, original wrappers as issued. In near fine condition. Scarce, especially signed and inscribed.

American philosopher and logician Saul Kripke has made some of the most important and original contributions to the field of formal mathematical logic, particularly modal logic which extends classical logic to include modalities. Kripke wrote his first completeness theorem, A Completeness Theorem in Modal Logic at the age of 17, before graduating high school, and had it published a year later.