alogic1
/ˌeɪˈlɒdʒɪk/Chiefly Philosophy and Psychology
noun
Absence of logic; the quality or fact of not being influenced or determined by logic or rationality. Usually in neutral rather than pejorative sense: compare illogic.
Origin
1930s; earliest use found in Journal of Philosophy. From a- + logic.
alogic2
/eɪˈlɒdʒɪk/adjective
That does not follow logic; contrary to logic; illogical.
Origin
Mid 17th century (in an earlier sense). From (i) Middle French, French alogique.