An Introduction to the Philosophy of Mathematics Book

An Introduction to the Philosophy of Mathematics


  • Author : Mark Colyvan
  • Publisher : Cambridge University Press
  • Release Date : 2012-06-14
  • Genre: Mathematics
  • Pages : 188
  • ISBN 10 : 9780521826020
  • Total Read : 82
  • File Size : 9,7 Mb

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An Introduction to the Philosophy of Mathematics Summary:

This introduction to the philosophy of mathematics focuses on contemporary debates in an important and central area of philosophy. The reader is taken on a fascinating and entertaining journey through some intriguing mathematical and philosophical territory, including such topics as the realism/anti-realism debate in mathematics, mathematical explanation, the limits of mathematics, the significance of mathematical notation, inconsistent mathematics and the applications of mathematics. Each chapter has a number of discussion questions and recommended further reading from both the contemporary literature and older sources. Very little mathematical background is assumed and all of the mathematics encountered is clearly introduced and explained using a wide variety of examples. The book is suitable for an undergraduate course in philosophy of mathematics and, more widely, for anyone interested in philosophy and mathematics.

Philosophy of Mathematics Book

Philosophy of Mathematics


  • Author : Øystein Linnebo
  • Publisher : Princeton University Press
  • Release Date : 2020-03-24
  • Genre: Mathematics
  • Pages : 216
  • ISBN 10 : 9780691202297
  • Total Read : 96
  • File Size : 18,9 Mb

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Philosophy of Mathematics Summary:

A sophisticated, original introduction to the philosophy of mathematics from one of its leading thinkers Mathematics is a model of precision and objectivity, but it appears distinct from the empirical sciences because it seems to deliver nonexperiential knowledge of a nonphysical reality of numbers, sets, and functions. How can these two aspects of mathematics be reconciled? This concise book provides a systematic, accessible introduction to the field that is trying to answer that question: the philosophy of mathematics. Øystein Linnebo, one of the world's leading scholars on the subject, introduces all of the classical approaches to the field as well as more specialized issues, including mathematical intuition, potential infinity, and the search for new mathematical axioms. Sophisticated but clear and approachable, this is an essential book for all students and teachers of philosophy and of mathematics.

Lectures on the Philosophy of Mathematics Book
Score: 5
From 1 Ratings

Lectures on the Philosophy of Mathematics


  • Author : Joel David Hamkins
  • Publisher : MIT Press
  • Release Date : 2021-03-09
  • Genre: Mathematics
  • Pages : 352
  • ISBN 10 : 9780262542234
  • Total Read : 66
  • File Size : 20,6 Mb

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Lectures on the Philosophy of Mathematics Summary:

An introduction to the philosophy of mathematics grounded in mathematics and motivated by mathematical inquiry and practice. In this book, Joel David Hamkins offers an introduction to the philosophy of mathematics that is grounded in mathematics and motivated by mathematical inquiry and practice. He treats philosophical issues as they arise organically in mathematics, discussing such topics as platonism, realism, logicism, structuralism, formalism, infinity, and intuitionism in mathematical contexts. He organizes the book by mathematical themes--numbers, rigor, geometry, proof, computability, incompleteness, and set theory--that give rise again and again to philosophical considerations.

Philosophy of Mathematics Book

Philosophy of Mathematics


  • Author : Paul Benacerraf
  • Publisher : Cambridge University Press
  • Release Date : 1984-01-27
  • Genre: Science
  • Pages : null
  • ISBN 10 : 9781107268135
  • Total Read : 73
  • File Size : 13,9 Mb

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Philosophy of Mathematics Summary:

The twentieth century has witnessed an unprecedented 'crisis in the foundations of mathematics', featuring a world-famous paradox (Russell's Paradox), a challenge to 'classical' mathematics from a world-famous mathematician (the 'mathematical intuitionism' of Brouwer), a new foundational school (Hilbert's Formalism), and the profound incompleteness results of Kurt Gödel. In the same period, the cross-fertilization of mathematics and philosophy resulted in a new sort of 'mathematical philosophy', associated most notably (but in different ways) with Bertrand Russell, W. V. Quine, and Gödel himself, and which remains at the focus of Anglo-Saxon philosophical discussion. The present collection brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers. It is a substantially revised version of the edition first published in 1964 and includes a revised bibliography. The volume will be welcomed as a major work of reference at this level in the field.

