Nonlogical vs. Illogical

Nonlogicaladjective

Not logical; not pertaining to logic.

Illogicaladjective

Contrary to logic; lacking sense or sound reasoning.

‘I received an illogical reply and that left me standing there feeling confused.’;

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;

‘a confused set of instructions’; ‘a confused dream about the end of the world’; ‘disconnected fragments of a story’; ‘scattered thoughts’;