An error in reasoning
inconsistency, illogicality, sophism, sophistry, casuistry, quibble, quibbling, evasion, deceit, deception, delusion, equivocation, subterfuge, Jesuitry, misinterpretation, erroneousness, inexactness, error, deviation from truth, perversion, bias, prejudice, preconception, non sequitur, deceptive belief, deceptiveness, aberration, falsity, false notion, misleading appearance, illusion, speciousness, equivoke, artifice, ambiguity, solecism, paradox, miscalculation, quirk, flaw, cavil, irrelevancy, erratum, invalidity, heresy, heterodoxy.
Antonyms logic*, reason*, law*.