Axiom vs. a priori

Many libertarians use the word axiom when they mean “a (synthetic) a priori statement.” Rothbard and Hoppe use “axiom” in their writings (though they do talk about “a priori” statements, e.g., when Hoppe discusses the a priori of argumentation).

The use of axiom in this sense is not a precise use. An axiom is often referred to as a mathematical axiom. The difference between the two uses is that mathematical axioms are just postulated while when Rothbard and Hoppe refer to axioms they are referring to statements that are only deniable with contradiction. It is important the we do not use words that can be mistaken to have two or more different meanings for many people. ^[1]See my post about the use of “cannot” when talking about the a priori of argumentation.

To clarify what a (synthetic) a priori statement is, a (synthetic) a priori statement is a statement that tells us something “verifiable prior to any particular experience” and that tells us something “beyond what may be inferred from individual definitions of the words used in a claim.” ^[2]Chapter 0 in A Spontaneous Order by Chase Rachels.

For example, we can know before entering into any argumentation that “humans are capable of argumentation and hence know the meaning of truth and validity.” ^[3] Quote by Hans-Hermann Hoppe. See my post about the correct definition of the a priori of argumentation. This statement also tells us something beyond the individual words because from this fact we can construct a rationalist ethics via deduction that proves as unjustifiable any other assignment of property rights other than a libertarian assignment of property rights.