The Physical Church–Turing Thesis: Modest or Bold?

Abstract
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.
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DOI 10.1093/bjps/axr016
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References found in this work BETA
Could a Machine Think?Paul M. Churchland & Patricia S. Churchland - 1990 - Scientific American 262 (1):32-37.
Hypercomputation and the Physical Church-Turing Thesis.Paolo Cotogno - 2003 - British Journal for the Philosophy of Science 54 (2):181-223.
Deciding Arithmetic Using SAD Computers.Mark Hogarth - 2004 - British Journal for the Philosophy of Science 55 (4):681-691.
SAD Computers and Two Versions of the Church–Turing Thesis.Tim Button - 2009 - British Journal for the Philosophy of Science 60 (4):765-792.
The Extent of Computation in Malament–Hogarth Spacetimes.P. D. Welch - 2008 - British Journal for the Philosophy of Science 59 (4):659-674.

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SAD Computers and Two Versions of the Church–Turing Thesis.Tim Button - 2009 - British Journal for the Philosophy of Science 60 (4):765-792.
Hypercomputation and the Physical Church-Turing Thesis.Paolo Cotogno - 2003 - British Journal for the Philosophy of Science 54 (2):181-223.
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