"Can we REFUTE the Church-Turing thesis on the basis of the material presented
in this book? In a sense we can.
But one has to be aware of the fact that to 'prove' and to 'refute'
are perhaps not the right expressions, especially when, as in our case, the
hypothesis top be refuted has no unique meaning..........
....The categories of 'proof' and 'refutation' have no ABSOLUTE meaning, and
no COMPLETE proof or COMPLETE refutation is possible." [all emphasis his]
Later... p 477 "....in terms of processes of reality [as opposed to
mathematics]. What does an 'effective' process mean?
A reasonable answer is that EVERY CAUSAL PROCESS SHOULD BE CONSIDERED
AN EFFECTIVE PROCESS. In the verbal explanations of the concept, a usual
synonym for 'effective' is 'well-defined' or 'reproduceable'. ....why...well
defined?.....to be able to control.....for humans and man-made machines this
means the EXECUTION of the process by repeatable means. ....A real-world
process can not be controlled by performing it. Instead, it can be controlled
(and repeated) by manipulating the causes for the process."
This seems pertinant to the notion of causal structure.
tThen he gives versions of CTH.....
natural sciences: all physically realizable dynamics are equivalent to
computation..
biology version: "Living organisms are nothing more than comples biological
machines" F Crick "Of molecules and men" (1967).I hope this helps a bit.
Don Mikulecky, MCV/VCU, Mikulecky@gems.vcu.edu