axiom
Part of speech: noun
Morphological type: simple
Topics: human-sciences
logic
mathematics
philosophy
sciences
Etymology: From Middle French axiome in the 15th century, from Latin axiōma (“axiom; principle”), from Ancient Greek ἀξίωμα (axíōma, “that which is thought to fit, a requisite, that which a pupil is required to know beforehand, a self-evident principle”), from ἀξιόω (axióō, “to think fit or worthy, to require, to demand”), from ἄξιος (áxios, “fit, worthy”, literally “weighing as much as; of like value”), from ἄγω (ágō, “to weigh (down)”).
Inflected forms:
form: axioms
pos: noun
tags: plural
form: axiomata
pos: noun
tags: plural
Senses:
gloss: A seemingly self-evident or necessary truth which is based on assumption; a principle or proposition which cannot actually be proved or disproved.
pos: noun
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.
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.
Can we then find axioms as self-evident as those of Arithmetic, on which we can build as on a sure foundation, which could be shaken only by a scepticism which should attack the whole fabric of our knowledge?
gloss: 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).
pos: noun
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; […]
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.
The axioms of arithmetic imply that when you expand (a + b)², for example, you get a² + 2ab + b² in the following way: (a + b)² is equal to (a + b)(a + b). Each term in one parentheses multiplies the terms in the other: a × a = a² ; a × b = ab; b × a = ab; b × b = b². Combining the terms, a² + ab + ab + b² = a² + 2ab + b². In a similar way, a² – b², a squared number subtracted from another squared number, called a difference of squares, becomes (a – b)(a + b), which becomes a² + ab – ab – b², which is a² – b².
gloss: An established principle in some artistic practice or science that is universally received.
pos: noun
examples: 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.
For a moment Frank recoiled, with a young man's antipathy, from the idea of his sister turning out a femme savante; but having fortunately retained the axiom that "there is no offence in blue stockings provided the petticoats are long enough to hide them," […] he rejoiced that, doomed to live with a foolish old woman like her aunt, and a knot of stupid country neighbours, his sister had provided for herself in the old library a host of invaluable acquaintances, with whom she could live, and move, and have her being.
Related words: conjecture
corollary
demonstration
hypothesis
law
lemma
porism
postulate
premise
principle
proof
proposition
theorem
theory
truism
Derived words: axiomatic
axiomatical
axiomatically
axiomatisation
axiomatization
axiomatise
axiomatize
axiomic
axiomless
axiomlike
axiom of countable choice
axiom of extensionality
axiom schema
axiom scheme
axiom system
closure axiom
field axiom
Luce's choice axiom
nonaggression axiom
non-aggression axiom
Pasch's axiom
Peano axiom
Wightman axiom
Translations: