Turing-Church thesis, constructve mathematics and intuitionist logic

Abstract

At a first glance the Theory of computation relies on potential infinity and an organization aimed at solving a problem. Under such aspect it is like Mendeleev theory of chemistry. Also its theoretical development reiterates that of this scientific theory: it makes use of doubly negated propositions and its reasoning proceeds through ad absurdum proofs; a final, universal predicate of equivalence of all definitions of a computations is translated into an equality one, and at the same time intuitionist logic into classical logic. Yet, the last step of this development of current theory includes both a misleading notion of thesis and intuitive notions (e.g. the partial computable function, as stressed by some scholars). A program for a rational re-construction of the theory according to the theoretical development of the above mentioned theories is sketchy suggested.

The very nature of Turing-Church's thesis. Sketch of a program for a rational re-formulation of the theory of computation