On explicandum versus explicatum

Settimo Termini

pp. 113-124

in: Rudolf Seising, Veronica Sanz González (eds), Soft computing in humanities and social sciences, Berlin, Springer, 2012

Abstract

The aim of this paper is twofold. First of all I want to present some old ideas revisited in the light of some of the many interesting new developments occurred in the course of these last ten years in the field of the foundations of fuzziness. Secondly I desire to present a tentative general framework in which it is possible to compare different attitudes and different approaches to the clarification of the conceptual problems arising from fuzziness and soft computing. In the paper, then, I shall use some names as banners to indicate a (crucial) problem (i.e., Carnap's problem, von Neumann's problem, Galileian science, Aristotelian science and so on). As it will be clear by reading the paper, the association of a name to a certain problem should not be considered as the result of a historically based profound investigation but only as a sort of slogan for a specific position and point of view. It is well known that Rudolf Carnap in the first pages of his Logical foundations of probability faced the (difficult) problem of the ways and procedures according to which a prescientific concept (which by its very nature is inexact) is trasformed into a (new) exact scientific concept. He called this transformation (the transition from the explicandum, the informal, qualitative, inexact prescientific notion to the explicatum, its scientific, quantitative, exact substitute) the procedure of explication, a procedure which, as Carnap immediately observed, presents a paradoxical aspect. While in ordinary scientific problems, he, in fact, observes, "both the datum and the solution are, under favorable conditions, formulated in exact terms ... in a problem of explication the datum, viz., the explicandum, is not given in exact terms; if it were, no explication would be necessary. Since the datum is inexact, the problem itself is not stated in exact terms; and yet we are asked to give an exact solution. This is one of the puzzling peculiarities of explication". One of the leading ideas of the paper will be to use the distinction made by Carnap between "explicandum" and "explicatum" to analyze a few conceptual questions arising in Fuzzy Set Theory (and Soft Computing).

Cited authors

Aristoteles

Carnap Rudolf