The Church-Turing Thesis (Stanford Encyclopedia of …

(Smolensky 1988: 3)That there exists a most general formulation of machine and that itleads to a unique set of input-output functions has come to be calledChurch’s thesis.

There are various equivalent formulations of the Church-Turing thesis

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 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.

Tags: Theses and Hypothesis PPT

For instance, the claim that the universal Turing machine can do anymathematical task that can be done by any machine—aclaim very different from Turing’s—is sometimes referredto as the Church-Turing thesis.This loosening of established terminology is unfortunate, since it caneasily lead to misunderstandings and confusion.