Tracking Reason: Proof, Consequence, and Truth

Tracking Reason: Proof, Consequence, and Truth

by Jody Azzouni
     
 

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ISBN-10: 019518713X

ISBN-13: 9780195187137

Pub. Date: 11/18/2005

Publisher: Oxford University Press, USA

When ordinary people—mathematicians among them—take something to follow (deductively) from something else, they are exposing the backbone of our self-ascribed ability to reason. Jody Azzouni investigates the connection between that ordinary notion of consequence and the formal analogues invented by logicians. One claim of the book is that, despite our

Overview

When ordinary people—mathematicians among them—take something to follow (deductively) from something else, they are exposing the backbone of our self-ascribed ability to reason. Jody Azzouni investigates the connection between that ordinary notion of consequence and the formal analogues invented by logicians. One claim of the book is that, despite our apparent intuitive grasp of consequence, we do not introspect rules by which we reason, nor do we grasp the scope and range of the domain, as it were, of our reasoning. This point is illustrated with a close analysis of a paradigmatic case of ordinary reasoning: mathematical proof.

Product Details

ISBN-13:
9780195187137
Publisher:
Oxford University Press, USA
Publication date:
11/18/2005
Pages:
256
Product dimensions:
9.30(w) x 6.20(h) x 1.00(d)

Table of Contents

General Introduction
Part I. Truth
1. Truth and Truth Conditions
2. The Transcendence of Truth
3. Anaphorically Unrestricted Quantifiers
4. Regimentation and Paradox
5. The Inconsistency of Natural Languages
Conclusion to Part I
Part II. Mathematical Proof
6. The Uniqueness of Mathematics as a Social Practice
7. The Derivation-Indicator View of Mathematical Practice
8. How to Nominalize Formalism
Conclusion to Part II
Part III. Semantics an the Notion of Consequence: Introduction to Part II
9. Semantics and the Notion of Consequence
Conclusion to Part III
General Conclusion
Bibliography
Index

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