Tracking Reason: Proof, Consequence, and Truth

Tracking Reason: Proof, Consequence, and Truth

by Jody Azzouni
     
 

ISBN-10: 019518713X

ISBN-13: 9780195187137

Pub. Date: 11/18/2005

Publisher: Oxford University Press, USA

Ordinary people - mathematicians among them - grasp when they take something to follow (deductively) from something ease. This is the backbone of our self-ascribed ability to reason. This book investigates the connection between that ordinary notion of consequence and the formal analogues developed by logicians. One crucial claim of the book is that, despite our…  See more details below

Overview

Ordinary people - mathematicians among them - grasp when they take something to follow (deductively) from something ease. This is the backbone of our self-ascribed ability to reason. This book investigates the connection between that ordinary notion of consequence and the formal analogues developed by logicians. One crucial claim of the book is that, despite our apparent intuitive grasp of when something follows from something else, we have no introspective access to the rules by which we reason, nor to the scope and range of the domain, as it were, of our reasoning. The 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

1Truth and truth conditions13
2The transcendence of truth37
3Anaphorically unrestricted quantifiers60
4Regimentation and paradox74
5The inconsistency of natural languages92
6The uniqueness of mathematics as a social practice123
7The derivation-indicator view of mathematical practice140
8How to nominalize formalism168
9Semantics and the notion of consequence194

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