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Issue 21 – Synthesis

Num°21 SYNTHESIS
Copertina

A ROAD TOWARDS A NEW PARADIGM

EDITORIAL

A pivot of philosophical epistemology from Kant onwards, the concept of synthesis in all its practical, theoretical, and methodological meanings does not yet seem to have found a satisfactory description and definition. It is Kant’s merit to have identified in the idea of synthesis – understood as something different from that of mere reversal of the analysis – one of the central questions of philosophy. However, as Maddalena argues in his essay, this achievement has remained equivocal or partial, as can be readily recognized in the Hegelian philosophy on which Pagano focuses in his study in the current issue. The idea of Kantian synthesis therefore remains an expression of a need – that of being able to have certainties even in the realm of empirical knowledge, certainties that take on some element different from concepts and which can assimilate the surrounding reality.

The results of the successive operations of adjustment to the fundamental Kantian intuition have been the object of varying evaluations. To sum up, I think it is interesting to recall the path drawn by Jean Cavaillès, a young and already established French philosopher of mathematics, killed in 1944 by the Nazis, whom he had actively fought in the ranks of the resistance. The hypothesis of Cavaillès, based above all on the end of the logicist hypothesis sanctioned by Gödel’s theorems, was that basically all philosophy following Kant had tried to amend the work of the German philosopher while remaining within a “philosophy of consciousness.” This philosophy led, on the one hand, to a concept of science as demonstration, both in the axiomatic version of Hilbert and in the phenomenological version of Husserl, and, on the other hand, to the idea of immediate intuitions, such as those of the first Wittgenstein or Brouwer. Both paths took Kant’s conception to its extreme consequences, correcting and amending it, but they had also sanctioned its end, just as in other ways Hegel himself had done in the nineteenth century, according to the famous reconstruction of Pareyson. The idea of a synthesis based on analysis that became demonstrativeness was overtly challenged by Gödel and was overthrown in subsequent mathematical history, well-documented here by Zalamea’s study on Grothendieck. This overthrowing has been rarely commented on by philosophers.

The crisis of the paradigm of the “philosophy of consciousness” prompted the need to entirely rethink the paradigm in mathematics and in other forms of knowledge. One of the possible hypotheses, defended by another French philosopher of mathematics, Albert Lautman, was Heidegger’s evenemential conception. However, this formulation was insufficient to serve as the basis of real steps or actual methodologies by means of which knowledge takes place. From this point of view, the tradition of mathematics and its foundation in the “gesture” that established it, remained unexplained and in fact inexplicable. However, except for some reference to a conception of mathematics and science as a “gesture,” Cavaillès did not present solutions. As a result, his interrupted work continued to be the manifestation of a need for a radical rethinking of synthesis and of the entire rational paradigm, which continues to hinge on the synthetic-analytical distinction, willingly or unwillingly. The well-known research of Morton White, Willard V. O. Quine, and Saul Kripke on the same subject went in the same direction, of course. We have not wanted to insist on their research here because it has been investigated for a long time within a paradigm that does not seem to have succeeded in correcting Kant’s work or in totally overthrowing it.

The present issue obviously does not claim to go beyond the manifestation of this need to overthrow the paradigm, although at the same time it suggests some theoretical hypotheses both from the point of view of philosophy (Maddalena) and mathematics (Zalamea). Of course, in addition to interest in the historical investigation of the concept of synthesis, which should be reaffirmed (Pagano), the issue aims at showing that whatever idea of synthesis one wants to propose, it will have to fulfill the task of including in itself policies and practices, as Spazio Filosofico asserts with the distinction among its parts. In this sense, Mary Parker Follett’s idea of integration (Santarelli) seems to be one of the possible versions of a new form of synthesizing, and a pragmatic version of the theory of decision, especially in its economic-social application (Baggio), looks promising as well. The studies on poetic synthesis in self-understanding offered by T.S. Eliot (Gigli), the hypotheses on literary creativity (Perez), and on musical creativity (Mazzola) also show the need to radically reformulate the paradigm.

It is, therefore, as in the usual spirit of Spazio Filosofico, an approach to problems and suggestions on various levels that pushes us to consider the philosophical issue as central to scientific and public life.

Giovanni Maddalena

Matteo Santarelli

 

Issue 21 – Synthesis

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Numero 21 SYNTHESIS September, 2018 - Autore:,   Condividi

 

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