, Volume 21, Issue 1, pp 83-96

On the Possibilities of Hypercomputing Supertasks

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Abstract

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.

I am very grateful to Paul Benacerraf, Adam Elga and Athanssios Kehagias for comments and for illuminating discussion. I am also very grateful to two anonymous reviewers for Minds and Machines, and two for the British Journal for the Philosophy of Science.