Illogical vs. Alogical
Illogicaladjective
Contrary to logic; lacking sense or sound reasoning.
Illogicaladjective
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.
Illogicaladjective
lacking in correct logical relation
Illogicaladjective
lacking orderly continuity;
Alogicaladjective
Not based upon logic or reasoned argument.
Alogicaladjective
Opposed to logic.
