If you believe [functionalism] to be false … then … you hold that consciousness could be modelled in a computer program in the same way that, say, the weather can be modelled … If you accept functionalism, however, then you should believe that consciousness is a computational process.
Kleene, S. The equivalence of the analyses bears only on the question of the extent of what is humanly computable, not on the question of whether the functions generatable by machines could extend beyond the functions generatable by human computers even human computers who work forever and have access to unlimited quantities of paper and pencils.
For example: A man provided with paper, pencil, and rubber, and subject to strict discipline, is in effect a universal machine.
For example, the entry on Turing in the Blackwell Companion to the Philosophy of Mind contains the following claims: we can depend on there being a Turing machine that captures the functional relations of the brain, for so long as these relations between input and output are functionally well-behaved enough to be describable by … mathematical relationships … we know that some specific version of a Turing machine will be able to mimic them.
If the computer wishes to alter, say, squares then he or she performs successive operations. Wang, H. Several computational models allow for the computation of Church-Turing non-computable functions.
The Church-Turing thesis is about computation as this term was used inviz. Newell Yet the analyses Newell is discussing are of the concept of an effective method, not of the concept of a machine-generatable function. As previously mentioned, this convergence of analyses is generally considered very strong evidence for the Church-Turing thesis, because of the diversity of the analyses.
Some Key Remarks by Turing Turing prefaced his first description of a Turing machine with the words: We may compare a man in the process of computing a … number to a machine. Doyle, J. The method of storing real numbers on the tape is left unspecified in this purely logical model.