The Cambridge encyclopedia of the language sciences
Cambridge University Press
Logicians generally employ coherence and consistency as synonyms naming the absence of contradictions in a group of SENTENCES, propositions, or beliefs, where a contradiction is the conjunction of a proposition and its negation. In metaphysical terms, logical incoherence or contradiction is the impossible instantiation of a property and some other, incompatible property, as in "the circle was square." Epistemically, a contradiction is an irrational belief in both a proposition and its denial.
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ISBN of the source publication: 9780521866897
Livingston, P. (2011). Coherence, logical. In P. C. Hogan (Ed.), The Cambridge encyclopedia of the language sciences (pp. 173-173). Cambridge: Cambridge University Press.