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A statement or proposition that is considered to be true without need of proof. An axiom need not be self-evident but should be consistent with the other axioms of a logical system.

The term "axiom" comes from the Greek axios meaning "worthy" and was used by many Greek philosophers and mathematicians, including Aristotle. Curiously, Euclid, whose axioms are best known of all, seems to have favored a more general phrase meaning "common notion."

Closely related is the postulate which is a less arbitrary or basic assumption, provisionally accepted for some particular purpose but more freely open to substitution.

Related entries

   • axiom of choice
   • axiomatic method

Related categories

   • LOGIC