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Philosophia Mathematica Advance Access published online on May 13, 2009
Philosophia Mathematica, doi:10.1093/philmat/nkp007
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© The Author [2009]. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org

Book Review

JODY AZZOUNI. Tracking Reason: Proof, Consequence and Truth

Conrad Asmus*

* School of Philosophy, Anthropology and Social Inquiry, University of Melbourne, Melbourne, VIC 3010, Australia. conrad.asmus@gmail.com

JODY AZZOUNI. Tracking Reason: Proof, Consequence and Truth. New York: Oxford University Press, 2006. ISBN 978-0-19-518713-7. Pp. vi + 248.

The first 150 words of the full text of this article appear below.


   1. Introduction
 
Tracking Reason is an ambitious work touching on a vast range of topics including (but not limited to): mathematical proof, mathematical practice, the ontological commitment of theories, nominalism, formalism, first-order versus second-order logic, logical consequence, reductive theories of logical consequence, interpretational and representational theories of consequence, syntactic accounts of consequence, ‘Opacity to introspection of the rules by which we reason’ (p. 207), 1 truth, truth predicates, the transcendent nature of truth predicates, inter-translatability of languages, deflationism, propositional quantification, inconsistency in natural languages and regimentation of natural languages. This abundant landscape of philosophy has a number of different tracks for traversing it. As indicated by the subtitle of the book, there are three main topics: Proof, Consequence and Truth. This provides the first way of reading the book. Azzouni argues that the logic at work in different practices (particularly mathematics) is often introspectively invisible to the practitioners. A mathematical proof . . . [Full Text of this Article]


   2. Truth
 

   3. Proof
 

   4. Consequence
 

   5. Regimentation and Paradox
 

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