I’ve just finished a paper corresponding more or less to my 2005 Eastern APA talk on the Physical Church-Turing thesis.
The topic is a bit far from the concerns of mainstream philosophers of mind, but still relevant. It’s about what can be physically computed, which is relevant to what can be computed by the mind-brain. If anyone wishes to take a look at the paper, I am very interested in receiving feedback on it.
To give you some idea of what I’m up to, here is the abstract:
This paper calls for more action on how to properly understand and evaluate the Church-Turing thesis (CT).Following an established recent trend, I distinguish between what I call Logical CT, which is the thesis supported by the original arguments for CT, and Physical CT.I then distinguish between bold formulations of Physical CT, according to which anything that can be done by a physical system is computable by a Turing machine, and modest formulations, according to which any function that is physically computable is computable by a Turing machine.I argue that Bold Physical CT is not relevant to the epistemological concerns that motivate CT, and hence it is not suitable as a physical analogue of Logical CT.The correct physical analogue of Logical CT is Modest Physical CT, which is formulated in terms of a notion of physical computability.I propose to explicate such a 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 an observer to obtain the desired values of a function.Finally, I suggest that current proposals for machines that falsify Physical CT are still far from doing so, because they have not been shown to satisfy the usability constraint.