The Bold Physical Church-Turing Thesis
Gualtiero Piccinini · Oxford University Press eBooks · 2015
This chapter distinguishes between the Mathematical Church-Turing thesis—the thesis supported by the original arguments for the Church-Turing thesis—and the Physical Church-Turing thesis (Physical CT). It then distinguishes 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. It explicates 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, it argues that Bold Physical CT is not relevant to the epistemological concerns that motivate CT and hence not suitable as a physical analogue of Mathematical CT.