Godel on computability

Philosophia Mathematica 14 (2):189-207 (2006)
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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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10.1093/philmat/nkj005

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Wilfried Sieg
Carnegie Mellon University

Citations of this work

The Physical Church–Turing Thesis: Modest or Bold?Gualtiero Piccinini - 2011 - British Journal for the Philosophy of Science 62 (4):733-769.
Gödel’s Philosophical Challenge.Wilfried Sieg - 2020 - Studia Semiotyczne 34 (1):57-80.

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References found in this work

On Computable Numbers, with an Application to the Entscheidungsproblem.Alan Turing - 1936 - Proceedings of the London Mathematical Society 42 (1):230-265.
An Unsolvable Problem of Elementary Number Theory.Alonzo Church - 1936 - Journal of Symbolic Logic 1 (2):73-74.
Mechanical procedures and mathematical experience.Wilfried Sieg - 1994 - In Alexander George (ed.), Mathematics and Mind. Oxford University Press. pp. 71--117.

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