types of points and lineshas sanctioned the distinction, even in the field of knowledge, between common language and technical language, clarifying once and for all that it is the the type of link established between the symbol and the meaning that provides the symbol with its significance.Already in antiquity, the criticism raised by the sophists against the use of a common' language had established the premises for the definition of a technical, or pseudo-technical, language, which would be later adopted by Euclid in his Elements. Here, the first twenty-eight propositions, thanks to the uniqueness of the relations that link human intuitions to the properties of geometric entities, define absolute geometry; geometry, that is, which doesn't necessitate any preformulated theorem for its enunciation. In contrast, the other propositions, formulated with the aid of the fifth postulate, have demonstrated the impossibility of any axiomatic system whatever being always coherent with the reality of the natural world. This is why nineteenth century mathematicians and humanists disputed even the most concrete of the mathematical sciences, namely the arithmetic. The demonstrability' was actually a notion weaker than the truth.THE LOGIC OF FORMAL SYSTEMS WITHIN ARCHITECTURAL RESEARCHThe problems of interpretation, description, prediction and synthesis, and therefore the operative choices, are in fact resolved by the perceptive capacity of the intelligence. The procedures linked to the concept of "variable linguistic" [Chomsky, 1966; Zadeh, 1978] or of "calculation with words" [Zadeh, 1965] have proved themselves more adapted to describing choices of everyday life. It is, therefore, no wonder that in every field of knowledge deductive-inductive logic gives way to other types of logic considered more fluid.Euclidian logic is founded on the possibility of always deducing new theorems. Instead, propositional logic is founded on the possibilities of al...
