A Socratic Dialogue

Socrates: "Sophocles, do you beleive in the validity of logic?"
Sophocles: "Well, how do you defined logic, Socrates?"
Socrates: "Logic is defined as that which is not illogical, and, that which is illogical is defined
as that which does not involve a logical contradiction, such as, asserting that
A and not A, can exist in the same time and in the same place."
Sophocles" "So, if I assert that A and not A can exist in the same time and the same place,
then I would be both wrong and illogical."
Socrates: "Yes, Sophocles, that would be true."
Sophocles: "Well, I suppose I would have to agree that with your definition, that logic is valid."
Socrates: "Then, Sophocles, you can no longer engage in fallacious arguments that involve
a logical contradiction."
Sophocles: "Yes, that is true. Logic compels that."