SAD computers and two versions of the Church–Turing thesis

British Journal for the Philosophy of Science 60 (4):765-792 (2009)
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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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Tim Button
University College London

Citations of this work

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.
The Philosophy of Computer Science.Raymond Turner - 2013 - Stanford Encyclopedia of Philosophy.
Supertasks and Arithmetical Truth.Jared Warren & Daniel Waxman - 2020 - Philosophical Studies 177 (5):1275-1282.
Technology and Mathematics.Sven Ove Hansson - 2020 - Philosophy and Technology 33 (1):117-139.

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References found in this work

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.

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