Axioms as Undeniable

"People disagree about axioms," we often hear. "What is self-evident to one may not be self-evident to another. How then can a man know that his axioms are objectively true? How can he ever be sure he is right?"

This argument starts by accepting the concept of "disagreement," which it uses to challenge the objectivity of any axioms, including existence, consciousness, and identity. The following condensed dialogue suggests one strategy by which to reveal the argument's contradictions. The strategy begins with A, the defender of axioms, purporting to reject outright the concept of "disagreement."

A. "Your objection to the self-evident has no validity. There is no such thing as disagreement. People agree about everything."

B. "That's absurd. People disagree constantly, about all kinds of things."

A. "How can they? There's nothing to disagree about, no subject matter. After all, nothing exists."

B. "Nonsense. All kinds of things exist. You know that as well as I do."

A. "That's one. You must accept the existence axiom even to utter the term 'disagreement.' But, to continue, I still claim that disagreement is unreal. How can people disagree, since they are unconscious beings who are unable to hold ideas at all?"

B. "Of course people hold ideas. They are conscious beings---you know that."

A. "There's another axiom. But even so, why is disagreement about ideas a problem? Why should it suggest that one or more of the parties is mistaken? Perhaps all of the people who disagree about the very same point are equally, objectively right."

B. "That's impossible. If two ideas contradict each other, they can't both be right. Contradictions can't exist in reality. After all, things are what they are. A is A."

Existence, consciousness, identity are presupposed by every statement and by every concept, including that of "disagreement." (They are presupposed even by invalid concepts, such as "ghost" or "analytic" truth.) In the act of voicing his objection, therefore, the objector has conceded the case. In any act of challenging or denying the three axioms, a man reaffirms them, no matter what the particular content of his challenge. The axioms are invulnerable.

The opponents of these axioms pose as defenders of truth, but it is only a pose. Their attack on the self-evident amounts to the charge: "Your belief in an idea doesn't necessarily make it true; you must prove it, because facts are what they are independent of your beliefs." Every element of this charge relies on the very axioms that these people are questioning and supposedly setting aside.