Philosophy's Loss of Logic to Mathematics

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Publisher : Springer
ISBN 13 : 3319951475
Total Pages : 233 pages
Book Rating : 4.3/5 (199 download)

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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 and published by Springer. This book was released on 2018-07-12 with total page 233 pages. 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.

Introduction to Mathematical Philosophy

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Publisher :
ISBN 13 :
Total Pages : 224 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Introduction to Mathematical Philosophy by : Bertrand Russell

Download or read book Introduction to Mathematical Philosophy written by Bertrand Russell and published by . This book was released on 1920 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Principia Mathematica

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Publisher :
ISBN 13 :
Total Pages : 688 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Principia Mathematica by : Alfred North Whitehead

Download or read book Principia Mathematica written by Alfred North Whitehead and published by . This book was released on 1910 with total page 688 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Art of Logic in an Illogical World

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Publisher : Basic Books
ISBN 13 : 154167250X
Total Pages : 296 pages
Book Rating : 4.5/5 (416 download)

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Book Synopsis The Art of Logic in an Illogical World by : Eugenia Cheng

Download or read book The Art of Logic in an Illogical World written by Eugenia Cheng and published by Basic Books. This book was released on 2018-09-11 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: How both logical and emotional reasoning can help us live better in our post-truth world In a world where fake news stories change election outcomes, has rationality become futile? In The Art of Logic in an Illogical World, Eugenia Cheng throws a lifeline to readers drowning in the illogic of contemporary life. Cheng is a mathematician, so she knows how to make an airtight argument. But even for her, logic sometimes falls prey to emotion, which is why she still fears flying and eats more cookies than she should. If a mathematician can't be logical, what are we to do? In this book, Cheng reveals the inner workings and limitations of logic, and explains why alogic -- for example, emotion -- is vital to how we think and communicate. Cheng shows us how to use logic and alogic together to navigate a world awash in bigotry, mansplaining, and manipulative memes. Insightful, useful, and funny, this essential book is for anyone who wants to think more clearly.

The Origin of the Logic of Symbolic Mathematics

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Publisher : Indiana University Press
ISBN 13 : 0253005272
Total Pages : 593 pages
Book Rating : 4.2/5 (53 download)

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Book Synopsis The Origin of the Logic of Symbolic Mathematics by : Burt C. Hopkins

Download or read book The Origin of the Logic of Symbolic Mathematics written by Burt C. Hopkins and published by Indiana University Press. This book was released on 2011-09-07 with total page 593 pages. Available in PDF, EPUB and Kindle. Book excerpt: Burt C. Hopkins presents the first in-depth study of the work of Edmund Husserl and Jacob Klein on the philosophical foundations of the logic of modern symbolic mathematics. Accounts of the philosophical origins of formalized concepts—especially mathematical concepts and the process of mathematical abstraction that generates them—have been paramount to the development of phenomenology. Both Husserl and Klein independently concluded that it is impossible to separate the historical origin of the thought that generates the basic concepts of mathematics from their philosophical meanings. Hopkins explores how Husserl and Klein arrived at their conclusion and its philosophical implications for the modern project of formalizing all knowledge.

An Aristotelian Realist Philosophy of Mathematics

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Publisher : Springer
ISBN 13 : 1137400730
Total Pages : 316 pages
Book Rating : 4.1/5 (374 download)

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Book Synopsis An Aristotelian Realist Philosophy of Mathematics by : J. Franklin

Download or read book An Aristotelian Realist Philosophy of Mathematics written by J. Franklin and published by Springer. This book was released on 2014-04-09 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is as much a science of the real world as biology is. It is the science of the world's quantitative aspects (such as ratio) and structural or patterned aspects (such as symmetry). The book develops a complete philosophy of mathematics that contrasts with the usual Platonist and nominalist options.

Proofs and Refutations

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Publisher : Cambridge University Press
ISBN 13 : 9780521290388
Total Pages : 190 pages
Book Rating : 4.2/5 (93 download)

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Book Synopsis Proofs and Refutations by : Imre Lakatos

Download or read book Proofs and Refutations written by Imre Lakatos and published by Cambridge University Press. This book was released on 1976 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proofs and Refutations is for those interested in the methodology, philosophy and history of mathematics.

