What Is Mathematics, Really?

What Is Mathematics, Really?

by Reuben Hersh
     
 

ISBN-10: 0195130871

ISBN-13: 9780195130874

Pub. Date: 07/28/1999

Publisher: Oxford University Press, USA


Most philosophers of mathematics treat it as isolated, timeless, ahistorical, inhuman. Reuben Hersh argues the contrary, that mathematics must be understood as a human activity, a social phenomenon, part of human culture, historically evolved, and intelligible only in a social context. Hersh pulls the screen back to reveal mathematics as seen by professionals,

Overview


Most philosophers of mathematics treat it as isolated, timeless, ahistorical, inhuman. Reuben Hersh argues the contrary, that mathematics must be understood as a human activity, a social phenomenon, part of human culture, historically evolved, and intelligible only in a social context. Hersh pulls the screen back to reveal mathematics as seen by professionals, debunking many mathematical myths, and demonstrating how the "humanist" idea of the nature of mathematics more closely resembles how mathematicians actually work. At the heart of his book is a fascinating historical account of the mainstream of philosophy--ranging from Pythagoras, Descartes, and Spinoza, to Bertrand Russell, David Hilbert, and Rudolph Carnap--followed by the mavericks who saw mathematics as a human artifact, including Aristotle, Locke, Hume, Mill, and Lakatos.
What is Mathematics, Really? reflects an insider's view of mathematical life, and will be hotly debated by anyone with an interest in mathematics or the philosophy of science.

Product Details

ISBN-13:
9780195130874
Publisher:
Oxford University Press, USA
Publication date:
07/28/1999
Edition description:
New Edition
Pages:
368
Product dimensions:
9.00(w) x 6.10(h) x 1.10(d)
Lexile:
1090L (what's this?)

Table of Contents

Preface: Aims and Goals Outline of Part One. The deplorable state of philosophy of mathematics. A parallel between the Kuhn-Popper revolution in philosophy of science and the present situation in philosophy of mathematics. Relevance for mathematics education. xi(6)
Acknowledgments xvii(4)
Dialogue with Laura xxi
Part One 3(88)
1 Survey and Proposals Philosophy of mathematics is introduced by an exercise on the fourth dimension. Then comes a quick survey of modern mathematics, and a presentation of the prevalent philosophy--Platonism. Finally, a radically different view-- humanism.
3(21)
2 Criteria for a Philosophy of Mathematics What should we require of a philosophy of mathematics? Some standard criteria aren't essential. Some neglected ones are essential.
24(11)
3 Myths/Mistakes/Misunderstandings Anecdotes from mathematical life show that humanism is true to life.
35(13)
4 Intuition/Proof/Certainty All are subjects of long controversy. Humanism shows them in a new light.
48(24)
5 Five Classical Puzzles Is mathematics created or discovered? What is a mathematical object? Object versus process. What is mathematical existence? Does the infinite exist?
72(19)
Part Two 91(144)
6 Mainstream Before the Crisis From Pythagoras to Descartes, philosophy of mathematics is a mainstay of religion.
91(28)
7 Mainstream Philosophy at Its Peak From Spinoza to Kant, philosophy of mathematics and religion supply mutual aid.
119(18)
8 Mainstream Since the Crisis A crisis in set theory generates searching for an indubitable foundation for mathematics. Three major attempts fail.
137(28)
9 Foundationism Dies/Mainstream Lives Mainstream philosophy is still hooked on foundations.
165(17)
10 Humanists and Mavericks of Old Humanist philosophy of mathematics has credentials going back to Aristotle.
182(16)
11 Modern Humanists and Mavericks Modern mathematicians and philosophers have developed modern humanist philosophies of mathematics.
198(22)
12 Contemporary Humanists and Mavericks Mathematicians and Others are contributing to humanist philosophy of mathematics.
220(15)
Summary and Recapitulation 235(14)
13 Mathematics Is a Form of Life Philosophy and teaching interact. Philosophy and politics. A self-graded report card.
235(14)
Mathematical Notes/Comments Mathematical issues from chapters 1-13. A simple account of square circles. A complete minicourse in calculus. Boolos's three-page proof of Godel's Incompleteness Theorem. 249(68)
Bibliography 317(18)
Index 335

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