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Philosophy's Loss of Logic to Mathematics

2018-07-12 Philosophy
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Release : 2018-07-12
Genre : Philosophy
Kind : eBook
Book Rating : 475/5 ( reviews)

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Book Synopsis Philosophy's Loss of Logic to Mathematics by : Woosuk Park

Download or read book Philosophy's Loss of Logic to Mathematics written by Woosuk Park. This book was released on 2018-07-12. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a historical explanation of important philosophical problems in logic and mathematics, which have been neglected by the official history of modern logic. It offers extensive information on Gottlob Frege’s logic, discussing which aspects of his logic can be considered truly innovative in its revolution against the Aristotelian logic. It presents the work of Hilbert and his associates and followers with the aim of understanding the revolutionary change in the axiomatic method. Moreover, it offers useful tools to understand Tarski’s and Gödel’s work, explaining why the problems they discussed are still unsolved. Finally, the book reports on some of the most influential positions in contemporary philosophy of mathematics, i.e., Maddy’s mathematical naturalism and Shapiro’s mathematical structuralism. Last but not least, the book introduces Biancani’s Aristotelian philosophy of mathematics as this is considered important to understand current philosophical issue in the applications of mathematics. One of the main purposes of the book is to stimulate readers to reconsider the Aristotelian position, which disappeared almost completely from the scene in logic and mathematics in the early twentieth century.

Mathematical Thought

2013-06-29 Science
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Release : 2013-06-29
Genre : Science
Kind : eBook
Book Rating : 072/5 ( reviews)

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Book Synopsis Mathematical Thought by : E.W. Beth

Download or read book Mathematical Thought written by E.W. Beth. This book was released on 2013-06-29. Available in PDF, EPUB and Kindle. Book excerpt: In contributing a foreword to this book I am complying with a wish my husband expressed a few days before his death. He had completed the manuscript of this work, which may be considered a companion volume to his book Formal Methods. The task of seeing it through the press was undertaken by Mr. J. J. A. Mooij, acting director of the Institute for Research in Foundations and the Philosophy of Science (Instituut voor Grondslagenonderzoek en Filoso:fie der Exacte Wetenschappen) of the University of Amsterdam, with the help of Mrs. E. M. Barth, lecturer at the Institute. I wish to thank Mr. Mooij and Mrs. Barth most cordially for the care with which they have acquitted themselves of this delicate task and for the speed with which they have brought it to completion. I also wish to express my gratitude to Miss L. E. Minning, M. A. , for the helpful advice she has so kindly given to Mr. Mooij and Mrs. Barth during the proof reading. C. P. C. BETH-PASTOOR VII PREFACE A few years ago Mr. Horace S.

The Philosophical Presuppositions of Mathematical Logic

1925 Logic, Symbolic and mathematical
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Release : 1925
Genre : Logic, Symbolic and mathematical
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Book Rating : /5 ( reviews)

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Book Synopsis The Philosophical Presuppositions of Mathematical Logic by : Harold Robert Smart

Download or read book The Philosophical Presuppositions of Mathematical Logic written by Harold Robert Smart. This book was released on 1925. Available in PDF, EPUB and Kindle. Book excerpt:

The Search for Certainty : A Philosophical Account of Foundations of Mathematics

2002-06-06
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Release : 2002-06-06
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Kind : eBook
Book Rating : 172/5 ( reviews)

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Book Synopsis The Search for Certainty : A Philosophical Account of Foundations of Mathematics by : Marcus Giaquinto

Download or read book The Search for Certainty : A Philosophical Account of Foundations of Mathematics written by Marcus Giaquinto. This book was released on 2002-06-06. Available in PDF, EPUB and Kindle. Book excerpt: The nineteenth century saw a movement to make higher mathematics rigorous. This seemed to be on the brink of success when it was thrown into confusion by the discovery of the class paradoxes. That initiated a period of intense research into the foundations of mathematics, and with it the birth of mathematical logic and a new, sharper debate in the philosophy of mathematics. The Search for Certainty examines this foundational endeavour from the discovery of the paradoxes to the present. Focusing on Russell's logicist programme and Hilbert's finitist programme, Giaquinto investigates how successful they were and how successful they could be. These questions are set in the context of a clear, non-technical exposition and assessment of the most important discoveries in mathematical logic, above all G--ouml--;del's underivability theorems. More than six decades after those discoveries, Giaquinto asks what our present perspective should be on the question of certainty in mathematics. Taking recent developments into account, he gives reasons for a surprisingly positive response.

New Directions in the Philosophy of Mathematics

1998-02 Mathematics
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Release : 1998-02
Genre : Mathematics
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Book Rating : 980/5 ( reviews)

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Book Synopsis New Directions in the Philosophy of Mathematics by : Thomas Tymoczko

Download or read book New Directions in the Philosophy of Mathematics written by Thomas Tymoczko. This book was released on 1998-02. Available in PDF, EPUB and Kindle. Book excerpt: The traditional debate among philosophers of mathematics is whether there is an external mathematical reality, something out there to be discovered, or whether mathematics is the product of the human mind. This provocative book, now available in a revised and expanded paperback edition, goes beyond foundationalist questions to offer what has been called a "postmodern" assessment of the philosophy of mathematics--one that addresses issues of theoretical importance in terms of mathematical experience. By bringing together essays of leading philosophers, mathematicians, logicians, and computer scientists, Thomas Tymoczko reveals an evolving effort to account for the nature of mathematics in relation to other human activities. These accounts include such topics as the history of mathematics as a field of study, predictions about how computers will influence the future organization of mathematics, and what processes a proof undergoes before it reaches publishable form. This expanded edition now contains essays by Penelope Maddy, Michael D. Resnik, and William P. Thurston that address the nature of mathematical proofs. The editor has provided a new afterword and a supplemental bibliography of recent work.

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