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The British Journal for the Philosophy of Science Advance Access first published online on September 11, 2009
This version published online on September 29, 2009
The British Journal for the Philosophy of Science, doi:10.1093/bjps/axp038
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© The Author 2009. Published by Oxford University Press [on behalf of British Society for the Philosophy of Science]. All rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

SAD Computers and Two Versions of the Church–Turing Thesis

Tim Button

Darwin College, Cambridge University CB3 9EU, UK button{at}cantab.net


  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.

  1. SAD Computability
    1.1 The basic idea of SAD computation
    1.2 Avoiding supertasks
    1.3 Davies's model of SAD computation
    1.4 Hogarth's model of SAD computation
    1.5 Generalizing SAD computers

  2. Physical Computability
    2.1 The Physical Church–Turing Thesis
    2.2 Deterministic barriers to physical computation
    2.3 Probabilistic barriers to physical computation

  3. Effective Computability
    3.1 The Effective Church–Turing Thesis
    3.2 Hogarth's challenge to the Effective Church–Turing Thesis
    3.3 Arguing from SAD computability is a non-sequitur
    3.4 SAD computability is built from finitary computability

  4. Concluding Remarks

There were several errors in formatting in the original version of this paper, which have now been corrected.


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