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illogical (adj.)

"without sound reasoning according to rules of logic," 1580s, from assimilated form of in- (1) "not, opposite of" + logical. Related: Illogically.

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Definitions of illogical from WordNet

illogical (adj.)
lacking in correct logical relation;
Synonyms: unlogical
illogical (adj.)
lacking orderly continuity;
Synonyms: confused / disconnected / disjointed / disordered / garbled / scattered / unconnected
From wordnet.princeton.edu