Philosophy of Mathematics: An Introduction provides a critical analysis of the major philosophical issues and viewpoints in the concepts and methods of mathematics - from antiquity to the modern era.
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Offers beginning readers a critical appraisal of philosophical viewpoints throughout history
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Gives a separate chapter to predicativism, which is often (but wrongly) treated as if it were a part of logicism
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Provides readers with a non-partisan discussion until the final chapter, which gives the author’s personal opinion on where the truth lies
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Designed to be accessible to both undergraduates and graduate students, and at the same time to be of interest to professionals
Introduction.
Part I: Plato versus Aristotle:.
A. Plato.
1. The Socratic Background.
2. The Theory of Recollection.
3. Platonism in Mathematics.
4. Retractions: the Divided Line in Republic VI (509d−511e).
B. Aristotle.
5. The Overall Position.
6. Idealizations.
7. Complications.
8. Problems with Infinity.
C. Prospects.
Part II: From Aristotle to Kant:.
1. Medieval Times.
2. Descartes.
3. Locke, Berkeley, Hume.
4. A Remark on Conceptualism.
5. Kant: the Problem.
6. Kant: the Solution.
Part III: Reactions to Kant:.
1. Mill on Geometry.
2. Mill+
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