Abstract

The formal principle of inconsistency in logic, in the form in which it comes from Aristotle, asserts that two contradictory judgments are not both true. Since the 20th century logic has progressed towards ever higher formality, it might be more suitable to say that inconsistent sentences, rather than judgments, cannot be both true.1 The universally accepted and lectured classical calculus of sentences2 adopts this principle without reservations. Some of the more recent logical systems are limiting the scope of its applicability, and also the natural language in which we daily express our judgments and inferences accepts in some cases a simultaneous occurrence of contradictory sentences. This text sets out to present a brief and simplified outline of this state of affairs. The systems of logic that accept inconsistencies and the related issues concerning natural language will be presented against the background of classical logic.