I am trying to understand the hiearchy of foundational concepts in mathematics/logic.
Specifically, is it true that objects that are left undefined or primitive or atomic are in some sense "below" axioms? As an example, in Euclid's geometry a point is primitive (undefined, at least mathematically precisely) whereas the first postulate (axiom) talks about how to define a line segment from two points.
Halmos' Naive Set Theory (p2) seems to get the "natural" picture above backwards since it makes a point of using an axiom regarding the equality of sets as more fundamental (implying) membership in a set which it previously referred to as a primitive concept in axiomatic set theory.