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Philosophia Mathematica Advance Access originally published online on January 13, 2006
Philosophia Mathematica 2006 14(2):208-228; doi:10.1093/philmat/nkj004
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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's interpretation of intuitionism{dagger}

W. W. TAIT*

* Department of Philosophy, University of Chicago Chicago, Illinois 60637 U. S. A. wwtx{at}earthlink.net

Gödel regarded the Dialectica interpretation as giving constructive content to intuitionism, which otherwise failed to meet reasonable conditions of constructivity. He founded his theory of primitive recursive functions, in which the interpretation is given, on the concept of computable function of finite type. I will (1) criticize this foundation, (2) propose a quite different one, and (3) note that essentially the latter foundation also underlies the Curry-Howard type theory, and hence Heyting's intuitionistic conception of logic. Thus the Dialectica interpretation (in so far as its aim was to give constructive content to intuitionism) is superfluous.


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