In [[logic]], a '''consistent''' [[theory]] is one that does not contain a [[contradiction]]. The lack of contradiction can be defined in either [[semantic]] or [[syntactic]] terms. The semantic definition states that a [[theory]] is consistent if it has a [[model]]; this is the sense used in traditional [http://en.wikipedia.org/wiki/Term_logic Aristotelian logic], although in contemporary [[mathematical]] [[logic]] the term satisfiable is used instead. The [[syntactic]] definition states that a [[theory]] is consistent if there is no [[formula]] P such that both P and its negation are provable from the [[axioms]] of the theory under its associated deductive system. | In [[logic]], a '''consistent''' [[theory]] is one that does not contain a [[contradiction]]. The lack of contradiction can be defined in either [[semantic]] or [[syntactic]] terms. The semantic definition states that a [[theory]] is consistent if it has a [[model]]; this is the sense used in traditional [http://en.wikipedia.org/wiki/Term_logic Aristotelian logic], although in contemporary [[mathematical]] [[logic]] the term satisfiable is used instead. The [[syntactic]] definition states that a [[theory]] is consistent if there is no [[formula]] P such that both P and its negation are provable from the [[axioms]] of the theory under its associated deductive system. |