Any error of reasoning. Reasoning may fail in many ways, and a great variety of fallacies have been distinguished and named. The main division is into formal fallacies in which something purports to be deductively valid reasoning but is not, and informal fallacies in which some other mistake is made. Such mistakes may include the introduction of irrelevancies, failure to disambiguate terms, vagueness, misplaced precision, and so on. Many fallacies that have been named are here referred to under their names: See argumentum ad…, four-term fallacy, gambler’s fallacy, ignoratio elenchi, vicious circle.