Metaphysical Myths, Mathematical Practice

The Ontology and Epistemology of the Exact Sciences

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Hardcover | 27 June 1994

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264 Pages

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Most philosophers of mathematics try to show either that the sort of knowledge mathematicians have is similar to the sort of knowledge specialists in the empirical sciences have or that the kind of knowledge mathematicians have, although apparently about objects such as numbers, sets, and so on, isn't really about those sorts of things as well. Jody Azzouni argues that mathematical knowledge really is a special kind of knowledge with its own special means of gathering evidence. He analyses 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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"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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Non-Fiction Mathematics History of Mathematics Science Science in General Philosophy of Science Philosophy of Mathematics Philosophy Social & Political Philosophy

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Published: 15th May 2008

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Acknowledgments
Mathematical Practice and Its Puzzles
Metaphysical Inertness	p. 3
Metaphysical Inertness and Reference	p. 6
The Virtues of (Second-Order) Theft	p. 11
Intuitions about Reference and Axiom Systems	p. 18
Comparing Mathematical Terms and Empirical Terms I	p. 31
Comparing Mathematical Terms and Empirical Terms II	p. 48
The Epistemic Role Puzzle	p. 55
Benacerraf's Puzzle	p. 58
Comparing Puzzles	p. 60
Quine's Approach I	p. 64
Quine's Approach II	p. 71
The Stuff of Mathematics: Posits and Algorithms
An Initial Picture	p. 80
Application and Truth	p. 88
Systems, Application, and Truth	p. 94
Quine's Objections to Truth by Convention	p. 105
Grades of Ontological Commitment	p. 118
Multiply Interpreting Systems	p. 132
Intuitions about Reference Revisited	p. 139
The Geography of the a Priori
Algorithms Again	p. 156
Some Observations on Metamathematics	p. 171
Incorrigible Co-empiricalness	p. 174
Why There Are No Incorrigible Co-empirical Truths	p. 192
Normative Considerations, the Success of Applied Mathematics, Concluding Thoughts	p. 204
Appendix	p. 215
Bibliography	p. 236
Index	p. 246
Table of Contents provided by Blackwell. All Rights Reserved.

Metaphysical Myths, Mathematical Practice

The Ontology and Epistemology of the Exact Sciences

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

Other Editions and Formats

Paperback

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