Evandro Gomes

By discussing Wittgenstein’s views on negation, inference, tautology, contradiction, consistency, and inconsistency, we analyze, in the early, middle, and late periods of his philosophical career, the status of the ex falso sequitur quodlibet, which states that from the false any formula can be demonstrated, or ex contradictione sequitur quodlibet, which states that, from a contradiction, any formula can be demonstrated. We also discuss the status of the necessarium ex quodlibet sequitur, or necessarium sequitur ad quodlibet, which states that a necessity can be demonstrated from any formula. We conclude that, while the ex falso and the necessarium ex are tautologies in the logic of the Tractatus and of his initial transitional period, they do not allow one to deduce anything from a contradiction or to deduce a necessity from anything; and, therefore, triviality is not entailed by the presence of contradictions. However, for most of his intermediary period, as well as in his late philosophy, the ex falso may or may not entail trivialization, for pragmatic reasons. Based on this, we investigate the presence of relevance and paraconsistency in Wittgenstein’s approach to logic.