Quine Mathematical Logic

QUINE, Willard Van Orman: A System of Logistic. Cambridge, MA Harvard University Press 1934 ; fester Einband / hard cover; 1. Ed.
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Quine's A System of Logic (1934) contributed significantly to the development of mathematical set theory. In 1936 he joined the Harvard faculty. His essay "New Foundations of Mathematical Logic" (1937) retained in principle Bertrand Russell's theory of types (a revision of set theory) but sought to avoid its complexities. Nevertheless, Quine's new theory had drawbacks. In Mathematical Logic (1940) he presented a superior system. His Set Theory and Its Logic (1963) traced relations between his own system of set theory and others. 1st Edition Hardcover 8vo - over 7¾ - 9¾" tall Book; 1st Edition

[SW: Mathematics, Logic]

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QUINE (W. V. O.): MATHEMATICAL LOGIC,

LOGIQUE-QUINE (W. V. O.).Mathematical logic.Cambridge, 1976, in-8°, cart. pl. toile ed., ss. jaq.

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[Quine, W.V.O.] Heijenoort, Jean van. El Desarrollo de la Teoria de la Cuantificacion. Universidad Nacional Autonoma de Mexico, 1976.
Jean Louis Maxime van Heijenoort (pronounced highenort) (July 23, 1912, Creil France - March 29, 1986, Mexico City) was a pioneer historian of mathematical logic. He was also a personal secretary to Leon Trotsky from 1932 to 1939, and from then until 1947, an American Trotskyist activist. Van Heijenoort came of age in straitened family circumstances because his Dutch immigrant father died when he was two. He nevertheless acquired a powerful traditional French formal education, to which his French writings attest. (He also published in Spanish.) Although he eventually became a naturalized American citizen, he visited France twice a year from 1958 until his death, and remained very attached to his French extended family and friends. After completing a Ph. D. in mathematics at New York University in 1949, he taught mathematics there but evolved into a logician and philosopher of mathematics, in good part because of the influence of Georg Kreisel. He began teaching philosophy, first part-time at Columbia University, then full-time at Brandeis University, 1965-77. He spent much of his last decade at Stanford University, writing and editing 8 books, including parts of the Collected Works of Kurt Gödel. The Source Book (van Heijenoort 1967), perhaps the most important book ever published on the history of logic and of the foundations of mathematics, is an anthology of translations. It begins with the first complete translation of Frege's 1879 Begriffsschrift, which is followed by 45 historically important short pieces on mathematical logic and axiomatic set theory, originally published between 1889 and 1931. The anthology ends with Gödel's landmark paper on the incompletability of Peano arithmetic. For more information on the period covered by this anthology, see Grattan-Guinness (2000). Nearly all the content of the Source Book was difficult to access in all but the best North American university libraries (e.g., even the Library of Congress did not acquire a copy of the Begriffsschrift until 1964), and all but four pieces had to be translated from one of six continental European languages. When possible, the author of the original text was asked to review the translation of his work, and suggest corrections and amendments. Each piece included editorial footnotes, all references were combined into one list, and many misprints, inconsistencies, and errors in the originals were corrected. Especially important are the remarkable introductions to each translation, most written by van Heijenoort himself. A few were written by Willard Quine and Burton Dreben. The Source Book did much to advance the view that modern logic begins with, and builds on, the Begriffsschrift. Grattan-Guinness (2000) argues that this perspective on the history of logic is mistaken, because Frege employed an idiosyncratic notation and was far less read than, say, Peano. Ironically, van Heijenoort (1967a) is oft-cited by those who prefer the alternative model theoretic stance on logic and mathematics. Much of the history of that stance, whose leading lights include George Boole, Charles Sanders Peirce, Ernst Schröder, Leopold Löwenheim, Thoralf Skolem, Alfred Tarski, and Jaakko Hintikka, is covered in Brady (2000). The Source Book deliberately scanted Peirce and Schröder, but devoted more pages to Skolem than to anyone other than Frege, and included Löwenheim (1915), the founding paper on model theory. Two of van Heijenoort's four wives each bore him a child. While living with Trotsky in Coyoacan, now a neighborhood of Mexico City, van Heijenoort's first wife left him after clashing with Trotsky's spouse. Van Heijenoort was also one of Frida Kahlo's lovers; in the film Frida, he is played by Felipe Fulop. Having parted company with Trotsky in 1939 for personal reasons, van Heijenoort was innocent of all circumstances leading to Trotsky's 1940 murder. Van Heijenoort himself was likewise murdered in Mexico City, 46 years later, by his estranged fourth spouse whom he was visiting at the time. She then took her own life. (Wikipedia)

8°. 56 pages. Original wrappers. Inscribed by Jean van Heijenoort to Willar Van Orman Quine: "To W.V.Quine - Cordially, J. van Heijenoort".

[SW: Association Copies, Association Copy, Inscribed, Logic, Logik, Pamphlets, Signed]

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[Quine, W.V.O.] Halmos, Paul R. Lectures on Boolean Algebras. Princeton, D.Van Nostrand Co., 1963.
Paul Richard Halmos (March 3, 1916 - October 2, 2006) was a Hungarian-born Jewish American mathematician who made fundamental advances in the areas of probability theory, statistics, operator theory, ergodic theory, functional analysis (in particular, Hilbert spaces), and mathematical logic. He was also recognized as a great mathematical expositor (Wikipedia).

8°. Small octavo, 147pp. First edition. Inscribed "To Van with thanks from Paul", to the cover, where the inscriber Halmos has wittily circled Quine's familiar name (Van) out of the publisher's name to incorporate it to the inscription. Some five pencil markings by Quine throughout, and an improvised paper bookmark on pp.24-25. Good, in publisher's printed wrappers.

[SW: Association Copies, Association Copy, Inscribed, Logic, Modern Thought, Rare Books, Signed]

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