platonism and anti platonism in mathematics

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Platonism And Anti Platonism In Mathematics

Author : Mark Balaguer
ISBN : 0195143981
Genre : Mathematics
File Size : 48. 21 MB
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In this book, Balaguer demonstrates that there are no good arguments for or against mathematical platonism. He establishes that both platonism and anti-platonism are defensible views and introduces a form of platonism ("full-blooded platonism") that solves all problems traditionally associated with the view, proceeding to defend anti-platonism (in particular, mathematical fictionalism) against various attacks--most notably the Quine-Putnam indispensability attack.

What Is Mathematics Really

Author : Reuben Hersh
ISBN : 0195130871
Genre : Mathematics
File Size : 87. 61 MB
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Reflecting an insider's view of mathematical life, the author argues that mathematics must be historically evolved, and intelligible only in a social context.

Platonism Naturalism And Mathematical Knowledge

Author : James Robert Brown
ISBN : 9781136580376
Genre : Philosophy
File Size : 44. 84 MB
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This study addresses a central theme in current philosophy: Platonism vs Naturalism and provides accounts of both approaches to mathematics, crucially discussing Quine, Maddy, Kitcher, Lakoff, Colyvan, and many others. Beginning with accounts of both approaches, Brown defends Platonism by arguing that only a Platonistic approach can account for concept acquisition in a number of special cases in the sciences. He also argues for a particular view of applied mathematics, a view that supports Platonism against Naturalist alternatives. Not only does this engaging book present the Platonist-Naturalist debate over mathematics in a comprehensive fashion, but it also sheds considerable light on non-mathematical aspects of a dispute that is central to contemporary philosophy.

An Aristotelian Realist Philosophy Of Mathematics

Author : J. Franklin
ISBN : 9781137400734
Genre : Mathematics
File Size : 69. 60 MB
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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.

Grundgesetze Der Arithmetik

Author : Gottlob Frege
ISBN : 3487098024
Genre : Mathematics
File Size : 38. 18 MB
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Truth In Mathematics

Author : Harold G. Dales
ISBN : 019851476X
Genre : Mathematics
File Size : 90. 17 MB
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The nature of truth in mathematics is a problem which has exercised the minds of thinkers from at least the time of the ancient Greeks. This book is an overview of the most recent work undertaken in this subject, and is unique in being the result of interactions between researchers from both philosophy and mathematics. The articles are written by world leaders in their respective fields and are of interest to researchers in both disciplines.

Philosophy Of Mathematics Oxford Bibliographies Online Research Guide

Author : Otavio Bueno
ISBN : 9780199810512
Genre :
File Size : 55. 73 MB
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This ebook is a selective guide designed to help scholars and students of social work find reliable sources of information by directing them to the best available scholarly materials in whatever form or format they appear from books, chapters, and journal articles to online archives, electronic data sets, and blogs. Written by a leading international authority on the subject, the ebook provides bibliographic information supported by direct recommendations about which sources to consult and editorial commentary to make it clear how the cited sources are interrelated related. This ebook is a static version of an article from Oxford Bibliographies Online: Philosophy, a dynamic, continuously updated, online resource designed to provide authoritative guidance through scholarship and other materials relevant to the study Philosophy. Oxford Bibliographies Online covers most subject disciplines within the social science and humanities, for more information visit www.oxfordbibligraphies.com.

Mathematik Empirische Wissenschaft Und Erkenntnistheorie

Author : Imre Lakatos
ISBN : 9783322910882
Genre : Science
File Size : 80. 79 MB
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Why Is There Philosophy Of Mathematics At All

Author : Ian Hacking
ISBN : 9781107729827
Genre : Science
File Size : 63. 40 MB
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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 mathematicians, it shows that proof and other forms of mathematical exploration continue to be living, evolving practices - responsive to new technologies, yet embedded in permanent (and astonishing) facts about human beings. It distinguishes several distinct types of application of mathematics, and shows how each leads to a different philosophical conundrum. Here is a remarkable body of new philosophical thinking about proofs, applications, and other mathematical activities.

Was Sind Und Was Sollen Die Zahlen

Author : Richard Dedekind
ISBN : 9783663027881
Genre : Mathematics
File Size : 25. 80 MB
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