IPA: /ɪˈlɒdʒɪkəlnəs/
KK: /ɪˈlɑdʒɪkəlnəs/
The state or quality of not being reasonable or logical in thought or reasoning.
The illogicalness of his argument made it hard to take him seriously.
Illogicalness → It is formed from "il-" (meaning not), "logical" (from Greek "logikos", meaning pertaining to reason), and "-ness" (meaning the state of being). The word describes the state of being not logical or lacking reason.
Think of 'not' ('il-') combined with 'reason' ('logical') to remember that 'illogicalness' means the state of being without reason.