Godel on computability

Philosophia Mathematica 14 (2):189-207 (2006)
Abstract
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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DOI 10.1093/philmat/nkj005
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The Physical Church–Turing Thesis: Modest or Bold?Gualtiero Piccinini - 2011 - British Journal for the Philosophy of Science 62 (4):733 - 769.
The Physical Church-Turing Thesis: Modest or Bold?G. Piccinini - 2011 - British Journal for the Philosophy of Science 62 (4):733-769.
Gödel's Introduction to Logic in 1939.P. Cassou-Nogues - 2009 - History and Philosophy of Logic 30 (1):69-90.
Hilbert's Axiomatics as ‘Symbolic Form’?Rossella Lupacchini - 2014 - Perspectives on Science 22 (1):1-34.

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