In logic, a consistent theory's one that doesn't contain a contradiction. The lack of contradiction can be defined in either semantic or syntactic terms. The semantic definition states that a theory's consistent if it's a model; this's the sense used in traditional Aristotelian logic, although in contemporary mathematical logic the term satisfiable's used instead. The syntactic definition states that a theory's consistent if there's no formula P such that both P and its negation are provable fr… (More on Inconsistency)