The axioms are unquestionable truths universally valid and evident, which are often used as principles in the construction of a theory or as a basis for an argument.
Between the ancient greek philosophers, an axiom was what seemed true without the need for any proof. In many contexts, axiom is synonymous with a postulate, law or principle.
A axiomatic system It is the set of axioms that define a certain theory and that constitute the simplest truths from which the new results of that theory are demonstrated.
Axiomatic systems play an important role in the exact sciences, especially 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 Euclid’s principles In classical geometry, the Peano axioms in Arithmetic, Newton’s laws in classical mechanics and Einstein’s postulates in the theory of relativity.
Axiomatic systems exist in many other sciences. For example, in Communication Theory, Paul Watzlawick and his colleagues presented the communication axioms, which define the behavioral effects of human communication.
The word axiom derives from the Greek noun αξιωμα, which means ‘what seems fair’ or ‘what is considered obvious, without the need for demonstration’. The term comes from the Greek verb αξιοειν (axioein), which means ‘value’, which in turn comes from αξιος (axios): ‘valuable’, ‘valid’ or ‘worthy’.
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