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Logic Journal of IGPL Advance Access originally published online on August 19, 2006
Logic Journal of IGPL 2006 14(5):745-754; doi:10.1093/jigpal/jzl008
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© The Author, 2006. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

After Gödel

Hilary Putnam

Department of Philosophy, Harvard University, Cambridge, MA 02138, USA.


  Abstract

This paper describes the enormous impact of Gödel's work on mathematical logic and recursion theory. After a brief description of the major theorems that Gödel proved, it focuses on subsequent work extending what he did, sometimes by quite different methods. The paper closes with a new result, applying Gödel's methods to show that if scientific epistemology (what Chomsky calls our "scientific competence") could be completely represented by a particular Turing machine, then it would be impossible for us to know that fact.

Key Words: Gödel • Tarski • Kripke • Chomsky • completeness • incompleteness • continuum hypothesis • axiom of choice • model theory • prime numbers • Diophantine equations • competence • epistemology


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