Of madness and many-valuedness: an investigation into Suszko's Thesis

Suszko’s Thesis is a philosophical claim regarding the nature of many-valuedness. It was formulated by the Polish logician Roman Suszko during the middle 70s and states the existence of “only but two truth values”. The thesis is a reaction against the notion of many-valuedness conceived by Jan Łukasiewicz. Reputed as one of the modern founders of many-valued logics, Łukasiewicz considered a third undetermined value in addition to the traditional Fregean values of Truth and Falsehood. For Łukasiewicz, his third value could be seen as a step beyond the Aristotelian dichotomy of Being and non-Being. According to Suszko, Łukasiewicz’s ideas rested on a confusion between algebraic values (what sentences describe/denote) and logical values (truth and falsity). Thus, Łukasiewicz’s third undetermined value is no more than an algebraic value, a possible denotation for a sentence, but not a genuine logical value. Suszko’s Thesis is endorsed by a formal result baptized as Suszko’s Reduction, a theorem that states every Tarskian logic may be characterized by a two-valued semantics. The present study is intended as a thorough investigation of Suszko’s thesis and its implications. The first part is devoted to the historical roots of many-valuedness and introduce Suszko’s main motivations in formulating the double character of truth-values by drawing the distinction in between algebraic and logical values. The second part explores Suszko’s Reduction and presents the developments achieved from it; the properties of two-valued semantics in comparison to many-valued semantics are also explored and discussed. Last but not least, the third part investigates the notion of logical values in the context of non-Tarskian notions of entailment; the meaning of Suszko’s thesis within such frameworks is also discussed. Moreover, the philosophical foundations for non-Tarskian notions of entailment are explored in the light of recent debates concerning logical pluralism.

Tramas da (ir)racionalidade contemporânea para a composição do mito-tecno-lógico

The plot myth-techno-logic, contemporary, was developed starting from the dualism myth-reason. In this study, we deepened the alluded dualism taking as reference the historical contexts of the Renaissance and of the Enlightenment, emphasizing the discussion of the economical rationalization as conductive thread of the western development, in which we identified the game of the rational and of the irrational, for assure the superiority of the reason. In the context of that game, we analyzed the implications of the modernization, for the education, in function of the instrumental rationality, responsible for the environment of adaptation of the technological instruments to the scenery of the contemporary modernization. The new context is constituted by points of union and of ruptures among the technique, the science and the myth. Through our analysis, we noticed that the basic needs for the contemporary society were linked to the changes in the production means, for which the machine determine the rhythm of the work and the quality of the product. However, the changes in the productive processes promoted the appearance of the commercial marks that, as we see it, they represented the synthesis of the perfect harmony of the myth, of the technique, of the science and of the technology, in the conduction of the economical rationalization to the contemporary modernization. Thus, the contemporary modernization it arrives us for the economical rationalization, developed with the support of the technician-scientific knowledge and communicated by the articulations of the myth-techno-logical

Uma reavaliação do pensamento lógico de George Boole à luz da história da matemática

The aim of the present study is to reevaluate the logical thought of the English mathematician George Boole (1815 - 1864). Thus, our research centers on the mathematical analysis of logic in the context of the history of mathematics. In order to do so, we present various biographical considerations about Boole in the light of events that happened in the 19th century and their consequences for mathematical production. We briefly describe Boole's innovations in the areas of differential equations and invariant theory and undertake an analysis of Boole's logic, especially as formulated in the book The Mathematical Analysis of Logic, comparing it not only with the traditional Aristotelian logic, but also with modern symbolic logic. We conclude that Boole, as he intended, expanded logic both in terms of its content and also in terms of its methods and formal elaboration. We further conclude that his purpose was the mathematical modeling of deductive reasoning, which led him to present an innovative formalism for logic and, because the different ways it can be interpreted, a new conception of mathematics