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axiom

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See also:Axiom

English

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WOTD – 16 March 2017

Etymology

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A statue honouring the GreekmathematicianEuclid (fl. 300b.c.e.) at theOxford University Museum of Natural History inOxford,Oxfordshire,England, UK
One of Euclid’sdistinctivepostulates, or axioms, is theparallel postulate, which states that if aline segmentintersects two straight lines forming twointerior angles(α and β in the diagram above) on the same side that sum to less than tworight angles, then the two lines, if extended indefinitely, meet on that side on which the angles sum to less than two right angles

FromMiddle Frenchaxiome in the 15th century, fromLatinaxiōma(axiom;principle), fromAncient Greekἀξίωμα(axíōma,that which isthought tofit, arequisite, that which apupil is required toknowbeforehand, aself-evident principle), fromἀξιόω(axióō,to think fit orworthy, torequire, todemand), fromἄξιος(áxios,fit, worthy, literallyweighing as much as; of likevalue), fromἄγω(ágō,to weigh (down)).

Pronunciation

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Noun

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Examples (mathematics)

Through a pair ofdistinctpoints there passes exactly onestraight line.
Allright angles arecongruent.

axiom (pluralaxiomsoraxiomata) (the latter is becoming less common and is sometimes considered archaic)

  1. (philosophy) Aseeminglyself-evident ornecessarytruth which is based onassumption; aprinciple orproposition which cannot actually beproved ordisproved.[2][3]
    • 1748 January,R. M., “To the Gent. who Signs Verax, V[olume] 17 p[age] 573. In Answer to His Defence of Mr Lyttelton's Expression, that Matter is not Inherent in the Deity.”, in “Sylvanus Urban” [pseudonym;Edward Cave], editor,The Gentleman's Magazine, and Historical Chronicle, volume XVIII, London: Printed by Edw[ard] Cave, atSt John's Gate,→OCLC,page 15, column 2:
      Neither can I reconcile this opinion of yours, with your argument brought from reaſon; if theaxiom 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 thataxiom?
    • 1837,William Enfield, “Chapter VIII. Of the Academic Sect. Section I. Of Plato and His Philosophy.”, inThe History of Philosophy, from the Earliest Periods: Drawn fromBrucker's Historia Critica Philosophiæ, London: Printed forThomas Tegg and Son, 73,Cheapside;R[ichard] Griffin and Co.,Glasgow; Tegg and Co.,Dublin; also, J. and S. A. Tegg,Sydney andHobart Town,→OCLC, book II,pages128–129:
      Theoretical philosophyPlato divides into three branches,Theological, Physical, andMathematical. OnTheology, the fundamental doctrine of Plato, as of all other ancient philosophers, is, that from nothing nothing can proceed. This universalaxiom, applied not only to the infinite efficient, but to the material cause, Plato, in hisTimæus, lays down as the ground of his reasoning concerning the origin of the world.
    • 1963 February, “Nobody runs this railway, mate”, inModern Railways, page73:
      Any publicity, runs theaxiom, is good publicity.
    • 1981,William Irwin Thompson,The Time Falling Bodies Take to Light: Mythology, Sexuality and the Origins of Culture, London: Rider/Hutchinson & Co., page16:
      "As above, so below" is anaxiom from Hermetic mysticism, and in this Hermetic vision of physiology the tongue is connected through the spinal column to the penis.
    • 1999,Bertrand Russell, edited by Charles R. Pigden,Russell on Ethics: Selections from the Writings of Bertrand Russell, London, New York, N.Y.:Routledge,→ISBN:
      Can we then findaxioms 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?
  2. (logic, mathematics, proof theory) Afundamentalassumption that serves as a basis fordeduction oftheorems; apostulate (sometimes distinguished from postulates as beinguniversally applicable, whereas postulates areparticular to a certain science or context).
    • 1734 April 10, “Philalethes Cantabrigiensis” [pseudonym;James Jurin],Geometry No Friend to Infidelity: Or, A Defence of SirIsaac Newton and the British Mathematicians, in a Letter to the Author ofThe Analyst, London: Printed for T. Cooper at the Globe in Ivy-Lane,→OCLC,page28:
      [] Geometry,an excellent Logic, as you obſerve,where the definitions are clear, where the Poſtulata cannot be refuſed, nor theAxioms denied;[]
    • 1992,Colin McLarty, “Rudimentary Structures in a Category”, inElementary Categories, Elementary Toposes (Oxford Logic Guides;21), Oxford:Clarendon Press; New York, N.Y.:Oxford University Press,→ISBN,page13:
      Theaxioms read as follows. For every composable pairf andg the compositefg{\displaystyle f\circ g} goes from the domain ofg to the codomain off. For each objectA the identity arrow1A{\displaystyle 1_{A}} goes fromA toA. Composing any arrow with an identity arrow (supposing that the two are composable) gives the original arrow. And composition is associative.
  3. Anestablishedprinciple in someartisticpractice orscience that isuniversallyreceived.
    Theaxioms of political economy cannot be considered absolute truths.
    • 1751,Giovanni Bianchi,A Dissertation against Blisters, Delivered in a Speech, before theLyncean Academy at Rimino, in June 1746, London: Printed by M. Cooper, at the Globe inPaternoster-Row, M. Sheepy, under theRoyal ExchangeCornhill; and J. Swan, opposite toNorthumberland-House byCharing-Cross,→OCLC,page40:
      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 theAxiom has it,cito, tuto, & jucunde, i.e. ſpeedily, ſafely, and pleaſantly.
    • 1822 January 18, “To the Christian Judge Bailey”, inThe Republican, volume V, number 3, Printed and published byR[ichard] Carlile, 55,Fleet Street,→OCLC,page337:
      That there is an incomprehended power in Nature, is anaxiom to which all must assent: but what that power is must be reduced to anaxiom likewise, before any defence of prophecy, miracle, or any kind of superstition, can be made on solid grounds.
    • 1835,A[lexander] Campbell, “Remission of Sins”, inA Connected View of the Principles and Rules by which theLiving Oracles may be Intelligibly and Certainly Interpreted: of the Foundation on which All Christians may Form One Communion: and of the Capital Positions Sustained in the Attempt to Restore the Original Gospel and Order of Things; Containing the Principal Extras of theMillennial Harbinger, Revised and Corrected, Bethany, Va.: Printed and published by M'Vay and Ewing,→OCLC,pages252–253:
      We proceed upon these as ouraxiomata 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. ThisPeter 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.
    • 1839, [Catherine Grace Frances Gore], “chapter IV”, inThe Cabinet Minister.[...] In Three Volumes, volume I, London:Richard Bentley,New Burlington Street,→OCLC,pages50–51:
      For a moment Frank recoiled, with a young man's antipathy, from the idea of his sister turning out afemme savante; but having fortunately retained theaxiom that "there is no offence inblue 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.

