(McArthur 1991: 401.) [The] Church/ Turing thesis ...
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Some prefer the name Turing-Church thesis.
Because the word ‘computable’ is here being employedsynonymously with ‘computable by an effective method’,this statement is entailed by the Church-Turing thesis, in conjunctionwith Turing’s result that there exist functions uncomputable byany standard Turing machine. However, to a casual reader of thetechnical literature, this statement and others like it may appear tosay more than they in fact do. That a function isuncomputable, in this sense, by any past, present, or futurereal machine, does not entail that the function in questioncannot be generated by some real machine (past, present, orfuture).
[and] [g]ranted that the [Church-Turing] thesis is correct, then...
A common formulation of the Church-Turing thesis in the technicalliterature is the following, where ‘computable’ is beingused synonymously with ‘effectively computable’:
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the Church-Turing Thesis and the Quantum ..
The error of confusing the Church-Turing thesis properly so calledwith one or another form of the maximality thesis has led to someremarkable claims in the foundations of psychology. For example, onefrequently encounters the view that psychology must becapable of being expressed ultimately in terms of the Turing machine(e.g., Fodor 1981: 130; Boden 1988: 259). To one who makes this error,conceptual space will seem to contain no room for mechanical models ofthe mind that are not equivalent to Turing machines. Yet it iscertainly possible that psychology will find the need to employ modelsof human cognition transcending Turing machines.
Classical physics and the Church--Turing Thesis
Yet the analyses Newell is discussing are of the concept of aneffective method, not of the concept of a machine-generatablefunction. The equivalence of the analyses bears only on the questionof the extent of what is humanly computable, not on the question ofwhether the functions generatable by machines could extend beyond thefunctions generatable by human computers (even human computers whowork forever and have access to unlimited quantities of paper andpencils). Indeed, Newell’s argument is undercut by the existenceof (notional) machines capable of generating functions that, givenTuring’s thesis, cannot be generated by any effectivemethod.