LATIN DICTIONARYLexicon Latīnum
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“illogically” in Latin

Riddle & Arnold A Copious and Critical English–Latin Lexicon, 1864

illogically
vitiose (faultily; e.g., concludere; opposed to recte concludere, Cic.): inconstanter (not consistently; e.g., loqui, Cic., Ac., 2, 17): inscite (in a bungling way; Vid: Cic., N.D., 2, 13, 36).

Quick answer

What is the Latin word for illogically?
The usual Latin words for “illogically” are vitiōsus, incōnstāns, īnscītus; also conclūdō, loquor. The right choice depends on the sense; see the distinctions below.

Entry from J. E. Riddle & T. K. Arnold, A Copious and Critical English–Latin Lexicon (rev. C. Anthon, New York: Harper, 1864), digitised by Fergus J. P. Walsh, CC BY-SA 4.0; Latin markup adapted by latindictionary.co.