Synonyms

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Hypernyms

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Hyponyms

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Holonyms

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Derived terms

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Translations

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philosophy: supposed self‐evident or necessary truth
mathematics: fundamental assumption
established principle in art or science

See also

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other terms of interest

References

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  1. ^Axiom” in John Walker, A Critical Pronouncing Dictionary [] , London: Sold by G. G. J. andJ. Robinſon, Paternoſter Row; and T.Cadell, in the Strand, 1791,→OCLC, page 103.
  2. ^William Dwight Whitney,Benjamin E[li] Smith, editors (1911), “axiom”, inThe Century Dictionary [], New York, N.Y.:The Century Co.,→OCLC.
  3. ^axiom”, inWebster’s Revised Unabridged Dictionary, Springfield, Mass.:G. & C. Merriam,1913,→OCLC.

Further reading

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Anagrams

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Czech

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Pronunciation

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Noun

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axiom inan

  1. axiom

Declension

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Declension ofaxiom (hard masculine inanimate)
singularplural
nominativeaxiomaxiomy
genitiveaxiomuaxiomů
dativeaxiomuaxiomům
accusativeaxiomaxiomy
vocativeaxiomeaxiomy
locativeaxiomuaxiomech
instrumentalaxiomemaxiomy

Derived terms

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Related terms

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Swedish

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Noun

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axiom n

  1. axiom

Declension

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Declension ofaxiom
nominativegenitive
singularindefiniteaxiomaxioms
definiteaxiometaxiomets
pluralindefiniteaxiomaxioms
definiteaxiomenaxiomens

Related terms

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