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A Completeness Theorem in Modal Logic. [In: The Journal of Symbolic Logic. Edited by Alonza Church, Leon Henkin, S.C. Kleene, Alice A. Lezerowitz & Alfons Borgers. Volume 24, Number 1, March 1959].


(No place), The Association for Symbolic Logic, 1959. 8vo. Orig. printed wrappers. An excellent copy in near mint condition, in- as well as externally. Pp. (1) - 14. (The entire volume: 96 pp.). ¶ The seminal first printing of Kripke's debut article, which provided the basis for his logic and for the model theory for modal logic in general. The work constitutes the very beginning of Kripke Semantics (often called possible world semantics).

Kripke's works in general are rare in fist editions. Many of them remain unpublished and are only known in privately circulated manuscripts.

The American philosopher Saul A. Kripke (born 1940) is an exceedingly important logician and philosopher of language and one of the most powerful and influential thinkers of analytic and Anglo-American philosophy. He is considered the greatest living philosopher and perhaps the greatest since Wittgenstein. In 2001 he was awarded the Schock Prize in Logic and Philosophy, which is considered the philosopical equivalent of the Nobel Prize.

Kripke, who grew up in Omaha in a religious Jewish family, was somewhat of a prodigy child. During grammar school he got intimately acquainted with and mastered to perfection algebra, geometry and calculus, and very early on he took up philosophy, which later became his career. Still a teenager, in high school, he wrote a work that was to change the face of philosophical logic forever, namely the groundbreaking paper "A Completeness Theorem for Modal Logic", which was printed a few years later, in 1959, in the Journal of Symbolic Logic, while he was in his first year at Harvard University. This seminal debut work proposed what later came to be known as Kripke models for modal logic. The story goes that the paper earned a letter from the department of mathematics urging Kripke to apply for a job there, to which he is said to have written an answer explaining "My mother said that I should finish high school and go to college first."

In 1962 he graduated from Harvard University, where he remained until 1968, first as a member of the Harvard Society of Fellows and then as a lecturer. During these years he developed the logical theories founded in the "Completeness Theorem" further and made seminal contributions to the field of logic and semantics.

Kripke Semantics is a formal semantics for non-classical logic systems that Kripke began developing in his teenage years, first published something on in 1959 (the present work) and further developed in the 60'ies and. The development of Kripke Semantics was no less than a breakthrough in the making of non-classical logics, of which no model theory existed before Kripke's.
With this work, Kripke laid the foundation for proving completeness theorems for modal logic, and for identifying the weakest normal modal logic, which is now named K after him.

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