This volume documents a lively exchange between five philosophers of mathematics. It also introduces a new voice in one
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English Pages 393 [397] Year 2006
Table of contents :
Content: AcknowledgmentsEditor's Introduction Philip HUGLY and Charles SAYWARD: Arithmetic and Ontology a Non-Realist Philosophy of ArithmeticPrefaceAnalytical Chapter 1. IntroductionPart One: Beginning with FregeChapter 2. Notes to GrundlagenChapter 3. Objectivism and Realism in Frege's Philosophy of ArithmeticPart Two: Arithmetic and Non-RealismChapter 4. The Peano AxiomsChapter 5. Existence, Number, and Realism Part Three: Necessity and RulesChapter 6. Arithmetic and Necessity Chapter 7. Arithmetic and RulesPart Four: The Three ThesesChapter 8. Thesis One Chapter 9. Thesis Two Chapter 10. Thesis ThreeReferences CommentariesColin Cheyne, Numbers, Reference, and Abstraction Sanford Shieh, What Is Non-Realism about Arithmetic? Jean Paul Van Bendegem, Non-Realism, Nominalism and Strict Fi-nitism. The Sheer Complexity of It All Replies to CommentariesPhilip Hugly and Charles Sayward, Replies to Commentaries About the Contributors Index