The Physical Church–Turing Thesis: Modest or Bold?
Gualtiero Piccinini · The British Journal for the Philosophy of Science · 2011
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. 1 The Mathematical Church–Turing Thesis 2 A Usability Constraint on Physical Computation 3 The Bold Physical Church–Turing Thesis 3.1 Lack of confluence 3.2 Unconstrained appeals to real-valued quantities 3.3 Falsification by irrelevant counterexamples 4 The Modest Physical Church–Turing Thesis 4.1 Hypercomputation: genuine and spurious 4.2 Relativistic hypercomputers 4.3 Other challenges to Modest Physical CT 5 Conclusion