Items related to In the Light of Logic (Logic and Computation in Philosophy)
Synopsis
In this collection of essays written over a period of twenty years, Solomon Feferman explains advanced results in modern logic and employs them to cast light on significant problems in the foundations of mathematics. Most troubling among these is the revolutionary way in which Georg Cantor elaborated the nature of the infinite, and in doing so helped transform the face of twentieth-century mathematics. Feferman details the development of Cantorian concepts and the foundational difficulties they engendered. He argues that the freedom provided by Cantorian set theory was purchased at a heavy philosophical price, namely adherence to a form of mathematical platonism that is difficult to support.
Beginning with a previously unpublished lecture for a general audience, Deciding the Undecidable, Feferman examines the famous list of twenty-three mathematical problems posed by David Hilbert, concentrating on three problems that have most to do with logic. Other chapters are devoted to the work and thought of Kurt Gödel, whose stunning results in the 1930s on the incompleteness of formal systems and the consistency of Cantors continuum hypothesis have been of utmost importance to all subsequent work in logic. Though Gödel has been identified as the leading defender of set-theoretical platonism, surprisingly even he at one point regarded it as unacceptable.
In his concluding chapters, Feferman uses tools from the special part of logic called proof theory to explain how the vast part--if not all--of scientifically applicable mathematics can be justified on the basis of purely arithmetical principles. At least to that extent, the question raised in two of the essays of the volume, Is Cantor Necessary?, is answered with a resounding no.
This volume of important and influential work by one of the leading figures in logic and the foundations of mathematics is essential reading for anyone interested in these subjects.
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About the Author
Solomon Feferman is at Stanford University.
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In the Light of Logic
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In the Light of Logic (Logic and Computation in Philosophy)
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In the Light of Logic
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In the Light of Logic (Logic and Computation in Philosophy Series)
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In the Light of Logic (Logic and Computation in Philosophy)
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Hardcover. Condition: Very Good. Dust Jacket Condition: Very Good. 1st Edition. First printing. Signed and inscribed on the half title page by the author - a gift inscription to Charles D. Parsons, the late professor of Philosophy of Mathematics and Kant scholar from Harvard University, who was a friend of Feferman. The book is signed and dated by Parsons on the ffep. Parsons made scant markings throughout the text in pen - mostly just lines in the margins next to specific points in the text, but some short written notes as well. The DJ and book are in VG condition. DJ has some surface scratching, bumping at top/bottom of spine and corners; DJ has a 0.5 in rip on back-top corner, which is creasing back a bit; DJ has small chips and rips at corners; DJ flap corners creased back. Hardcover boards have some minor bumping on bottom edges, and light cornerwear. Hinges and binding tight. Other than Parsons' markings, text is bright and clean and clear. Inscribed by Author(s). Seller Inventory # ABE-1729627358239
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In the Light of Logic
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ISBN 13: 9780195080308
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