1. Some remarks on the logic and epistemology of computation – João de Fernandes Teixeira (UFSC)

Abstract: The paper focuses on some logical and epistemological aspects of the notion of computation. The first part questions the Church-Turing thesis as a fundamental principle concerning the limits of computation and some of its consequences for Philosophy of Mind and Cognitive Science. The second part discusses one of the main presumptions of the traditional conception of computability, namely, its reliance on the absolute character of classical logic which is taken as an underlying framework.

The aim of this paper is twofold. First, I shall present some shortcomings of the standard conception of computation based on what was termed Church´s Thesis, i.e., the claim that the class of functions which can be computed by machines is identical to the class of functions that can be computed by Turing machines. Second, I shall emphatically point to a further theoretical limitation of our current, orthodox conception of computation, namely, its assumption of classical logic as the definitive background from which one could decide what machines can compute. Finally, I shall briefly examine some of the consequences of these two lines of criticism to Philosophy of Mind and to Cognitive Science. The inheritance of Church´s Thesis as well as of the assumption of classical logic as an absolute constraint to machine computation seem to have originated a myth - the myth that Turing´s article of 1936 sets forth once and for all the limits of what any machine can compute. Such a mythical interpretation of Turing´s conception of computation also gives rise to endless discussions concerning the existence of non-computable cognitive activities and possible asymmetries between minds and machines or human brains and machines. Examples of the inheritance of this mythical red herring are the work of John Lucas (1961) and, more recently, of Roger Penrose (1989, 1994). Furthermore, I suggest that philosophers of mind and cognitive scientists were too hasty in dispensing with the physical-symbol classical cognitivist approach to Artificial Intelligence. As we shall see, the rejection of the view that the brain´s cognitive activity can be simulated by a computing machine takes for granted the theoretical limitations we refer to, and, without offering a supporting argument, shun the possibility that the human brain might be a non-classical computing machine.


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