Philosophy Of Mathematics Selected Readings Pdf

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.

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Contents

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Contents

Select Frontmatter

• Frontmatter

  pp i-iv

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Select Contents

• Contents

  pp v-vi

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Select Preface to the second edition

• Preface to the second edition

  pp vii-viii

• • By Paul Benacerraf, Princeton, N.J., and Cambridge, Mass, Hilary Putnam, Princeton, N.J., and Cambridge, Mass
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Select Introduction

• Introduction

  pp 1-38

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Select Symposium on the foundations of mathematics

• Symposium on the foundations of mathematics

  pp 41-65

• • By Rudolf Carnap, Arend Heyting, Johann von Neumann
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Select Disputation

• Disputation

  pp 66-76

• • By Arend Heyting
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Select Intuitionism and formalism

• Intuitionism and formalism

  pp 77-89

• • By L. E. J. Brouwer
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Select Consciousness, philosophy, and mathematics

• Consciousness, philosophy, and mathematics

  pp 90-96

• • By L. E. J. Brouwer
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Select The concept of number

• The concept of number

  pp 130-159

• • By Gottlob Frege
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Select On the infinite

• On the infinite

  pp 183-201

• • By David Hilbert
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Select Hilbert's programme

• Hilbert's programme

  pp 207-238

• • By Georg Kreisel
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Select Empiricism, semantics, and ontology

• Empiricism, semantics, and ontology

  pp 241-257

• • By Rudolf Carnap
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Select On platonism in mathematics

• On platonism in mathematics

  pp 258-271

• • By Paul Bernays
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Select What numbers could not be

• What numbers could not be

  pp 272-294

• • By Paul Benacerraf
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Select Mathematics without foundations

• Mathematics without foundations

  pp 295-312

• • By Hilary Putnam
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Select The <span class='italic'>a priori</span>

• The a priori

  pp 315-328

• • By Alfred Jules Ayer
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Select Truth by convention

• Truth by convention

  pp 329-354

• • By W. V. Quine
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Select Carnap and logical truth

• Carnap and logical truth

  pp 355-376

• • By W. V. Quine
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Select On the nature of mathematical truth

• On the nature of mathematical truth

  pp 377-393

• • By Carl G. Hempel
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Select On the nature of mathematical reasoning

• On the nature of mathematical reasoning

  pp 394-402

• • By Henri Poincare
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Select Mathematical truth

• Mathematical truth

  pp 403-420

• • By Paul Benacerraf
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Select Models and reality

• Models and reality

  pp 421-444

• • By Hilary Putnam
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Select Part IV - The concept of set

• Part IV - The concept of set

  pp 445-446

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Select Russell's mathematical logic

• Russell's mathematical logic

  pp 447-469

• • By Kurt Gödel
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Philosophy Of Mathematics Selected Readings Pdf

Source: https://www.cambridge.org/core/books/philosophy-of-mathematics/F66E3934FD4B3854DA08FB39E2DD967D

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