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.
Contents
Acknowledgements; 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.
Reviews
"Azzouni's book is a well-conceived and worthwhile contribution. ...it is altogether closely argued, and stimulates serious reflection." Canadian Philosophical Reviews
"Interesting, important and well worth reading." Mark Balaguer, Journal of Symbolic Logic
". . . this is a very interesting and stimulating book. . . I repeatedly return to it to study its ideas and arguments, and to test my own views against them" --Michael D. Resnik, Philosophia Mathematica
"Metaphysical Myths is written in an engaging style and contains a wealth of informative references . . . . the book is rich with arguments that will more than repay careful study." --Philosophical Books
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