SAD computers and two versions of the Church–Turing thesis

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
Alan Turing (1936). On Computable Numbers, with an Application to the Entscheidungsproblem. Proceedings of the London Mathematical Society 42 (1):230-265.
Paolo Cotogno (2003). Hypercomputation and the Physical Church-Turing Thesis. British Journal for the Philosophy of Science 54 (2):181-223.
Mark Hogarth (2004). Deciding Arithmetic Using SAD Computers. British Journal for the Philosophy of Science 55 (4):681-691.

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Citations of this work BETA
Gualtiero Piccinini (2011). The Physical Church–Turing Thesis: Modest or Bold? British Journal for the Philosophy of Science 62 (4):733 - 769.

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