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The philosophy of mathematics : the invisible art

Author: W S Anglin
Publisher: Lewiston : Edwin Mellen Press, ©1997.
Series: Studies in the history of philosophy (Lewiston, N.Y.), v. 43.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

Organized around the distinction between finite and infinite, this text includes a brief overview of what different philosophers have said about infinity, and looks at some of the arguments to the  Read more...

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Additional Physical Format: Online version:
Anglin, W.S.
Philosophy of mathematics.
Lewiston : Edwin Mellen Press, ©1997
(OCoLC)625926585
Document Type: Book
All Authors / Contributors: W S Anglin
ISBN: 0773487069 9780773487062 088946300X 9780889463004
OCLC Number: 35968923
Description: x, 245 pages : illustrations ; 24 cm.
Contents: 1. Mathematics and Infinity. 1.1. Infinity in Ancient Times. 1.2. Infinity in the Middle Ages --
2. Mathematics and Infinity II. 2.1. Infinity at the Beginning of the Modern Era. 2.2. Infinity in the Nineteenth Century. 2.3. Infinity in the Twentieth Century --
3. Mathematics and Infinity III. 3.1. Considerations from Contemporary Mathematics. 3.2. Considerations from the History of Mathematics. 3.3. Considerations from Physics. 3.4. Considerations from Logic. 3.5. Considerations from Psychology. 3.6. Considerations from Epistemology. 3.7. Considerations from Theology. 3.8. Summary. 3.9. Appendix: Considerations from Irrationality --
4. Mathematics and Metaphysics. 4.1. Mathematical Objects. 4.2. The Fundamental Choice. 4.3. Nihilism and Truth. 4.4. A Second Choice. 4.5. Idealism. 4.6. Intuitionism. 4.7. A Third Choice. 4.8. Mathematical Materialism. 4.9. Formalism. 4.10. Platonism. 4.11. Summary. 4.12. Logicism. 4.13. Structuralism --
5. Mathematics and Truth. 5.1. Did Truth Get Lost? 5.2. Historical Background. 5.3. Truth and Meaning. 5.4. What is Truth? 5.5. Language Fuzziness. 5.6. Revolutions in Mathematics. 5.7. Appendix: Tarski on Truth --
6. Mathematics and Values. 6.1. Complete-Incomplete. 6.2. Rigorous-Intuitive. 6.3. Elementary-Advanced. 6.4. Simple-Complex. 6.5. Clarifying-Mystifying. 6.6. Specific-General. 6.7. Concrete-Abstract. 6.8. Constructive-Nonconstructive. 6.9. Practical-Impractical. 6.10. Elegant-Ugly. 6.11. Meaningful-Pointless. 6.12. Fruitful-Sterile. 6.13. Conclusion --
7. Mathematics and Values II. 7.1. The Rating Scheme. 7.2. The Example of the Medians. 7.3. The Example of the Primes. 7.4. Ethical Implications. 7.5. Appendix: Hardy's Ratings --
8. Mathematics and History. 8.1. A Caricature. 8.2. Is Math Good? 8.3. Individualism. 8.4. Nationalism. 8.5. Women. 8.6. Minorities. 8.7. Charity. 8.8. Chronological Organisation. 8.9. Dates. 8.10. Calculating Devices. 8.11. Astronomy. 8.12. Transcendence. 8.13. Rigour. 8.14. Details. 8.15. Fantasy Mathematics. 8.16. Epic or Comedy? 8.17. Sex. 8.18. Religion. 8.19. Advice --
9. Mathematics and Knowledge. 9.1. Infallible Knowledge. 9.2. Knowledge by Acquaintance. 9.3. A Priori Knowledge. 9.4. Knowledge a la Plantinga. 9.5. Computer Knowledge. 9.6. Conclusion. 9.7. Appendix: Terms in Epistemology --
10. Mathematics and Education. 10.1. Education for the Economic Status Quo. 10.2. Education for Democracy. 10.3. Education for the Development of the Individual. 10.4. Plato's View. 10.5. John of the Cross's View. 10.6. Comte's View. 10.7. Smith's View. 10.8. Jung's View. 10.9. Whitehead's View. 10.10. A Plea for Euclid. 10.11. Euclid and Ernest. 10.12. Euclidean Geometry Today --
11. Mathematics and Religion. 11.1. Infinity. 11.2. Platonism. 11.3. Truth. 11.4. Beauty. 11.5. History. 11.6. Education. 11.7. Ethics. 11.8. Physics. 11.9. Number Worship. 11.10. Islam. 11.11. Christianity --
12. Mathematics and Reference. 12.1. Reference and Language. 12.2. Crying Wolf. 12.3. Abstraction, Classes, and Equivalence Classes. 12.4. Reference and Hale. 12.5. Reference and Precision. 12.6. Reference and Inscrutability. 12.7. Reference and Ontology. 12.8. Reference and Numbers. 12.9. Reference and Large Numbers. 12.10. Reference and Benacerraf. 12.11. Reference and Azzouni. 12.12. Reference and Impredicativity. 12.13. Reference and Infinity.
Series Title: Studies in the history of philosophy (Lewiston, N.Y.), v. 43.
Responsibility: W.S. Anglin.

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