Minds and Machines 13 (1):87-101 (2003)
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Abstract |
We describe a possible physical device that computes a function that cannot be computed by a Turing machine. The device is physical in the sense that it is compatible with General Relativity. We discuss some objections, focusing on those which deny that the device is either a computer or computes a function that is not Turing computable. Finally, we argue that the existence of the device does not refute the Church–Turing thesis, but nevertheless may be a counterexample to Gandy's thesis.
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Keywords | Church–Turing thesis Gandy's thesis effective computation physical hypercomputation supertasks |
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Reprint years | 2004 |
DOI | 10.1023/A:1021365222692 |
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References found in this work BETA
Shadows of the Mind: A Search for the Missing Science of Consciousness.Roger Penrose - 1994 - Oxford University Press.
On Computable Numbers, with an Application to the N Tscheidungsproblem.Alan Turing - 1936 - Proceedings of the London Mathematical Society 42 (1):230-265.
The Undecidable: Basic Papers on Undecidable Propositions, Unsolvable Problems and Computable Functions.Martin Davis (ed.) - 1965 - Hewlett, NY, USA: Dover Publication.
Systems of Logic Based on Ordinals.Alan Mathison Turing - 1939 - London: Printed by C.F. Hodgson & Son.
View all 26 references / Add more references
Citations of this work BETA
The Physical Church–Turing Thesis: Modest or Bold?Gualtiero Piccinini - 2011 - British Journal for the Philosophy of Science 62 (4):733-769.
Computationalism, The Church–Turing Thesis, and the Church–Turing Fallacy.Gualtiero Piccinini - 2007 - Synthese 154 (1):97-120.
View all 19 citations / Add more citations
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