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ISBN 10: 0195166612
ISBN 13: 9780195166613
Author: Mark Colyvan
The Quine-Putnam indispensability argument in the philosophy of mathematics urges us to place mathematical entities on the same ontological footing as other theoretical entities essential to our best scientific theories. Recently, the argument has come under serious scrutiny, with many influential philosophers unconvinced of its cogency. This book not only outlines the indispensability argument in considerable detail but also defends it against various challenges.
1 Mathematics and Its Applications
1.1 Realism and Anti-realism in Mathematics
1.2 Indispensability Arguments
1.3 The Road Ahead
2 The Quinean Backdrop
2.1 Introducing Naturalism
2.2 Quinean Naturalism
2.3 The Methodologies of Philosophy and Science
2.4 The Causal Version of Naturalism
2.5 Holism
2.6 The First Premise Revisited
3 The Eleatic Principle
3.1 The Inductive Argument
3.2 The Epistemic Argument
3.3 The Argument from Causal Explanation
3.4 Causal Relevance
3.5 Rejecting Inference to the Best Explanation
3.6 The Content of Scientific Theories
3.7 The Moral
3.8 Recapitulation
4 Field's Fictionalism
4.1 The Science without Numbers Project
4.2 What Is It to Be Indispensable?
4.3 The Role of Confirmation Theory
4.4 The Role of Mathematics in Physical Theories
4.5 Review of Field's Fictionalism
5 Maddy's Objections
5.1 The Objections
5.2 Maddy's Naturalism
5.3 Defending the Indispensability Argument
5.4 Review of Maddy's Objections
6 The Empirical Nature of Mathematical Knowledge
6.1 The Obviousness of Some Mathematical Truth
6.2 The Unfalsifiability of Mathematics
6.3 The Sober Objection
6.4 Is Mathematics Contingent?
7 Conclusion
7.1 What the Argument Doesn't Show
7.2 The Benacerraf Challenges
7.3 A Slippery Slope?
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Tags: Mark Colyvan, Indispensability, Mathematics
