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WorldCat.org

<TABLE CELLSPACING=0 CELLPADDING=0><TR><TD>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.</TD><TD WIDTH=40></TD><TD VALIGN=TOP>xi</TD><TD VALIGN=TOP>(6)</TD></TR><TR><TD>Acknowledgments</TD><TD WIDTH=40></TD><TD VALIGN=TOP>xvii</TD><TD VALIGN=TOP>(4)</TD></TR><TR><TD>Dialogue with Laura</TD><TD WIDTH=40></TD><TD VALIGN=TOP>xxi</TD><TD></TD></TR><TR><TD>Part One</TD><TD WIDTH=40></TD><TD VALIGN=TOP>3</TD><TD VALIGN=TOP>(88)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>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.</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>3</TD><TD VALIGN=TOP>(21)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>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.</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>24</TD><TD VALIGN=TOP>(11)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>3  Myths/Mistakes/Misunderstandings   Anecdotes from mathematical life show that humanism is true to life.</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>35</TD><TD VALIGN=TOP>(13)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>4  Intuition/Proof/Certainty   All are subjects of long controversy. Humanism shows them in a new light.</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>48</TD><TD VALIGN=TOP>(24)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>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?</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>72</TD><TD VALIGN=TOP>(19)</TD></TR><TR><TD>Part Two</TD><TD WIDTH=40></TD><TD VALIGN=TOP>91</TD><TD VALIGN=TOP>(144)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>6  Mainstream Before the Crisis   From Pythagoras to Descartes, philosophy of mathematics is a mainstay of religion.</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>91</TD><TD VALIGN=TOP>(28)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>7  Mainstream Philosophy at Its Peak   From Spinoza to Kant, philosophy of mathematics and religion supply mutual aid.</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>119</TD><TD VALIGN=TOP>(18)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>8  Mainstream Since the Crisis A crisis in set theory generates searching for an indubitable foundation for mathematics. Three major attempts fail.</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>137</TD><TD VALIGN=TOP>(28)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>9  Foundationism Dies/Mainstream Lives   Mainstream philosophy is still hooked on foundations.</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>165</TD><TD VALIGN=TOP>(17)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>10  Humanists and Mavericks of Old   Humanist philosophy of mathematics has credentials going back to Aristotle.</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>182</TD><TD VALIGN=TOP>(16)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>11  Modern Humanists and Mavericks   Modern mathematicians and philosophers have developed modern humanist philosophies of mathematics.</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>198</TD><TD VALIGN=TOP>(22)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>12  Contemporary Humanists and Mavericks   Mathematicians and Others are contributing to humanist philosophy of mathematics.</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>220</TD><TD VALIGN=TOP>(15)</TD></TR><TR><TD>Summary and Recapitulation</TD><TD WIDTH=40></TD><TD VALIGN=TOP>235</TD><TD VALIGN=TOP>(14)</TD></TR><TR><TD><TABLE CELLSPACING=0 CELLPADDING=0><TR><TD WIDTH=20></TD><TD>13  Mathematics Is a Form of Life   Philosophy and teaching interact. Philosophy and politics. A self-graded report card.</TD></TR></TABLE></TD><TD WIDTH=40></TD><TD VALIGN=TOP>235</TD><TD VALIGN=TOP>(14)</TD></TR><TR><TD>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.</TD><TD WIDTH=40></TD><TD VALIGN=TOP>249</TD><TD VALIGN=TOP>(68)</TD></TR><TR><TD>Bibliography</TD><TD WIDTH=40></TD><TD VALIGN=TOP>317</TD><TD VALIGN=TOP>(18)</TD></TR><TR><TD>Index</TD><TD WIDTH=40></TD><TD VALIGN=TOP>335</TD><TD></TD></TR></TABLE>

Tries to refine the philosophy of mathematics to reflect what mathematicians really do, and argues that mathematics must be understood in a social context

What is mathematics, really?