axiom

noun

1. A seemingly self-evident or necessary truth which is based on assumption; a principle or proposition which cannot actually be proved or disproved.

   “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.”

   “Any publicity, runs the axiom, is good publicity.”

   “"As above, so below" is an axiom from Hermetic mysticism, and in this Hermetic vision of physiology the tongue is connected through the spinal column to the penis.”

2. 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).

   “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; […]”

   “The axioms read as follows. For every composable pair f and g the composite f#92;circg goes from the domain of g to the codomain of f. For each object A the identity arrow 1#95;A goes from A to A. Composing any arrow with an identity arrow (supposing that the two are composable) gives the original arrow. And composition is associative.”

3. An established principle in some artistic practice or science that is universally received.

   “The axioms of political economy cannot be considered absolute truths.”

   “But these innovating Medicaſters have introduced a Practice not only very precarious, but in many Reſpects extremely dangerous, and quite devoid of any one of the Qualities which conſtitute a good Remedy, viz. to cure the Patient, as the Axiom has it, cito, tuto, & jucunde, i.e. ſpeedily, ſafely, and pleaſantly.”

   “That there is an incomprehended power in Nature, is an axiom to which all must assent: but what that power is must be reduced to an axiom likewise, before any defence of prophecy, miracle, or any kind of superstition, can be made on solid grounds.”

   “We proceed upon these as our axiomata in all our reasonings, preachings, writings—1st. unfeigned faith; 2d. a good conscience; 3d. a pure heart; 4th. love. The testimony of God apprehended produces unfeigned or genuine faith; faith obeyed, produces a good conscience. This Peter defines to be the use of baptism, the answer of a good conscience. This produces a pure heart, and then the consummation is love—love to God and man.”