North Texas Objectivist Society (NTOS) Message Board › Metaphysics: The peculiarity of the primary axiomatic concepts
Axioms are usually considered to be propositions identifying a fundamental, self-evident truth. But explicit propositions as such are not primaries: they are made of concepts. The base of man's knowledge—of all other concepts, all axioms, propositions and thought—consists of axiomatic concepts.
An axiomatic concept is the identification of a primary fact of reality, which cannot be analyzed, i.e., reduced to other facts or broken into component parts. It is implicit in all facts and in all knowledge. It is the fundamentally given and directly perceived or experienced, which requires no proof or explanation, but on which all proofs and explanations rest.
The first and primary axiomatic concepts are "existence," "identity" (which is a corollary of "existence") and "consciousness." One can study what exists and how consciousness functions; but one cannot analyze (or "prove") existence as such, or consciousness as such. These are irreducible primaries. (An attempt to "prove" them is self-contradictory: it is an attempt to "prove" existence by means of nonexistence, and consciousness by means of unconsciousness.)
Existence, identity and consciousness are concepts in that they require identification in conceptual form. Their peculiarity lies in the fact that they are perceived or experienced directly, but grasped conceptually. They are implicit in every state of awareness, from the first sensation to the first percept to the sum of all concepts. After the first discriminated sensation (or percept), man's subsequent knowledge adds nothing to the basic facts designated by the terms "existence," "identity," "consciousness"—these facts are contained in any single state of awareness; but what is added by subsequent knowledge is the epistemological need to identify them consciously and self-consciously. The awareness of this need can be reached only at an advanced stage of conceptual development, when one has acquired a sufficient volume of knowledge—and the identification, the fully conscious grasp, can be achieved only by a process of abstraction.
—Ayn Rand, Introduction to Objectivist Epistemology, “Axiomatic Concepts”