Authors
Tim Button
University College London
Abstract
Recent work on hypercomputation has raised new objections against the Church–Turing Thesis. In this paper, I focus on the challenge posed by a particular kind of hypercomputer, namely, SAD computers. I first consider deterministic and probabilistic barriers to the physical possibility of SAD computation. These suggest several ways to defend a Physical version of the Church–Turing Thesis. I then argue against Hogarth's analogy between non-Turing computability and non-Euclidean geometry, showing that it is a non-sequitur. I conclude that the Effective version of the Church–Turing Thesis is unaffected by SAD computation
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DOI 10.1093/bjps/axp038
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References found in this work BETA

The Logical Basis of Metaphysics.Michael DUMMETT - 1991 - Harvard University Press.
On Computable Numbers, with an Application to the Entscheidungsproblem.Alan Turing - 1936 - Proceedings of the London Mathematical Society 42 (1):230-265.
An Introduction to Gödel's Theorems.Peter Smith - 2007 - Cambridge University Press.
An Introduction to Gödel's Theorems.Peter Smith - 2009 - Bulletin of Symbolic Logic 15 (2):218-222.

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Citations of this work BETA

Computation in Physical Systems.Gualtiero Piccinini - 2010 - Stanford Encyclopedia of Philosophy.
The Physical Church-Turing Thesis: Modest or Bold?Gualtiero Piccinini - 2011 - British Journal for the Philosophy of Science 62 (4):733-769.
Supertasks and Arithmetical Truth.Jared Warren & Daniel Waxman - 2020 - Philosophical Studies 177 (5):1275-1282.
The Philosophy of Computer Science.Raymond Turner - 2013 - Stanford Encyclopedia of Philosophy.

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The Church-Turing Thesis.B. Jack Copeland - 2008 - In Edward N. Zalta (ed.), The Stanford Encyclopedia of Philosophy. The Metaphysics Research Lab, Stanford University.
Quantum Speed-Up of Computations.Itamar Pitowsky - 2002 - Proceedings of the Philosophy of Science Association 2002 (3):S168-S177.
Deciding Arithmetic Using SAD Computers.Mark Hogarth - 2004 - British Journal for the Philosophy of Science 55 (4):681-691.

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