Definitions of Axioms

Axioms are universally valid and obvious unquestionable truths, which are often used as principles in the construction of a theory or as the basis for an argument.

The word axiom derives from the Greek noun αξιωμα, which means ‘what seems fair’ or ‘what is considered obvious, without demonstration.’ The term comes from the Greek verb αξιοειν (axioein), which means ‘to value’, which in turn comes from αξιος (axios): ‘valuable’, ‘valid’ or ‘worthy’.

Among ancient Greek philosophers, an axiom was what seemed true without the need for any proof. In many contexts, axiom is synonymous with postulate, law or principle.

An axiomatic system is the set of axioms that define a certain theory and that constitute the simplest truths of which the new results of that theory are demonstrated.

Axiomatic systems have an important role in the exact sciences, especially in mathematics and physics, and the results demonstrated in multiple theories of these sciences are generally called theorems or laws.

Among the various axiomatics of mathematics and physics, the principles of Euclid in Classical Geometry, the axes of Peano in Arithmetic, Newton‘s laws in classical mechanics and Einstein’s postulates in the Theory of relativity gained notoriety.

There are axiomatic systems in many other sciences. For example, in Communication Theory, Paul Watzlawick and his colleagues presented the axioms of communication, which define the behavioral effects of human communication.