Rand describes axiomatic concepts as the identification of a primary fact of reality, which can not be analyzed, i.e., reduced to other facts or broken into component parts.
The second edition of this book provided an axiomatic theory of expected utility, which allowed mathematical statisticians and economists to treat decision-making under uncertainty.
Examples are the axiomatic moral view called the non-aggression principle and the political rules governing the behavior of one country toward another.
In science, abiogenesis is an independent hypothesis from evolutionary theory, which takes it as axiomatic that self-replicating life existed in the distant past, whatever its origin.
