Adriana RossiDepartment of "Cultura del progetto" II University of Naples, Faculty of Architecture , Aversa, Italy To speed up loading times,
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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 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 space of architecture can be declined at different scales of reading and intervention, permitting a gamut of representations that ranges from maximum abstraction with respect of the concrete space, to maximum detail. Each path allows for the rediscussion of the outcome of a formative process which orientates solutions and objectives. The result reflects Colin Rowe's [Rowe, 1984] teaching of Chomsky [Ciorra, 1993] or the mathematical logic laying at the base of the "variable linguistic" or of the ‘calculation with words' conceived by Zadeh [Zadeh, 1978]. The use of a method and the application of a process as "the art of thought" remind one also of the geometric experiments of Francesco Borromini or of his greatest admirer Guarino Guarini. Borromini chooses a geometrical figure, an equilateral triangle, to demonstrate how the unconventional use of this shape-structure could become the matrix of new architectural conceptions. The church of S. Carlo alle Quattro Fontane (1637-41) or the church of S. Ivo alla Sapienza (1643-60) show how the geometric-mathematical language is able to drive the formative intentionality over the conventional aspects. In the same way the process of geometrical deformation, brought to a head by Guarino Guarini treating the section of a cylinder, reveals how geometrical language can be a ‘weak' structure of thought able to investigate : "...against the certainty of reason... an anguished passion and working thought... suspended in time" [Griseri, 1967] (Figure 6). In our century Jacques Derrida has clarified better than any other intellectual how the lay-out of geometric research, in grasping the original sense of the constituent act, can succeed in expressing a new image of the world [Derrida, 1962]. In the architecture of Peter Eisenman, but also in that of Borromini or of Guarini, almost nothing remains of the hermetic exactness of geometric reasoning, but much of the geometric language shines through.
Finally, let us mention the so called principle of incompatibility.
The essence of this principle is that as the complexity of a
system increases, our ability to make precise and yet significant
statements about its behaviour diminishes until a threshold is
reached beyond which precision and significance (or relevance)
become almost mutually exclusive characteristics. It is in this
sense that precise quantitative analyses of the behaviour of
humanistic systems are not likely to have much relevance to the
real-world societal, political, economic, and other types of
problems which involve humans either as individuals or in groups
[Zadeh, 1973].
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