illogical, unlogical (adj)

lacking in correct logical relation

confused, disconnected, disjointed, disordered, garbled, illogical, scattered, unconnected (adj)

lacking orderly continuity

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

illogical (Adjective)

Contrary to logic; lacking sense or sound reasoning.

illogical

As the study of argument is of clear importance to the reasons that we hold things to be true, logic is of essential importance to rationality. Arguments may be logical if they are "conducted or assessed according to strict principles of validity", while they are rational according to the broader requirement that they are based on reason and knowledge. Logic and rationality have each been taken as fundamental concepts in philosophy. They are not one of the same thing. Philosophical rationalism in its most extreme form is the doctrine that knowledge can ultimately be founded on pure reason, while logicism is the doctrine that mathematical concepts, among others are reducible to pure logic.