Morality and Mathematics

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Publisher : Oxford University Press
ISBN 13 : 0192556800
Total Pages : 208 pages
Book Rating : 4.1/5 (925 download)

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Book Synopsis Morality and Mathematics by : Justin Clarke-Doane

Download or read book Morality and Mathematics written by Justin Clarke-Doane and published by Oxford University Press. This book was released on 2020-03-12 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: To what extent are the subjects of our thoughts and talk real? This is the question of realism. In this book, Justin Clarke-Doane explores arguments for and against moral realism and mathematical realism, how they interact, and what they can tell us about areas of philosophical interest more generally. He argues that, contrary to widespread belief, our mathematical beliefs have no better claim to being self-evident or provable than our moral beliefs. Nor do our mathematical beliefs have better claim to being empirically justified than our moral beliefs. It is also incorrect that reflection on the genealogy of our moral beliefs establishes a lack of parity between the cases. In general, if one is a moral antirealist on the basis of epistemological considerations, then one ought to be a mathematical antirealist as well. And, yet, Clarke-Doane shows that moral realism and mathematical realism do not stand or fall together — and for a surprising reason. Moral questions, insofar as they are practical, are objective in a sense that mathematical questions are not, and the sense in which they are objective can only be explained by assuming practical anti-realism. One upshot of the discussion is that the concepts of realism and objectivity, which are widely identified, are actually in tension. Another is that the objective questions in the neighborhood of factual areas like logic, modality, grounding, and nature are practical questions too. Practical philosophy should, therefore, take center stage.

Mathematics: A Concise History and Philosophy

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Publisher : Springer Science & Business Media
ISBN 13 : 1461208750
Total Pages : 253 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Mathematics: A Concise History and Philosophy by : W.S. Anglin

Download or read book Mathematics: A Concise History and Philosophy written by W.S. Anglin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a concise introductory textbook for a one-semester (40-class) course in the history and philosophy of mathematics. It is written for mathemat ics majors, philosophy students, history of science students, and (future) secondary school mathematics teachers. The only prerequisite is a solid command of precalculus mathematics. On the one hand, this book is designed to help mathematics majors ac quire a philosophical and cultural understanding of their subject by means of doing actual mathematical problems from different eras. On the other hand, it is designed to help philosophy, history, and education students come to a deeper understanding of the mathematical side of culture by means of writing short essays. The way I myself teach the material, stu dents are given a choice between mathematical assignments, and more his torical or philosophical assignments. (Some sample assignments and tests are found in an appendix to this book. ) This book differs from standard textbooks in several ways. First, it is shorter, and thus more accessible to students who have trouble coping with vast amounts of reading. Second, there are many detailed explanations of the important mathematical procedures actually used by famous mathe maticians, giving more mathematically talented students a greater oppor tunity to learn the history and philosophy by way of problem solving.

The Autonomy of Mathematical Knowledge

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Publisher : Cambridge University Press
ISBN 13 : 0521514371
Total Pages : 229 pages
Book Rating : 4.5/5 (215 download)

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Book Synopsis The Autonomy of Mathematical Knowledge by : Curtis Franks

Download or read book The Autonomy of Mathematical Knowledge written by Curtis Franks and published by Cambridge University Press. This book was released on 2009-10-08 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: This study reconstructs, analyses and re-evaluates the programme of influential mathematical thinker David Hilbert, presenting it in a different light.

Thinking about Mathematics

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Publisher : OUP Oxford
ISBN 13 : 0192893068
Total Pages : 323 pages
Book Rating : 4.1/5 (928 download)

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Book Synopsis Thinking about Mathematics by : Stewart Shapiro

Download or read book Thinking about Mathematics written by Stewart Shapiro and published by OUP Oxford. This book was released on 2000-07-13 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thinking about Mathematics covers the range of philosophical issues and positions concerning mathematics. The text describes the questions about mathematics that motivated philosophers throughout history and covers historical figures such as Plato, Aristotle, Kant, and Mill. It also presents the major positions and arguments concerning mathematics throughout the twentieth century, bringing the reader up to the present positions and battle lines.

