An axiom is a proposition that defeats its opponents by the fact that they have to accept it and use it in the process of any attempt to deny it.
The philosophy of Objectivism has three axioms that it holds are implicit in any claim to knowledge of any sort. They are as follows: “Existence exists.” “Consciousness perceives existence.” “An existent is itself.” (Often referred to as “A is A,” or the Law of Identity.) These three metaphysical axioms form the fundamental base of Objectivism. A corollary of the Law of Identity is the Law of Causality, which states that an entity acts as itself.
Being implicit from the beginning, existence, consciousness, and identity are outside the province of proof. Proof is the derivation of a conclusion from antecedent knowledge, and nothing is antecedent to axioms. Axioms are the starting points of cognition, on which all proofs depend.
One knows that the axioms are true not by inference of any kind, but by sense perception. When one perceives a tomato, for example, there is no evidence that it exists, beyond the fact that one perceives it; there is no evidence that it is something, beyond the fact that one perceives it; and there is no evidence that one is aware, beyond the fact that one is perceiving it. Axioms are perceptual self-evidences. There is nothing to be said in their behalf except: look at reality. What is true of tomatoes applies equally to oranges, buildings, people, music, and stars.
Existence, consciousness, identity are presupposed by every statement and by every concept, including the concept of disagreement.
No one can think or perceive for another man. If reality, without your help, does not convince a person of the self-evident, he has abdicated reason and cannot be dealt with any further.