Author: Alfred North Whitehead
Publisher:
ISBN:
Category : Logic, Symbolic and mathematical
Languages : en
Pages : 688

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Author: Rebecca Goldstein
Publisher: W. W. Norton & Company
ISBN: 0393327604
Category : Biography & Autobiography
Languages : en
Pages : 299

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"An introduction to the life and thought of Kurt Gödel, who transformed our conception of math forever"--Provided by publisher.

Author: Agustin Rayo
Publisher: MIT Press
ISBN: 0262039419
Category : Mathematics
Languages : en
Pages : 321

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Book Description
An introduction to awe-inspiring ideas at the brink of paradox: infinities of different sizes, time travel, probability and measure theory, and computability theory. This book introduces the reader to awe-inspiring issues at the intersection of philosophy and mathematics. It explores ideas at the brink of paradox: infinities of different sizes, time travel, probability and measure theory, computability theory, the Grandfather Paradox, Newcomb's Problem, the Principle of Countable Additivity. The goal is to present some exceptionally beautiful ideas in enough detail to enable readers to understand the ideas themselves (rather than watered-down approximations), but without supplying so much detail that they abandon the effort. The philosophical content requires a mind attuned to subtlety; the most demanding of the mathematical ideas require familiarity with college-level mathematics or mathematical proof. The book covers Cantor's revolutionary thinking about infinity, which leads to the result that some infinities are bigger than others; time travel and free will, decision theory, probability, and the Banach-Tarski Theorem, which states that it is possible to decompose a ball into a finite number of pieces and reassemble the pieces so as to get two balls that are each the same size as the original. Its investigation of computability theory leads to a proof of Gödel's Incompleteness Theorem, which yields the amazing result that arithmetic is so complex that no computer could be programmed to output every arithmetical truth and no falsehood. Each chapter is followed by an appendix with answers to exercises. A list of recommended reading points readers to more advanced discussions. The book is based on a popular course (and MOOC) taught by the author at MIT.

Author: Luca Incurvati
Publisher: Cambridge University Press
ISBN: 1108497829
Category : History
Languages : en
Pages : 255

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Book Description
Presents a detailed and critical examination of the available conceptions of set and proposes a novel version.

Author: Bertrand Russell
Publisher: W. W. Norton & Company
ISBN: 9780393314045
Category : Mathematics
Languages : en
Pages : 580

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Book Description
Russell's classic The Principles of Mathematics sets forth his landmark thesis that mathematics and logic are identical--that what is commonly called mathematics is simply later deductions from logical premises.

Author: Godehard Link
Publisher: Walter de Gruyter
ISBN: 3110199688
Category : Mathematics
Languages : en
Pages : 673

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Book Description
The papers collected in this volume represent the main body of research arising from the International Munich Centenary Conference in 2001, which commemorated the discovery of the famous Russell Paradox a hundred years ago. The 31 contributions and the introductory essay by the editor were (with two exceptions) all originally written for the volume. The volume serves a twofold purpose, historical and systematic. One focus is on Bertrand Russell's logic and logical philosophy, taking into account the rich sources of the Russell Archives, many of which have become available only recently. The second equally important aim is to present original research in the broad range of foundational studies that draws on both current conceptions and recent technical advances in the above-mentioned fields. The volume contributes therefore, to the well-established body of mathematical philosophy initiated to a large extent by Russell's work.

Author: Charles Allan Green
Publisher:
ISBN:
Category : Logic, Symbolic and mathematical
Languages : en
Pages : 114

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Author: Margaret Cuonzo
Publisher: MIT Press
ISBN: 0262321408
Category : Philosophy
Languages : en
Pages : 240

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Book Description
An introduction to paradoxes showing that they are more than mere puzzles but can prompt new ways of thinking. Thinkers have been fascinated by paradox since long before Aristotle grappled with Zeno's. In this volume in The MIT Press Essential Knowledge series, Margaret Cuonzo explores paradoxes and the strategies used to solve them. She finds that paradoxes are more than mere puzzles but can prompt new ways of thinking. A paradox can be defined as a set of mutually inconsistent claims, each of which seems true. Paradoxes emerge not just in salons and ivory towers but in everyday life. (An Internet search for “paradox” brings forth a picture of an ashtray with a “no smoking” symbol inscribed on it.) Proposing solutions, Cuonzo writes, is a natural response to paradoxes. She invites us to rethink paradoxes by focusing on strategies for solving them, arguing that there is much to be learned from this, regardless of whether any of the more powerful paradoxes is even capable of solution. Cuonzo offers a catalog of paradox-solving strategies—including the Preemptive-Strike (questioning the paradox itself), the Odd-Guy-Out (calling one of the assumptions into question), and the You-Can't-Get-There-from-Here (denying the validity of the reasoning). She argues that certain types of solutions work better in some contexts than others, and that as paradoxicality increases, the success of certain strategies grows more unlikely. Cuonzo shows that the processes of paradox generation and solution proposal are interesting and important ones. Discovering a paradox leads to advances in knowledge: new science often stems from attempts to solve paradoxes, and the concepts used in the new sciences lead to new paradoxes. As Niels Bohr wrote, “How wonderful that we have met with a paradox. Now we have some hope of making progress.”

Author: Micheal D. Winterburn
Publisher: Troubador Publishing Ltd
ISBN: 1783060263
Category : Philosophy
Languages : en
Pages : 232

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Book Description
Far from merely recycling what we already know about certain paradoxes, this book breaks entirely new ground by providing what everyone really wants: solutions. The king of all paradoxes is the Liar ('This statement is false.' If it is true, it is false; if it is false, it is true), which in its earliest form is over two and a half thousand years old. Throughout all this time it has resisted every attempt to fully understand it. This work finally unlocks the secrets of the Liar, exposing principles, patterns and formulae that have long lain hidden. Several other important paradoxes also come under the logical searchlight and they too surrender their treasures. Though paradoxes are inherently difficult, this book approaches them in a clear and entertaining manner, using plain English. Secrets of the Paradox is written for the general reader, yet is sufficiently rigorous to satisfy the demands of the professional philosopher. If you relish an intellectual challenge, this book is for you!

Author: Russell Zelany Christensen
Publisher:
ISBN: 9780473206482
Category : Liar paradox
Languages : en
Pages : 186

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Book Description