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Philosophia Mathematica Advance Access published online on October 1, 2009
Philosophia Mathematica, doi:10.1093/philmat/nkp015
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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

PETER SMITH. An Introduction to Gödel's Theorems

Craig Smorynski *

PETER SMITH. An Introduction to Gödel's Theorems. Cambridge: Cambridge University Press, 2007. ISBN 978-0-521-85784-0 (hbk), 978-0-521-67453-9 (pbk). Pp. xiv + 361.

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

As regards Gödel’s First Incompleteness Theorem and the matter of its proof, Gödel’s own paper has yet to be improved upon. Any additional exposition, and the number of such is legion, can offer sharpened formulations, generalisations, speculations on the meaning of the result, and, less rarely since around 1980, a proof of the Second Incompleteness Theorem. Aside from a few details concerning this last, Gödel’s Theorems themselves are really a simple matter, made complex by the insistence on sticking to as limited an arithmetical language as possible, and the expositor’s desire to embed the results in their appropriate setting—which setting is not clear as developments leading from them head off in different directions. This is the challenge that has been faced repeatedly in articles, chapters in textbooks and handbooks, and monographs. These last range through technical accounts (Mostowski, Stegmüller), popular accounts (Nagel and Newman, Franzén (whose Gödel’s Theorem: An Incomplete . . . [Full Text of this Article]


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