Illogical vs. Alogical: What's the Difference?

Illogical and Alogical Definitions
Illogical
Contradicting or disregarding the principles of logic.
Alogical
Beyond or outside the bounds of logic.
Illogical
Without logic; senseless.
Alogical
Not based upon logic or reasoned argument.
Illogical
Contrary to logic; lacking sense or sound reasoning.
I received an illogical reply and that left me standing there feeling confused.
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Alogical
Opposed to logic.
Illogical
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.
Illogical
Lacking in correct logical relation
Illogical
Lacking orderly continuity;
A confused set of instructions
A confused dream about the end of the world
Disconnected fragments of a story
Scattered thoughts