The Principles of Mathematics

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Publisher :
ISBN 13 :
Total Pages : 565 pages
Book Rating : 4.L/5 ( download)

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Book Synopsis The Principles of Mathematics by : Bertrand Russell

Download or read book The Principles of Mathematics written by Bertrand Russell and published by . This book was released on 1903 with total page 565 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Philosophy of Logic

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Publisher : Elsevier
ISBN 13 : 008046663X
Total Pages : 1219 pages
Book Rating : 4.0/5 (84 download)

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Book Synopsis Philosophy of Logic by :

Download or read book Philosophy of Logic written by and published by Elsevier. This book was released on 2006-11-29 with total page 1219 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers presented in this volume examine topics of central interest in contemporary philosophy of logic. They include reflections on the nature of logic and its relevance for philosophy today, and explore in depth developments in informal logic and the relation of informal to symbolic logic, mathematical metatheory and the limiting metatheorems, modal logic, many-valued logic, relevance and paraconsistent logic, free logics, extensional v. intensional logics, the logic of fiction, epistemic logic, formal logical and semantic paradoxes, the concept of truth, the formal theory of entailment, objectual and substitutional interpretation of the quantifiers, infinity and domain constraints, the Löwenheim-Skolem theorem and Skolem paradox, vagueness, modal realism v. actualism, counterfactuals and the logic of causation, applications of logic and mathematics to the physical sciences, logically possible worlds and counterpart semantics, and the legacy of Hilbert's program and logicism. The handbook is meant to be both a compendium of new work in symbolic logic and an authoritative resource for students and researchers, a book to be consulted for specific information about recent developments in logic and to be read with pleasure for its technical acumen and philosophical insights.- Written by leading logicians and philosophers- Comprehensive authoritative coverage of all major areas of contemporary research in symbolic logic- Clear, in-depth expositions of technical detail- Progressive organization from general considerations to informal to symbolic logic to nonclassical logics- Presents current work in symbolic logic within a unified framework- Accessible to students, engaging for experts and professionals- Insightful philosophical discussions of all aspects of logic- Useful bibliographies in every chapter

Is God a Mathematician?

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Publisher : Simon and Schuster
ISBN 13 : 1416594434
Total Pages : 320 pages
Book Rating : 4.4/5 (165 download)

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Book Synopsis Is God a Mathematician? by : Mario Livio

Download or read book Is God a Mathematician? written by Mario Livio and published by Simon and Schuster. This book was released on 2011-02-22 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bestselling author and astrophysicist Mario Livio examines the lives and theories of history’s greatest mathematicians to ask how—if mathematics is an abstract construction of the human mind—it can so perfectly explain the physical world. Nobel Laureate Eugene Wigner once wondered about “the unreasonable effectiveness of mathematics” in the formulation of the laws of nature. Is God a Mathematician? investigates why mathematics is as powerful as it is. From ancient times to the present, scientists and philosophers have marveled at how such a seemingly abstract discipline could so perfectly explain the natural world. More than that—mathematics has often made predictions, for example, about subatomic particles or cosmic phenomena that were unknown at the time, but later were proven to be true. Is mathematics ultimately invented or discovered? If, as Einstein insisted, mathematics is “a product of human thought that is independent of experience,” how can it so accurately describe and even predict the world around us? Physicist and author Mario Livio brilliantly explores mathematical ideas from Pythagoras to the present day as he shows us how intriguing questions and ingenious answers have led to ever deeper insights into our world. This fascinating book will interest anyone curious about the human mind, the scientific world, and the relationship between them.

The Oxford Handbook of Philosophy of Mathematics and Logic

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Publisher : OUP USA
ISBN 13 : 0195148770
Total Pages : 850 pages
Book Rating : 4.1/5 (951 download)

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Book Synopsis The Oxford Handbook of Philosophy of Mathematics and Logic by : Stewart Shapiro

Download or read book The Oxford Handbook of Philosophy of Mathematics and Logic written by Stewart Shapiro and published by OUP USA. This book was released on 2005-02-10 with total page 850 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covers the state of the art in the philosophy of maths and logic, giving the reader an overview of the major problems, positions, and battle lines. The chapters in this book contain both exposition and criticism as well as substantial development of their own positions. It also includes a bibliography.

The Mystery of the Aleph

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Publisher : Simon and Schuster
ISBN 13 : 0743422996
Total Pages : 278 pages
Book Rating : 4.7/5 (434 download)

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Book Synopsis The Mystery of the Aleph by : Amir D. Aczel

Download or read book The Mystery of the Aleph written by Amir D. Aczel and published by Simon and Schuster. This book was released on 2001-08-28 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: A compelling narrative that blends the story of infinity with the tragic tale of a tormented and brilliant mathematician.

Mathematics Through the Eyes of Faith

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Publisher : Harper Collins
ISBN 13 : 0062094912
Total Pages : 290 pages
Book Rating : 4.0/5 (62 download)

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Book Synopsis Mathematics Through the Eyes of Faith by : Russell Howell

Download or read book Mathematics Through the Eyes of Faith written by Russell Howell and published by Harper Collins. This book was released on with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Book description to come.