ax·i·om / ˈaksēəm/ • n. a statement or proposition that is regarded as being established, accepted, or self-evidently true: the axiom that supply equals demand. ∎  chiefly Math. a statement or proposition on which an abstractly defined structure is based.ORIGIN: late 15th cent.: from French axiome or Latin axioma, from Greek axiōma ‘what is thought fitting,’ from axios ‘worthy.’

axiom, axiomatic An axiom is an assumption, postulate, universally received principle, or self-evident truth. Most sociological theories rest on one or more undemonstrated axioms, for example, that all human action is rational, or—as in the case of Marxism—that the class struggle is the motor of history. Some sociologists refer to such axiomatic beliefs as ‘domain assumptions’ or ‘metatheoretical beliefs’. Thus, for example, in Metatheorizing in Sociology (1991), the American sociologist George Ritzer offers an explanation and defence of metatheorizing, which Ritzer defines as the investigation and analysis of theories. The book takes social theories themselves as the object of study, classifying and comparing them, and it includes a history of sociology using a meta-theoretical approach to trace the rise and demise of sociological paradigms.

axiom Assumption used as a basis for deductive reasoning. The axiomatic method is fundamental to the philosophy of modern mathematics: it was used by the Greeks and formalized early in the 20th century by David Hilbert. In an axiomatic system, certain undefined entities (terms) are taken and described by a set of axioms. Other, often unsuspected, relationships (theorems) are then deduced by logical reasoning. For example, the points, lines and angles of Euclidean geometry are connected by postulates; theorems, such as Pythagoras' theorem, can be deduced. This geometry describes measurements of position, distance and angle in space.

axiom In logic, a statement that is stipulated to be true for a particular chain of reasoning. See deduction.

axiom XV. — F. axiome or L. axiōma — Gr. axiōma self-evident principle, f. axioûn hold worthy, f. āxios worthy.
Hence axiomatic XVIII.