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 non-existence, and consciousness by means of unconsciousness.)