Before we start epistemology, we have to grasp a few points from metaphysics. Metaphysics studies the most fundamental nature of the universe, what is true of everything by virtue of its existing. Metaphysics boils down to a collection of axioms that define the realm of knowledge; thus, it is the starting point in a study of epistemology.
Axiom of existence. To Ayn Rand, existence is the fundamental, unquestionable fact. It's the self-evident starting point beyond which it is not correct to venture. She rejects questions like ``Why is existence here?'' and ``Why is it this way instead of that?'' Logically, she says, such questions are self-contradictory; they lead to an explanation in terms of non-existence, which is nothing (thus we are lead to such absurdities as ``nothing precedes beingness''). Existence is our starting point.
Axiom of consciousness. Ayn Rand also held that consciousness is a self-evident fact, consciousness here being the faculty of perceiving existence as it really is. (What does consciousness mean-bring into focus?) Again Ayn Rand rejects a whole host of questions like ``How do you know the world is not very different from what we think it is?'' as self-refuting.
Ayn Rand was fond of saying that Reality is absolute. This states the relationship between existence and consciousness. Facts aren't malleable; things are what they are; wishing won't make it so. Consciousness perceives reality, it doesn't create it.
The Axiom of identity states that a thing is something, it has a nature, an identity. (For example, tennis balls are round.) A corollary to identity is the law of non-contradiction: ``I thing can't be both A and non-A.'' I am a person, not a dog; this is a finger, not a fire-hose. Another corollary of identity is the Law of causality. Causality is the law of identity applied to action; the identity of an object determines how it will act. The world is a lawful, orderly place ruled by causal law. This view of causality is different than the usual one. We are taught to think in terms of ``actions'' and ``re-actions,'' actions leading to actions, ``I drop the ball (cause), it bounces back up (effect).'' While this is true, it is not a primary: the primary is ``the ball is bouncy (cause), so it bounces back up (effect).'' When I drop an egg, the effect is much different even though the dropping-action is the same.
In Objectivism, metaphysics-basically the three words existence, consciousness, and identity-are the starting points of knowledge. As AR put it, they ``sum up the essence of cognition: something exists of which I am conscious, I must discover its identity.'' Identity and causality define the realm of knowledge, what we are out to discover. The law of non-contradiction gives us our basic rule in logic: contradictions do not exist.