Consistency
General references
Neh 5:9; Mat 6:24; Luk 16:13; Rom 14:22; 1Co 10:21 Deceit; Expediency; Hypocrisy; Inconsistency; Obduracy; Prudence
Fuente: Nave’s Topical Bible
Consistency
(1) A logistic system (q.v.) is consistent if there is no theorem whose negation is a theorem. See Logic, formal, 1, 3, 6; also Proof theory.
Since this definition of consistency is relative to the choice if a particular notation as representing negation, the following definition is sometimes used instead(2) A logistic system is consistent if not every formula (not every sentence) is a theorem. In the case of many familiar systems, under the usual choice as to which notation represents negation, the equivalence of this sense of consistency to the previous one is immediate.
Closely related to (2), and applicable to logistic systems containing the pure propositional calculus (see Logic, formal, 1) or an appropriate part of it, is the notion of consistency in the sense of E. L. Post, according to which a system is consistent if a formula composed of a single propositional variable (say the formula p) is not a theorem. — A.C.