"Existence exists — and the act of grasping that statement implies two corollary axioms: that something exists which one perceives and that one exists possessing consciousness, consciousness being the faculty of perceiving that which exists.

If nothing exists, there can be no consciousness: a consciousness with nothing to be conscious of is a contradiction in terms. A consciousness conscious of nothing but itself is a contradiction in terms: before it could identify itself as consciousness, it had to be conscious of something. If that which you claim to perceive does not exist, what you possess is not consciousness.

Whatever the degree of your knowledge, these two — existence and consciousness — are axioms you cannot escape, these two are the irreducible primaries implied in any action you undertake, in any part of your knowledge and in its sum, from the first ray of light you perceive at the start of your life to the widest erudition you might acquire at its end. Whether you know the shape of a pebble or the structure of a solar system, the axioms remain the same: that it exists and that you know it.

To exist is to be something, as distinguished from the nothing of nonexistence, it is to be an entity of a specific nature made of specific attributes. Centuries ago, the man who was — no matter what his errors — the greatest of your philosophers, has stated the formula defining the concept of existence and the rule of all knowledge: A is A. A thing is itself. You have never grasped the meaning of his statement. I am here to complete it: Existence is Identity, Consciousness is Identification."
Ayn Rand, For the New Intellectual, 124