For clarification, in a deduction system, an axiom is a proposition that is true just because. Similarly, an axiom schema is a predicate, such that substituting its free variables with closed terms yields a proposition that is true just because.

Now, I repeat, how exactly is Lisp “just axioms”? What are the axioms in question? The mathematical ignorance of some of Lisp's proponents never ceases to amaze me.