"The prime requisite of a set of postulates is that it be consistent. Since the ordinary notion of consistency involves that of contradiction, which again involves negation, and since this function does not appear in general as a primitive in [the generalized set of postulates] a new definition must be given."
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Jean Van Heijenoort, From Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931, Harvard University Press, 1977, p. 276.
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Contradiction
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