stipulates that the dialectic nature of history will lead to the sublation, or synthesis, of its contradictions. Marx therefore postulated that history would logically make capitalism evolve into a socialist society where the means of production would equally serve the exploited and suffering class of society, thus resolving the prior contradiction between (a) and (b). Outside formal logic Colloquial usage can label actions or statements as contradicting each other when due (or perceived as due) to presuppositions which are contradictory in the logical sense. Proof by contradiction is used in mathematics to construct proofs. The scientific method uses contradiction to falsify bad theory. See also , a Monty Python sketch in which one of the two disputants repeatedly uses only contradictions in his argument Graham's hierarchy of disagreement Law of noncontradiction Notes and references Bibliography Józef Maria Bocheński 1960 Précis of Mathematical Logic, translated from the French and German editions by Otto Bird, D. Reidel, Dordrecht, South Holland. Jean van Heijenoort 1967 From Frege to Gödel: A Source Book in Mathematical Logic 1879-1931, Harvard University Press, Cambridge, MA, (pbk.) Ernest Nagel and James R. Newman 1958 Gödel's Proof, New York University Press, Card Catalog Number: 58-5610. External links Propositional calculus Marxist theory Mathematical logic Sentences by type Propositions Immediate inference Cognitive dissonance