The ancient Greeks knew that reasoning is a structured process governed, at least partially, by a system of explainable rules. Aristotele codified syllogisms; Euclide formulated geometric theorems; Vitruvius defined the criterion and referential key so that every architectural element could be proportioned according to an ideal model, symbolizing the aspirations and aptitudes of that particular civil society.In these forms of reasoning it is possible to distinguish contingent aspects with regard to the role which the use of a method and the application of a procedure play within any conceptual process: communicable by virtue of the codes and the prescribed norms, comparable in every time and place by virtue of the reproducibility of the procedures.Euclidian logic begins with the inductive definition of very simple concepts and gradually constructs a vast body of results, organised in such a way so that each concept depends on the previous. Thus, a strong and rigorous construction is derived that makes all operations perceptible, comprehensible and intelligible. But, unlike processes that are physically constructed, Euclidian reasoning does not materially crumble if its structural elements, that is, its demonstrations, are not coherent with the reality of the empirical world. This explains why deductive-inductive logic, subtended by the philosophical-scientific thought of classical culture, has unconditionally influenced almost all fields of knowledge for almost two thousand years.Physical-mathematical knowledge was the first to understand the conventional character that is typical of axiomatic reasoning: ".. which firstly, and in the most rigorous manner, became conscious of the symbolic character of its fundamental instruments" [Cassirer, 1929]. The attempt to render Euclid's works without contradictions has caused a review of the form in which scientific work is carried out [Saccheri, 1733]. The verification of the existence of many...
