Philosophy of Mathematics: The Invisible Art

Philosophy of Mathematics: The Invisible Art

by W. S. Anglin
     
 

ISBN-10: 0773487069

ISBN-13: 9780773487062

Pub. Date: 01/28/1997

Publisher: Mellen, Edwin Press, The

Product Details

ISBN-13:
9780773487062
Publisher:
Mellen, Edwin Press, The
Publication date:
01/28/1997
Series:
Studies in the History of Philosophy
Pages:
260

Table of Contents

1Mathematics and Infinity1
1.1Infinity in Ancient Times3
1.2Infinity in the Middle Ages17
2Mathematics and Infinity II23
2.1Infinity at the Beginning of the Modern Era23
2.2Infinity in the Nineteenth Century29
2.3Infinity in the Twentieth Century33
3Mathematics and Infinity III39
3.1Considerations from Contemporary Mathematics39
3.2Considerations from the History of Mathematics40
3.3Considerations from Physics40
3.4Considerations from Logic41
3.5Considerations from Psychology42
3.6Considerations from Epistemology44
3.7Considerations from Theology44
3.8Summary46
3.9Appendix: Considerations from Irrationality46
4Mathematics and Metaphysics49
4.1Mathematical Objects49
4.2The Fundamental Choice50
4.3Nihilism and Truth51
4.4A Second Choice52
4.5Idealism53
4.6Intuitionism54
4.7A Third Choice56
4.8Mathematical Materialism57
4.9Formalism58
4.10Platonism59
4.11Summary64
4.12Logicism66
4.13Structuralism66
5Mathematics and Truth69
5.1Did Truth Get Lost?69
5.2Historical Background70
5.3Truth and Meaning72
5.4What is Truth?73
5.5Language Fuzziness80
5.6Revolutions in Mathematics81
5.7Appendix: Tarski on Truth83
6Mathematics and Values85
6.1Complete-Incomplete87
6.2Rigorous-Intuitive89
6.3Elementary-Advanced93
6.4Simple-Complex95
6.5Clarifying-Mystifying97
6.6Specific-General98
6.7Concrete-Abstract99
6.8Constructive-Nonconstructive101
6.9Practical-Impractical103
6.10Elegant-Ugly104
6.11Meaningful-Pointless109
6.12Fruitful-Sterile111
6.13Conclusion112
7Mathematics and Values II113
7.1The Rating Scheme113
7.2The Example of the Medians114
7.3The Example of the Primes119
7.4Ethical Implications122
7.5Appendix: Hardy's Ratings123
8Mathematics and History129
8.1A Caricature129
8.2Is Math Good?131
8.3Individualism132
8.4Nationalism133
8.5Women135
8.6Minorities136
8.7Charity137
8.8Chronological Organisation138
8.9Dates139
8.10Calculating Devices140
8.11Astronomy141
8.12Transcendence141
8.13Rigour142
8.14Details143
8.15Fantasy Mathematics143
8.16Epic or Comedy?144
8.17Sex145
8.18Religion147
8.19Advice148
9Mathematics and Knowledge151
9.1Infallible Knowledge151
9.2Knowledge by Acquaintance156
9.3A Priori Knowledge160
9.4Knowledge a la Plantinga163
9.5Computer Knowledge166
9.6Conclusion168
9.7Appendix: Terms in Epistemology168
10Mathematics and Education171
10.1Education for the Economic Status Quo171
10.2Education for Democracy172
10.3Education for the Development of the Individual173
10.4Plato's View173
10.5John of the Cross's View174
10.6Comte's View175

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