antilogy

n. contradiction, refutation

In logic, a contradiction consists of a logical incompatibility between two or more propositions. It occurs when the propositions, taken together, yield two conclusions which form the logical inversions of each other. Illustrating a general tendency in applied logic, Aristotle’s law of noncontradiction states that “One cannot say of something that it is and that it is not in the same respect and at the same time.”
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(n.)
A contradiction between any words or passages in an author.
  

n.
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antilogy /æn'tilədʤi/
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