## “A Completeness Theorem in Modal Logic” WITH Abstracts of “Distinguished Constituents”, “Semantical Analysis of Modal Logic”, “The Problem of Entailment” in The Journal of Symbolic Logic Vol. 24, Issue No. 1, March 1959 pp. 1-14 WITH Vol. 24, Issue No. 4, Dec. 1959 pp. 323-324

Princeton: Association for Symbolic Logic, 1959. 1st Edition. FIRST EDITION, FIRST IMPRESSION IN PRISTINE ORIGINAL WRAPS 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.

“Universally hailed” for this work, 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). 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 (algebraic semantics existed, but were considered 'syntax in disguise'). (Wikipedia).

Saul Kripke grew up in Omaha, Nebraska, and in 1959, he mailed this paper to The Journal of Symbolic Logic. As the story goes, the Kripke wrote his completeness theorem in modal logic at age 17; the paper was sent out for comments, to, among a number of others, the head of the Harvard mathematics department. 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. In this paper, Kripke begins by stating: “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” (Kripke, 2)

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.” (Kripke, 3).

The December issue of the Journal is also included as it contains abstracts of other Kripke papers received by the Journal in 1959: “Distinguished Constituents”, “Semantical Analysis of Modal Logic”, “The Problem of Entailment”. Also included are the three other issues of The Journal of Symbolic Logic from 1959, this to make a complete set. All four issues are in near fine condition.

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, where he remained until 1968, first as a member of the Harvard Society of Fellows and then as a lecturer. Subsequently, his 1970 lectures "Naming and Necessity" was a focal point for restructuring the philosophy of language. 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 #731

CONDITION & DETAILS: Four first edition, first impression issues in original wraps. New Jersey: The Association for Symbolic Logic. Octavo. 10 x 7 inches; 250 x 150mm. All four issues are in near fine condition both inside and out.

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Price:
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