# There are numerous examples of this extended usage in theliterature.

Perhaps some writers are simply misled by theterminological practice that has grown up whereby a thesis concerningwhich there is little real doubt, the Church-Turing thesis properlyso-called, and a different thesis of unknown truth-value, are referredto indiscriminately as Churchs thesis or the Church-Turing thesis(albeit with accompanying hedges like strong form and physicalversion).

## (McArthur 1991: 401.) [The] Church/ Turing thesis ...

### Some prefer the name Turing-Church thesis.

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.

### [and] [g]ranted that the [Church-Turing] thesis is correct, then...

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.

## The Argument about the Church-Turing Thesis

Yet it was *not* the conjecture that these writers set out inthe quote, but Turing’s and Church’s theses properly socalled, that were formulated and generally accepted in the 1930s and1940s.

## Alan Turing Scrapbook - Turing Machines

A common formulation of the Church-Turing thesis in the technicalliterature is the following, where ‘computable’ is beingused synonymously with ‘effectively computable’:

## Alan Turing - a short biography

[T]he Physical Church-Turing Thesis … is the conjecture thatwhatever physical computing device (in the broader sense) or physicalthought-experiment will be designed by any future civilization, itwill always be simulateable by a Turing machine. (Andréka,Németi, and Németi 2009: 500)