Uma Aplicação do Hexágono Lógico: organizando sistematicamente os conceitos de razão e causalidade [An application of the logical hexagon: a systematic organization of the concepts of reason and causality]

Este trabalho tem como objetivo fornecer uma aplicação do hexágono lógico aos conceitos metafísicos de razão e de causalidade. Após uma breve apresentação da abordagem de Blanché, passa-se à construção das estruturas geométricas. Primeiramente, são apresentadas duas tríades – razão lógica, acaso, causa; razão, não-causa, non sequitur. Em seguida, apresenta-se o hexágono lógico como a díade das duas primeiras estruturas. Conclui-se que o hexágono lógico é uma estrutura capaz de organizar sistematicamente os conceitos de razão e de causalidade. [This paper aims to show an application of the logical hexagon to the metaphysical concepts of reason and causality. After a brief presentation of Blanché’s approach, we proceed to build the geometrical structures. First, we show two triads – logical reason, chance, cause; reason, non-cause, non sequitur. Then we present the logical hexagon as a dyad built out of the first two structures. We conclude that the logical hexagon is able to organize the concepts of reason and causality in a systematic way.]

La transmission d'Aristote par les Arabes à la chrétienté occidentale. Une trouvaille relative au De Interpretatione

In chapter VII of On Interpretation, Aristotle alters a system of three pairs of natural contradictory propositions, in that he ignores the pair where two natural universals Men are white, Men are not white oppose each other contradictorily. This alteration has serious consequences: the two natural pairs, which Aristotle considers exclusively: All men are white versus Some men are not white and Some men are white versus No man is white are illegitimately identified to the two pairs of logical contradictories constituting the logical square: A versus 0 and I versus E respectively. Thus, the level of natural language and that of logic are confused. The unfortunate Aristotelian alteration is concealed by the translation of propositions known as indeterminates. To translate these, which, semantically, are particulars, all scholars, except for P.Gohlke, employ the two natural universals excluded by the master! The work of I. Pollak, published in Leipzig in 1913, reveals the origin of this nearly universal translation mistake: the Arabic version upon which AI-Farabi unfortunately bases his comment. In adding the vertices Y and U to the four ones of the square, the logical hexagon of Robert Blanche allows for the understanding of the manner in which the logical system and the natural system are linked.