Metaphysical Myths, Mathematical Practice: The Ontology and Epistemology of the Exact Sciencesby Jody Azzouni
Pub. Date: 05/28/2004
Publisher: Cambridge University Press
Jody Azzouni argues in this original and exciting study that mathematical knowledge really is a special kind of knowledge with its own special means of gathering evidence. He analyzes the linguistic pitfalls and misperceptions philosophers in this field are often prone to, and explores the misapplications of epistemic principles from the empirical sciences to the exact sciences. What emerges is a picture of mathematics both sensitive to mathematical practice, and to the ontological and epistemological issues that concern philosophers.
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Table of ContentsAcknowledgements; Part I. Mathematical Practice and its Puzzles: 1. Metaphysical inertness; 2. Metaphysical inertness and reference; 3. The virtues of (second-order) theft; 4. Intuitions about reference and axiom systems; 5. Comparing mathematical terms and empirical terms I; 6. Comparing mathematical terms and empirical terms II; 7. The epistemic role puzzle; 8. Benacerraf's puzzle; 9. Comparing puzzles; 10. Quine's approach I; 11. Quine's approach II; Part II. The Stuff of Mathematics: Posits and Algorithms: 12. Introduction; 13. An initial picture; 14. Application and truth; 15. Systems, application and truth; 16. Quine's objections to truth by convention; 17. Grades of ontological commitment; 18. Multiply interpreting systems; 19. Intuitions about reference revisited; Part III. The Geography of the A Priori: 20. Introduction; 21. Algorithms again; 22. Some observations on metamathematics; 23. Incorrigible co-empiricalness; 24. Why there are no incorrigible co-empirical truths; 25. Normative considerations, the success of applied mathematics, concluding thoughts; Appendix; Bibliography; Index.
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