Diogo Dias

Pluralismo lógico é a tese de que há mais de uma lógica adequada. Diversos autores apontam Carnap como um dos precursores do pluralismo lógico. Mais que isso, afirmam que o Princípio de Tolerância consiste em uma das primeiras formulações explícitas de um pluralismo lógico. Não obstante, há poucas e esparsas investigações detalhadas para avaliar se o Princípio de Tolerância implica necessariamente em um pluralismo lógico e, caso implique, de qual tipo. O objetivo deste artigo é analisar o Princípio de Tolerância, bem como o contexto no qual tal princípio está inserido e, por fim, investigar qual a relação entre esse princípio e o pluralismo lógico.

Some strategies to turn any logic into a paraconsistent system are examined. In the environment of universal logic, we show how to paraconsistentize logics at the abstract level using a transformation in the class of all abstract logics called paraconsistentization by consistent sets. Moreover, by means of the notions of paradeduction and paraconsequence we go on applying the process of changing a logic converting it into a paraconsistent system. We also examine how this transformation can be performed using multideductive abstract logics. To conclude, the conceptual notion paraconsistent orbit of a logic is proposed.

This article begins with a general and abstract definition of logic and, particularly, of paraconsistent logics, to establish a common ground for the discussion. Briefly stating, these kinds of logics have the property of being non-explosive, that is, it is not possible to infer any conclusion from contradictory premises. Using these definitions, it is possible to analyze some of the philosophical aspects of paraconsistent logics, in particular, the relation between the notion of explosion and the law of non-contradiction, as well as the syntactic/semantic possibility and, above all, the metaphysical possibility of paraconsistent logics. I further analyze a stronger position towards paraconsistency, namely: the claim that there are true contradictions. This articles concludes with some possible critiques to paraconsistent logics – and their refutations as well –, and pose some open questions for further work.

Logical pluralism is the claim that there is more than one adequate logic. Many authors consider Carnap as one of the forerunners of logical pluralism. More than that, they claim that Carnap’s Principle of Tolerance consists in one of the first explicit formulations a logical pluralism. Nonetheless, there is little detailed investigation to evaluate if the Principle of Tolerance necessarily implies a logical pluralism, and if so, of which kind. The aim of this paper is to analyze the Principle of Tolerance, as well as its context, and to investigate the relation between such principle and logical pluralism.