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Lectures on the Philosophy of Mathematics

Lectures on the Philosophy of Mathematics
  • Author : Joel David Hamkins
  • Publsiher : MIT Press
  • Release : 02 February 2021
  • ISBN : 0262362651
  • Pages : 352 pages
  • Rating : 4/5 from 21 ratings
GET THIS BOOKLectures 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.


Lectures on the Philosophy of Mathematics

Lectures on the Philosophy of Mathematics
  • Author : Joel David Hamkins
  • Publisher : MIT Press
  • Release : 02 February 2021
GET THIS BOOKLectures on the Philosophy of Mathematics

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,


Philosophy of Mathematics

Philosophy of Mathematics
  • Author : Paul Benacerraf,Hilary Putnam
  • Publisher : Cambridge University Press
  • Release : 27 January 1984
GET THIS BOOKPhilosophy of Mathematics

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


Philosophy of Mathematics

Philosophy of Mathematics
  • Author : Anonim
  • Publisher : Elsevier
  • Release : 08 July 2009
GET THIS BOOKPhilosophy of Mathematics

One of the most striking features of mathematics is the fact that we are much more certain about the mathematical knowledge we have than about what mathematical knowledge is knowledge of. Are numbers, sets, functions and groups physical entities of some kind? Are they objectively existing objects in some non-physical, mathematical realm? Are they ideas that are present only in the mind? Or do mathematical truths not involve referents of any kind? It is these kinds of questions that have


Kant’s Philosophy of Mathematics

Kant’s Philosophy of Mathematics
  • Author : C.J. Posy
  • Publisher : Springer Science & Business Media
  • Release : 09 March 2013
GET THIS BOOKKant’s Philosophy of Mathematics

Kant's views about mathematics were controversial in his own time, and they have inspired or infuriated thinkers ever since. Though specific Kantian doctrines fell into disrepute earlier in this century, the past twenty-five years have seen a surge of interest in and respect for Kant's philosophy of mathematics among both Kant scholars and philosophers of mathematics. The present volume includes the classic papers from the 1960s and 1970s which spared this renaissance of interest, together with updated postscripts by their


Philosophy of Mathematics and Economics

Philosophy of Mathematics and Economics
  • Author : Thomas A. Boylan,Paschal F. O'Gorman
  • Publisher : Routledge
  • Release : 09 April 2018
GET THIS BOOKPhilosophy of Mathematics and Economics

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


Philosophy of Mathematics

Philosophy of Mathematics
  • Author : James Robert Brown
  • Publisher : Routledge
  • Release : 09 August 2005
GET THIS BOOKPhilosophy of Mathematics

Philosophy of Mathematics is an excellent introductory text. This student friendly book discusses the great philosophers and the importance of mathematics to their thought. It includes the following topics: * the mathematical image * platonism * picture-proofs * applied mathematics * Hilbert and Godel * knots and nations * definitions * picture-proofs and Wittgenstein * computation, proof and conjecture. The book is ideal for courses on philosophy of mathematics and logic.


Philosophy of Mathematics

Philosophy of Mathematics
  • Author : Øystein Linnebo
  • Publisher : Princeton University Press
  • Release : 24 March 2020
GET THIS BOOKPhilosophy of Mathematics

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,


Introduction to Mathematical Philosophy

Introduction to Mathematical Philosophy
  • Author : Bertrand Russell
  • Publisher : Cosimo, Inc.
  • Release : 01 April 2007
GET THIS BOOKIntroduction to Mathematical Philosophy

Not to be confused with the philosophy of mathematics, mathematical philosophy is the structured set of rules that govern all existence. Or, in a word: logic. While this branch of philosophy threatens to be an intimidating and abstract subject, it is one that is surprisingly simple and necessarily sensible, particularly at the pen of writer Bertrand Russell, who infuses this work, first published in 1919, with a palpable and genuine desire to assist the reader in understanding the principles he illustrates.


An Introduction to the Philosophy of Mathematics

An Introduction to the Philosophy of Mathematics
  • Author : Mark Colyvan
  • Publisher : Cambridge University Press
  • Release : 14 June 2012
GET THIS BOOKAn Introduction to the Philosophy of Mathematics

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



Why Is There Philosophy of Mathematics At All?

Why Is There Philosophy of Mathematics At All?
  • Author : Ian Hacking
  • Publisher : Cambridge University Press
  • Release : 30 January 2014
GET THIS BOOKWhy Is There Philosophy of Mathematics At All?

This truly philosophical book takes us back to fundamentals - the sheer experience of proof, and the enigmatic relation of mathematics to nature. It asks unexpected questions, such as 'what makes mathematics mathematics?', 'where did proof come from and how did it evolve?', and 'how did the distinction between pure and applied mathematics come into being?' In a wide-ranging discussion that is both immersed in the past and unusually attuned to the competing philosophical ideas of contemporary


Thinking about Mathematics

Thinking about Mathematics
  • Author : Stewart Shapiro
  • Publisher : OUP Oxford
  • Release : 13 July 2000
GET THIS BOOKThinking about Mathematics

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.


Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century

Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century
  • Author : Paolo Mancosu
  • Publisher : Oxford University Press on Demand
  • Release : 08 March 1999
GET THIS BOOKPhilosophy of Mathematics and Mathematical Practice in the Seventeenth Century

The seventeenth century saw dramatic advances in mathematical theory and practice than any era before or since. With the recovery of many of the classical Greek mathematical texts, new techniques were introduced, and within 100 years, analytic geometry, the geometry of indivisibles, the arithmetic of infinites, and the calculus had been developed. Although many technical studies have been devoted to these innovations, Paolo Mancosu provides the first comprehensive account of the relationship between mathematical advances of the seventeenth century and the


The Philosophy of Mathematical Practice

The Philosophy of Mathematical Practice
  • Author : Paolo Mancosu
  • Publisher : Oxford University Press on Demand
  • Release : 19 June 2008
GET THIS BOOKThe Philosophy of Mathematical Practice

This book gives a coherent and unified presentation of a new direction of work in philosophy of mathematics. This new approach in philosophy of mathematics requires extensive attention to mathematical practice and provides philosophical analyses of important novel characteristics of contemporary (twentieth century) mathematics and of many aspects of mathematical activity-such as visualization, explanation, understanding etc.-- which escape purely formal logicaltreatment.The book consists of a lengthy introduction by the editor and of eight chapters written by some of


Kant's Philosophy of Mathematics: Volume 1, The Critical Philosophy and its Roots

Kant's Philosophy of Mathematics: Volume 1, The Critical Philosophy and its Roots
  • Author : Carl Posy,Ofra Rechter
  • Publisher : Cambridge University Press
  • Release : 31 January 2020
GET THIS BOOKKant's Philosophy of Mathematics: Volume 1, The Critical Philosophy and its Roots

The late 1960s saw the emergence of new philosophical interest in Kant's philosophy of mathematics, and since then this interest has developed into a major and dynamic field of study. In this state-of-the-art survey of contemporary scholarship on Kant's mathematical thinking, Carl Posy and Ofra Rechter gather leading authors who approach it from multiple perspectives, engaging with topics including geometry, arithmetic, logic, and metaphysics. Their essays offer fine-grained analysis of Kant's philosophy of mathematics in the context of his Critical