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The Collaborative International Dictionary
Antilogy

Antilogy \An*til"o*gy\ ([a^]n*t[i^]l"[-o]*j[y^]), n.; pl. Antilogies (-j[i^]z). [Gr. 'antilogi`a, fr. 'anti`logos contradictory; 'anti` against + le`gein to speak.] A contradiction between any words or passages in an author.
--Sir W. Hamilton.

Wiktionary
antilogy

n. (context rhetoric English) A contradiction in related terms or ideas. Usually an inconsistency in syllogisms, of a person or group supposedly of one set of ideals.

Usage examples of "antilogy".

SPIRIT OF THE PITIES But O, the intolerable antilogy Of making figments feel!