My understanding has always been that an axiomatic system requires certain undefined terms, called *primitives*, upon which the system’s defined terms and axioms are built. The point, obviously, is to avoid circular definitions.

For arithmetic, “successor” is undefined. (Successor is a term used to state the Induction Axiom). For geometry, “point” is undefined. And for systems of 2-logic, both “true” and “false” are undefined.

Does there in fact exist a deductive system that has no undefined terms and no circular definitions?