Physical hypercomputation and the church–turing thesis
Minds and Machines 13 (1):87-101 (2003)
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.Author's Profile
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2004
DOI
10.1023/a:1021365222692
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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.
Hypercomputation and the Physical Church‐Turing Thesis.Paolo Cotogno - 2003 - British Journal for the Philosophy of Science 54 (2):181-223.
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.
Shadows of the Mind: A Search for the Missing Science of Consciousness.Roger Penrose - 1994 - Oxford University Press.
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.