_________________________________________________________________ Revista Eletrônica Informação e Cognição, v.4, n.1, p.61-73, 2002-2005. ISSN:1807-8281 Le logica impecabile del irrational Walter Carnielli Gruppo de Logica Theoric e Applicate CLE/IFCH — Universidade Estatal de Campinas 13081-970 Campinas, SP — Brasil carniell@cle.unicamp.br 1 “Io pensa que il poterea ducer a resultatos fructifere si alicun de iste logicos, qui trova satisfaction e placer in disveloppar systemas symbolic, imitarea lê exemplo de Leibniz, Descartes, Peano e Couturat, e dirigerea lor pensamento al problema de projectar un lingua international.” Rudolf Carnap, in “Carnap’s Intellectual Autobiography”, The Library of Living Philosophers, Inc. 1963 (ed. P. A. Shilpp) English abstract This paper is written in INTERLINGUA 2 , 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. 1. Parve historia e importantia philosophic del paraconsistentia Le historia del investigation logic super le inconsistente o le contradictori non es longe. Le duo (assi considerate) fundatores, laborante in modo independente e vidente le question ab differente perspectivas, esseva le logico polonese Stanislaw Jaskowski e le logico brasilian Newton C. A. da Costa. Le prime publicava su ideas in lingua polonese in 1948 e 1949, e ha apparite in lingua anglese solo in 1968 (cf. [Jas48]). Le secunde introduceva su ideas in un these durante le annos sexanta, e ha apparite in lingua anglese in [dC74]. Comoqunque, per alcune persone, le duo fundatores son tre (un ver situation contradictori): le logic norte-american David Nelson in 1949 jam publicava in [Nel49] ideas e resultates supra theorias matematic “inconsistente” sed non “supracomplete”. In su proposition per un logica discussive (o discursive) Jaskowski (in [Jas48]) argumenta que le principio aristotelic que affirma “Le principio que duo assertiones contradictori non son ambes ver es le plus certe de totes” (apud J. Lukasiewicz in [Luk10]) non poterea esser transferite intro le logica moderne sin prudentia. Ergo le principio aristotelic de non-contradiction, “Duo assertiones contradictori non son ambes ver”, deberea esser 1 Un version de iste articulo appare in lingua romanian in le publication Krisis (cf. [Car98]). Le recerca ha essite partialmente financiate per CNPq e CAPES (Brasil). 2 Io vole regratiar a Emerson José Silveira da Costa per su adjuta in le scriptura de iste texto in INTERLINGUA.