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The British Journal for the Philosophy of Science 2003 54(2):181-223; doi:10.1093/bjps/54.2.181
© 2003 by British Society for the Philosophy of Science
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Hypercomputation and the Physical Church-Turing Thesis

Paolo Cotogno1

1 via Corsica 301, I–25125 Brescia, Italy. pc-logic{at}cydon.com

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.

1 Introduction

2 Computability and incomputability

3 The physical interpretation of the Church-Turing Thesis

4 Supertasks and infinite computation

5 Computation on non-well-founded domains

6 Analog computation

7 Quantum computation

8 Retrocausal computation

9 Conclusions


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SAD Computers and Two Versions of the Church-Turing Thesis
Brit J Philos Sci, December 1, 2009; 60(4): 765 - 792.
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