Axioms are foundational statements in reasoning and arguments, accepted as true without requiring proof.
Their definition varies across fields, from self-evident truths in classic philosophy to starting points for reasoning in modern logic. In mathematics, axioms can be logical or non-logical, with the latter often called postulates or assumptions, forming the basis of mathematical theories.
The process of axiomatization involves deriving a system of knowledge from a small set of well-understood sentences.
Axioms are used as starting points for logical derivation, though the meaning and truth of axioms remain subjects of debate in mathematical philosophy. Non-logical axioms, while not always self-evident, play a crucial role in building mathematical theories through formal logical expressions.