THE BROAD CONCEPTION OF COMPUTATION

A myth has arisen concerning Turing's article of 1936, namely that Tur ing set forth a fundamental principle concerning the limits of what ca n be computed by machine-a myth that has passed into cognitive science and the philosophy of minds to wide and pernicious effect. This suppo sed principle, sometimes incorrectly termed the Church-Turing thesis, is the claim that the class of functions that can be computed by machi nes is identical to the class of functions that can be computed by Tur ing machines. In point of fact, Turing himself nowhere endorses or eve n states this claim (nor does Church). The author describes a number o f notional machines, both analog and digital, that can compute more th an a universal Turing machine. These machines are exemplars of the cla ss of nonclassical computing machines. Nothing known at present rules out the possibility that machines in this class will one day be built or that the brain itself is such a machine. These theoretical consider ations undercut a number of foundational arguments that are commonly r ehearsed in cognitive science and gesture toward a new class of cognit ive models.