Minds and Machines 21 (1):83-96 (2011)
This paper investigates the view that digital hypercomputing is a good reason for rejection or re-interpretation of the Church-Turing thesis. After suggestion that such re-interpretation is historically problematic and often involves attack on a straw man (the ‘maximality thesis’), it discusses proposals for digital hypercomputing with Zeno-machines , i.e. computing machines that compute an infinite number of computing steps in finite time, thus performing supertasks. It argues that effective computing with Zeno-machines falls into a dilemma: either they are specified such that they do not have output states, or they are specified such that they do have output states, but involve contradiction. Repairs though non-effective methods or special rules for semi-decidable problems are sought, but not found. The paper concludes that hypercomputing supertasks are impossible in the actual world and thus no reason for rejection of the Church-Turing thesis in its traditional interpretation.
|Keywords||computing computability hypercomputing effective computing supertask Church-Turing thesis Copeland Benacerraf accelerated Turing machine Zeno machine|
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References found in this work BETA
Computability and Logic.George Boolos, John Burgess, Richard P. & C. Jeffrey - 2007 - Cambridge University Press.
The Mind Doesn't Work That Way: The Scope and Limits of Computational Psychology.Jerry A. Fodor - 2000 - MIT Press.
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