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Abstract: In his Discourse on the Method of Rightly Conducting the Reason, and Seeking Truth in the Sciences, Rene Descartes sought \clear and certain knowledge of all that is useful in life." Almost three centuries later, in \The foundations of mathematics," David Hilbert tried to \recast mathematical de nitions and inferences in such a way that they are unshakable." Hilbert's program relied explicitly on formal systems (equivalently, computational systems) to provide certainty in mathematics. The... (Update)
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BibTeX entry: (Update)
@misc{ o'donnell-sources,
author = "Michael J. O'Donnell",
title = "The Sources of Certainty in Computation and Formal Systems",
url = "citeseer.ist.psu.edu/314276.html" }
Citations (may not include all citations):72 North-Holland (context) - Takeuti - 1975
34 The American Mathematical Monthly (context) - Hamming, ectiveness - 1980
31 Recursive unsolvability of a problem of thue (context) - Post - 1965
31 Recursive unsolvability of a problem of thue (context) - Post - 1947
28 Studies in Logic and the Foundations of Mathematics (context) - Curry, Hindley et al. - 1972
9 Finite combinatory processes (context) - Post - 1965
7 What the tortoise said to Achilles (context) - Carroll - 1965
4 Discourse on the method of rightly conducting the reason (context) - Descartes - 1964
4 Discourse on the Method of Rightly Conducting the Reason (context) - Descartes
3 Abhandlungen aus dem mathematischen Seminar der Hamburgerisc.. (context) - Hilbert, der Mathematik - 1928
2 Form and Function (context) - Lane - 1986
2 ethode Pour Bien Conduire Sa Raison et Chercher la Verite .. (context) - Descartes - 1941
2 ethode Pour Bien Conduire Sa Raison et Chercher la Verite .. (context) - Descartes
1 With two sections by William Craig (context) - Curry, Feys et al. - 1958
1 English translation with discussion (context) - Hilbert, Unendliche et al. - 1926
1 Outlines of a Formalist Philosophy of Mathematics (context) - Curry - 1958
1 Reprinted with discussion (context) - Post, processes et al. - 1936
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