and S2 are in K2; otherwise it is placed in K1", and "A formula having the form ~S is placed in K2, if S is in K1; otherwise it is placed in K1". Hence Nagel and Newman can now define the notion of tautologous: "a formula is a tautology if and only if it falls in the class K1, no matter in which of the two classes its elements are placed". This way, the property of "being tautologous" is described—without reference to a model or an interpretation. Post observed that, if the system were inconsistent, a deduction in it (that is, the last formula in a sequence of formulas derived from the tautologies) could ultimately yield S itself. As an assignment to variable S can come from either class K1 or K2, the deduction violates the inheritance characteristic of tautology (i.e., the derivation must yield an evaluation of a formula that will fall into class K1). From this, Post was able to derive the following definition of inconsistency—without the use of the notion of contradiction: In other words, the notion of "contradiction" can be dispensed when constructing a proof of consistency; what replaces it is the notion of "mutually exclusive and exhaustive" classes. An axiomatic system need not include the notion of "contradiction". Philosophy Adherents of the epistemological theory of coherentism typically claim that as a necessary condition of the justification of a belief, that belief must form a part of a logically non-contradictory system of beliefs. Some dialetheists, including Graham Priest, have argued that coherence may not require consistency. Pragmatic contradictions A pragmatic contradiction occurs when the very statement of the argument contradicts the claims it purports. An inconsistency arises, in this case, because the act of utterance, rather than the content of what is said, undermines its conclusion. Dialectical materialism In dialectical materialism: Contradiction—as derived from Hegelianism—usually refers to an opposition inherently existing within one realm, one unified force or object. This contradiction, as opposed to metaphysical thinking, is not an objectively impossible thing, because these contradicting forces exist in objective reality, not cancelling each other out, but actually defining each other's existence. According to Marxist theory, such a contradiction can be found, for example, in the fact that: (a) enormous wealth and productive powers coexist alongside: (b) extreme poverty and misery; (c) the existence of (a) being contrary to the existence of (b). Hegelian and Marxist theory