Meaning, Metaphysics, and Contradiction

International audienceThe spread of paraconsistent logics and dialetheism has produced a good deal of discussion of the principle referred to as "Law of Contradiction," or, better, "Law of Non Contradiction" (LNC). Dialetheists typically think that some sentences, called dialetheias, are both true and false. Given that negation turns truth into falsehood and vice versa (a view on negation that most-though, admittedly, not all-dialetheists accept), the negation of a dialetheia is both true and false, so it is a dialetheia. A conjunction of a dialetheia with its negation is itself a dialetheia. If by "contradiction" is meant the conjunction of a sentence and its negation, it follows that some contradictions are true and false. As a result of this, the LNC fails (although it is a very peculiar failure: in most versions of dialetheism the LNC nonetheless is a logical law, in a sense to be explained later). Much of the discussion on this topic has been very interesting and valuable, even if a part of it seems to have also outlined a failure to make it clear what the Law in question is. It is obvious that the LNC is supposed to somehow forbid, or exclude, contradictions. But a study of the literature on the subject has recently allowed Patrick Grim to identify about 240 different options in the formulation of the relevant notions. In this paper, some evidence is provided that different formulations may be interpreted as reflecting one basic idea. A taxonomy that will be useful later is the following