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The Collaborative International Dictionary
Illogicalness

Illogical \Il*log"ic*al\, a. Ignorant or negligent of the rules of logic or correct reasoning; as, an illogical disputant; contrary of the rules of logic or sound reasoning; as, an illogical inference. -- Il*log"ic*al*ly, adv. -- Il*log"ic*al*ness, n.

Wiktionary
illogicalness

n. The quality of being illogical.

WordNet
illogicalness

n. invalid or incorrect reasoning [syn: illogicality, illogic] [ant: logicality, logicality]