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Philosophia Mathematica Advance Access originally published online on January 13, 2006
Philosophia Mathematica 2006 14(2):189-207; doi:10.1093/philmat/nkj005
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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

Gödel on computability{dagger}

Wilfried Sieg*

* Department of Philosophy, Carnegie Melon University Pittsburgh, Pennsylvania 15213, U. S. A. sieg{at}cmu.edu

The identification of an informal concept of ‘effective calculability’ with a rigorous mathematical notion like ‘recursiveness’ or ‘Turing computability’ is still viewed as problematic, and I think rightly so. I analyze three different and conflicting perspectives Gödel articulated in the three decades from 1934 to 1964. The significant shifts in Gödel's position underline the difficulties of the methodological issues surrounding the Church-Turing Thesis.


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