Le logica impecabile del irrational

Abstract

This paper is written in INTERLINGUA2, a form of modern Latin without declensions whose use in science was initiated by G. Peano, preceded by Descartes and Leibniz. I am following here the IALA conventions for INTERLINGUA of 1952. To the best of my knowledge, this is the first text in logic or philosophy ever written in INTERLINGUA. The paper offers an introduction to some philosophical and logical questions concerned with the problem of the contradictory in logic, traditionally seen as some form of irrationality, as well as a comparison between some distinct positions, their logical approaches and reciprocal criticisms. A brief account of the history of the subject is also sketched. In particular, some recent results about the logics of formal inconsistency (LFIs), the society semantics and its general form, the possible-translations semantics, are emphasized here not only as a new method for combining logics, but also as an impeccable foundation to what is taken to be as the irrational. These syntactical and semantical tools have the double intention of, on the one hand, to systematize and to precisely define an ample class of logic systems, and on the other hand to offer alternative semantic interpretations to certain less studied non-classical logics, while making possible to combine simple logics so as to obtain other logics with a richer structure. We try to assess here the interest, the degree of success and the capability the LFIs and of the possible-translations semantics (as well as its associate, the society semantics) as conceptual contrivances to overcome the irrational.