Philosophy of Mathematics Book

Philosophy of Mathematics


  • Author : Ahmet Cevik
  • Publisher : CRC Press
  • Release Date : 2021-11-09
  • Genre: Mathematics
  • Pages : 352
  • ISBN 10 : 9781000468809
  • Total Read : 74
  • File Size : 9,8 Mb

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Philosophy of Mathematics Summary:

The philosophy of mathematics is an exciting subject. Philosophy of Mathematics: Classic and Contemporary Studies explores the foundations of mathematical thought. The aim of this book is to encourage young mathematicians to think about the philosophical issues behind fundamental concepts and about different views on mathematical objects and mathematical knowledge. With this new approach, the author rekindles an interest in philosophical subjects surrounding the foundations of mathematics. He offers the mathematical motivations behind the topics under debate. He introduces various philosophical positions ranging from the classic views to more contemporary ones, including subjects which are more engaged with mathematical logic. Most books on philosophy of mathematics have little to no focus on the effects of philosophical views on mathematical practice, and no concern on giving crucial mathematical results and their philosophical relevance, consequences, reasons, etc. This book fills this gap. The book can be used as a textbook for a one-semester or even one-year course on philosophy of mathematics. "Other textbooks on the philosophy of mathematics are aimed at philosophers. This book is aimed at mathematicians. Since the author is a mathematician, it is a valuable addition to the literature." - Mark Balaguer, California State University, Los Angeles "There are not many such texts available for mathematics students. I applaud efforts to foster the dialogue between mathematics and philosophy." - Michele Friend, George Washington University and CNRS, Lille, France

Philosophy of Mathematics and Economics Book

Philosophy of Mathematics and Economics


  • Author : Thomas A. Boylan
  • Publisher : Routledge
  • Release Date : 2018-04-09
  • Genre: Business & Economics
  • Pages : 242
  • ISBN 10 : 9781351124546
  • Total Read : 86
  • File Size : 12,7 Mb

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Philosophy of Mathematics and Economics Summary:

With the failure of economics to predict the recent economic crisis, the image of economics as a rigorous mathematical science has been subjected to increasing interrogation. One explanation for this failure is that the subject took a wrong turn in its historical trajectory, becoming too mathematical. Using the philosophy of mathematics, this unique book re-examines this trajectory. Philosophy of Mathematics and Economics re-analyses the divergent rationales for mathematical economics by some of its principal architects. Yet, it is not limited to simply enhancing our understanding of how economics became an applied mathematical science. The authors also critically evaluate developments in the philosophy of mathematics to expose the inadequacy of aspects of mainstream mathematical economics, as well as exploiting the same philosophy to suggest alternative ways of rigorously formulating economic theory for our digital age. This book represents an innovative attempt to more fully understand the complexity of the interaction between developments in the philosophy of mathematics and the process of formalisation in economics. Assuming no expert knowledge in the philosophy of mathematics, this work is relevant to historians of economic thought and professional philosophers of economics. In addition, it will be of great interest to those who wish to deepen their appreciation of the economic contours of contemporary society. It is also hoped that mathematical economists will find this work informative and engaging.

Philosophy of Mathematics Book
Score: 4.5
From 3 Ratings

Philosophy of Mathematics


  • Author : James Robert Brown
  • Publisher : Psychology Press
  • Release Date : 1999
  • Genre: Science
  • Pages : 215
  • ISBN 10 : 9780415122757
  • Total Read : 92
  • File Size : 9,7 Mb

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Philosophy of Mathematics Summary:

Philosophy of Mathematicsis clear and engaging, and student friendly The book discusses the great philosophers and the importance of mathematics to their thought. Among topics discussed in the book are the mathematical image, platonism, picture-proofs, applied mathematics, Hilbert and Godel, knots and notation definitions, picture-proofs and Wittgenstein, computation, proof and conjecture.

Philosophy of Mathematics Book

Philosophy of Mathematics


  • Author : David Bostock
  • Publisher : John Wiley & Sons
  • Release Date : 2009-03-09
  • Genre: Mathematics
  • Pages : 332
  • ISBN 10 : 9781405189927
  • Total Read : 95
  • File Size : 6,8 Mb

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Philosophy of Mathematics Summary:

Philosophy of Mathematics: An Introduction provides a critical analysis of the major philosophical issues and viewpoints in the concepts and methods of mathematics - from antiquity to the modern era. Offers beginning readers a critical appraisal of philosophical viewpoints throughout history Gives a separate chapter to predicativism, which is often (but wrongly) treated as if it were a part of logicism Provides readers with a non-partisan discussion until the final chapter, which gives the author?s personal opinion on where the truth lies Designed to be accessible to both undergraduates and graduate students, and at the same time to be of interest to professionals