Journal Article

The Physical Church–Turing Thesis: Modest or Bold?

Gualtiero Piccinini

in The British Journal for the Philosophy of Science

Published on behalf of British Society for the Philosophy of Science

Volume 62, issue 4, pages 733-769
Published in print December 2011 | ISSN: 0007-0882
Published online August 2011 | e-ISSN: 1464-3537 | DOI: http://dx.doi.org/10.1093/bjps/axr016
The Physical Church–Turing Thesis: Modest or Bold?

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This article defends a modest version of the Physical Church-Turing thesis (CT). Following an established recent trend, I distinguish between what I call Mathematical CT—the thesis supported by the original arguments for CT— and Physical CT. I then distinguish between bold formulations of Physical CT, according to which any physical process—anything doable by a physical system—is computable by a Turing machine, and modest formulations, according to which any function that is computable by a physical system is computable by a Turing machine. I argue that Bold Physical CT is not relevant to the epistemological concerns that motivate CT and hence not suitable as a physical analog of Mathematical CT. The correct physical analog of Mathematical CT is Modest Physical CT. I propose to explicate the notion of physical computability in terms of a usability constraint, according to which for a process to count as relevant to Physical CT, it must be usable by a finite observer to obtain the desired values of a function. Finally, I suggest that proposed counterexamples to Physical CT are still far from falsifying it because they have not been shown to satisfy the usability constraint.

1The Mathematical Church–Turing Thesis

2A Usability Constraint on Physical Computation

3The Bold Physical Church–Turing Thesis

  3.1Lack of confluence

  3.2Unconstrained appeals to real-valued quantities

  3.3Falsification by irrelevant counterexamples

4The Modest Physical Church–Turing Thesis

  4.1Hypercomputation: genuine and spurious

  4.2Relativistic hypercomputers

  4.3Other challenges to Modest Physical CT

5Conclusion

Journal Article.  14394 words.  Illustrated.

Subjects: Philosophy of Science ; Science and Mathematics

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