Metamathematics and mind: The implications of undecidability results for theories of human cognition

The metamathematical undecidability results of Godel, Church, and Turing are often claimed to have negative implications for mechanist theories of mind. Anti-mechanists view these results as the basis for an argument-form known as the mathematical objection to mechanism, which proceeds by (1) identifying a task t for which there exists an unsolvability result, (2) showing that a human can perform task t, and (3) noting that if mechanism is correct, then humans must share the same limitations as machines; it follows that mechanism is false. The mathematical objection is of extreme interest because it is one of the most rare of events--a knock-down argument in metaphysics.;In this dissertation, the confusions are sorted out and the precise relationships among mechanism, physicalism, and Turing machines are articulated. A surprising result is that physicalism must be completely distinguished from a certain class of mechanist theories (including mechanism via Turing machines); thus the mathematical objection has no immediate consequences for physicalism. On the other hand, in order for mechanism via Turing machines to be interesting, it must at least claim that human reasoning processes are mechanizable; an argument to this effect, currently lacking in the literature, is provided.;Once a mechanist theory of interesting strength has been articulated, the conditions which must be satisfied by a successful instance of the mathematical objection are clearly set out. The strength of this analysis is illustrated by application to the anti-mechanistic argument of J. R. Lucas in "Minds, Machines, and Godel," yielding a precise account of that argument's failure.;Versions of the mathematical objection have been offered in the literature. Although none is regarded as successful, there is considerable disagreement concerning where exactly these arguments fail, due to confusions on both sides of the debate concerning the nature of mechanist theories. Primary among these confusions has been the failure to distinguish adequately among differing non-equivalent types of mechanist theories; another arises from the fact that varieties of mechanism are not all of the same strength (where strength is measured by the size of the class of phenomena claimed mechanizable).