I can validate an axiom by observing what the axiom claims. I cannot validate an axiom, as it is the most fundamental rule on which everything else in philosophy is built.
I think you mean " I can validate … I cannot prove …"
Lexicon: Validation
“Validation” in the broad sense includes any process of relating mental contents to the facts of reality. Direct perception, the method of validating axioms, is one such process. “Proof” designates another type of validation. Proof is the process of deriving a conclusion logically from antecedent knowledge.
edit: There is nothing antecedent to existence, thus the designation of it as a primary, and its relation to all other ideas as one of primacy. (“Primacy” does not simply mean “important”, it has a technical meaning.)
As an example:
Primacy of Existence cannot be proven
A. Proof cannot begin by premising facts external to consciousness because that begs the question.
B. Proof cannot begin by premising facts about consciousness as that contradicts the thesis that facts external to consciousness must be known first before awareness of awareness is possible.
C. There are no other kinds of premises.
D. Primacy of Existence cannot be a conclusion.
E. “P of E” is self-evident not arbitrary or an act of faith.
F. “P of E” is axiomatic because existence is implicit in any and all instances of awareness, any attempt to deny it affirms it.
G. The third person external perspective when used to explain consciousness is implicitly a primacy of existence perspective.
Primacy of Consciousness cannot be proven
A. Proof cannot begin by premising facts external to consciousness because that contradicts the thesis.
B. Proof cannot begin by premising facts about consciousness as that begs the question.
C. There are no other kinds of premises.
D. Primacy of Consciousness cannot be a conclusion.
E. “P of C” is not self-evident, it relies on prior a metaphysical dualism, a theory.
F. “P of C” is not axiomatic because “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.” That other something is necessarily first, the true primacy.
G. The third person external perspective when used to explain consciousness is implicitly a (contradictory) primacy of existence perspective.