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Hypercomputation and the Physical Church-Turing Thesis

Paolo Cotogno
The British Journal for the Philosophy of Science
Vol. 54, No. 2 (Jun., 2003), pp. 181-223
Stable URL: http://www.jstor.org/stable/3541964
Page Count: 43
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Hypercomputation and the Physical Church-Turing Thesis
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Abstract

A version of the Church-Turing Thesis states that every effectively realizable physical system can be defined by Turing Machines ('Thesis P'); in this formulation the Thesis appears an empirical, more than a logico-mathematical, proposition. We review the main approaches to computation beyond Turing definability ('hypercomputation'): supertask, non-well-founded, analog, quantum, and retrocausal computation. These models depend on infinite computation, explicitly or implicitly, and appear physically implausible; moreover, even if infinite computation were realizable, the Halting Problem would not be affected. Therefore, Thesis P is not essentially different from the standard Church-Turing Thesis.

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