Metamathematics and the Philosophy of Mind

Abstract

The metamathematical theorems of Gödel and Church are frequently applied to the philosophy of mind, typically as rational evidence against mechanism. Using methods of Post and Smullyan, these results are presented as purely mathematical theorems and various such applications are discussed critically. In particular, J. Lucas's use of Gödel's theorem to distinguish between conscious and unconscious beings is refuted, while more generally, attempts to extract philosophy from metamathematics are shown to involve only dramatizations of the constructivity problem in foundations. More specifically, philosophical extrapolations from metamathematics are shown to involve premature extensions of Church's thesis.

Logic and Limits of Knowledge and Truth

“…Among its many replies see esp. Webb, 1968, andBenacerraf, 1967. 3The notion of a 'formal system' is stretched well beyond familiar limits in the course of the discussion, however. 4Which are the basic truths of a body of knowledge, of course, may be relative to the choice of transformation rules.…”

Computers and the nature of man: a historian’s perspective on controversies about artificial intelligence

“…Most important for our present purposes is that some of his critics accused Lucas of holding too exalted a view of man. For instance, if a specific machine cannot assert the true-though-unprovable Gödel formula, people cannot always do this either [41,44]. Further, rather than suggest that our self-knowledge shows we are not machines, one can reverse the argument and say that, since formal systems cannot know themselves, Lucas's argument really implies that human self-knowledge is impossible [2, p. 30].…”