Atticus Rare Books

A Completeness Theorem in Modal Logic (pp. 1-14) WITH Abstracts of Distinguished Constituents (pp. 323) Semantical Analysis of Modal Logic (pp. 323-324) WITH The Problem of Entailment (p. 324) in The Journal of Symbolic Logic Vol. 24, Issues Number 1-4, 1959 [BOUND FULL VOLUME SEMINAL PAPER MODAL LOGIC]

Kripke, Saul A.

Princeton: Association for Symbolic Logic, 1959. 1st Edition. FULL VOLUME, BOUND FIRST EDITION OF SAUL KRIPKE’S SEMINAL FIRST PAPER ON MODAL LOGIC, “A Completeness Theorem in Modal Logic”. The paper presents Kripke’s important ideas on the semantics of modal logic, or the logic of modal notions like necessity and possibility. Included are all 4 journal issues for 1959, one of which is inclusive of abstracts of 3 other papers Kripke sent to the Journal. 

Kripke was “universally hailed” for “A Completeness Theorem in Modal Logic” (this paper) In it, he 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 217). Kripke semantics “is a formals semantics for non-classical logic systems… first conceived for modal logics, and later adapted to intuitionistic logic and other non-classical systems. The discovery of Kripke semantics was a breakthrough in the theory of non-classical logics, because the model theory of such logics was almost non-existent before Kripke” (Wikipedia). 

As the story goes, in 1959 and at the age of seventeen, Kripke wrote his completeness theorem in modal logic at age 17; he mailed the paper to the journal and it was sent out for comments, to, among a number of others, the head of the Mathematics at Harvard. This person then wrote Kripke urging him to apply for a job at Harvard. The reply he received read: "My mother said that I should finish high school and go to college first” (ibid). 

Kripke’s initial intuitive idea was that a proposition is necessary if and only if it is true in all possible worlds. Kripke’s paper begins: “The present paper attempts to state and prove a completeness theorem for the system S5, supplemented by first-order quantifiers and the sign of equality” (Kripke, JSL, 24,1, 1959, 1). He then notes: ““The basis of the informal analysis which motivated these definitions is that a proposition is necessary if and only if it is true in all “possible worlds”. (It is not necessary for our present purposes to analyze the concept of a “possible world” any further.) ... In modal logic, however, we wish to know not only about the 6 real world but about other conceivable worlds” (ibid). 

Shortly, Kripke then wrote “In trying to construct a definition of universal logical validity, it seems plausible to assume not only that the universe of discourse may contain an arbitrary number of elements and that predicates may be assigned any given interpretations in the actual world, but also that any combination of possible worlds may be associated with the real world with respect to some group of predicates. In other words, it is plausible to assume that no further restrictions need be placed on D, G, and K, except the standard one that D be non-empty. This assumption leads directly to our definition of universal validity.” (ibid).

The December issue of the journal is also bound in; it contains abstracts of the other Kripke papers received the Journal in 1959: “Distinguished Constituents”, “Semantical Analysis of Modal Logic”, “The Problem of Entailment”. Also included are the two other issues of The Journal of Symbolic Logic from 1959, this to make a complete set. We separately offer Issue No. 4 alone.

Saul Kripke (1940- ) is an American philosopher and logician who was awarded the Rolf Schock Prize in Logic and Philosophy in 2001. He is best known for five major contributions to philosophy beginning with this paper, the starting point for Kripke Semantics. In 1962 Kripke graduated from Harvard University… Now associated with Princeton, additional areas of note include his contributions to set theory, his theory of truth and his interpretation of Wittgenstein's work. Item #962

CONDITION & DETAILS: Princeton: Association for Symbolic Logic, 1959. 4to. 9.75 x 7 inches. Light institutional stamps on text block and one small stamp at the foot of the front pastedown. Tightly bound in black cloth, gilt-lettered at the spine. Bright and clean inside and out. Near fine condition.

Price: $700.00