axiom

1. (philosophy) A seemingly self-evident or necessary truth which is based on assumption; a principle or proposition which cannot actually be proved or disproved.Examples: "Near-synonyms: given, facticity"; "Neither can I reconcile this opinion of yours, with your argument brought from reaſon; if the axiom there laid down by you be true, it follows that, when matter began to exiſt in the divine mind, either matter became of the nature of the divine mind, i.e. active and intelligent, or elſe the divine mind became of the nature of matter, i.e. inert and unintelligent: this is a hard dilemma; have we not reaſon to ſuſpect that axiom?"; "Theoretical philosophy Plato divides into three branches, Theological, Physical, and Mathematical. On Theology, the fundamental doctrine of Plato, as of all other ancient philosophers, is, that from nothing nothing can proceed. This universal axiom, applied not only to the infinite efficient, but to the material cause, Plato, in his Timæus, lays down as the ground of his reasoning concerning the origin of the world."Synonyms: axioma#Noun, postulate#Noun

2. (logic, mathematics, proof theory) A fundamental assumption that serves as a basis for deduction of theorems; a postulate (sometimes distinguished from postulates as being universally applicable, whereas postulates are particular to a certain science or context).Examples: "Holonym: formal system"; "Near-synonyms: given, facticity"; "[…] Geometry, an excellent Logic, as you obſerve, where the definitions are clear, where the Poſtulata cannot be refuſed, nor the Axioms denied; […]"Synonyms: axioma#Noun, postulate#Noun