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Philosophia Mathematica Advance Access originally published online on March 8, 2006
Philosophia Mathematica 2006 14(2):262-264; doi:10.1093/philmat/nkl004
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Philosophia Mathematica (III), Vol. 14 No. 2 © The Author [2006]. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org

Book Review

TORKEL FRANZÉN. Gödel's Theorem: An Incomplete Guide to its Use and Abuse. Wellesley, Mass.: AK Peters, 2005. x + 172 pp. ISBN1–56881–238–8.

Stewart Shapiro*

* Department of Philosophy, Ohio State University Columbus, Ohio 43210 U.S.A.
Department of Logic and Metaphysics, St Andrews University St Andrews, Fife KY16 9AL Scotland. shapiro.4@osu.edu

The first 10% of the full text of this article appears below.

This short book has two main purposes. The first is to explain Kurt Gödel's first and second incompleteness theorems in informal terms accessible to a layperson, or at least a non-logician. The author claims that, to follow this part of the book, a reader need only be familiar with the mathematics taught in secondary school. I am not sure if this is sufficient. A grasp of the incompleteness theorems, even at the level of ‘the big picture’, might require some experience with the rigor of mathematical proof. Moreover, since the incompleteness theorems concern formal deductive systems, it would help for a potential reader of this book to have some familiarity with at least elementary logic.

There are, of course, a number . . . [Full Text of this Article]


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