Copyright © Philip M. Parker, INSEAD. Terms of Use.
Definition: Axiom |
AxiomNoun1. A saying that widely accepted on its own merits. 2. (logic) a proposition that is not susceptible of proof or disproof; its truth is assumed to be self-evident. Source: WordNet 1.7.1 Copyright © 2001 by Princeton University. All rights reserved. |
Date "axiom" was first used: 1485. (references) |
Etymology: Axiom \Ax"i*om\, noun. [Latin expression axioma, Greek that which is thought worthy, that which is assumed, basis of demonstration, principle, from to think worthy, from worthy, weighing as much as; compare to to lead, drive, also to weigh so much: cf French axiome. See Agent,]. (references) |
| Domain | Definition |
Computing | AXIOM |
Source: compiled by the editor from various references; see credits. | |
(From Wikipedia, the free Encyclopedia)
In epistemology, an axiom is a self-evident truth upon which other knowledge must rest, from which other knowledge is built up. To say the least, not all epistemologists agree that axioms, understood in that sense, exist.
As the word axiom is understood in mathematics, an axiom is not a proposition that is self-evident. Rather, it simply means a starting point in a logical system. For example, in some rings, the operation of multiplication is commutative, and in some it is not; those rings in which it is are said to satisfy the "axiom of commutativity of multiplication." Another name for an axiom is postulate. An axiom is an elementary basis for a formal logic system that together with the rules of inference define a logic.
For instance, (misquoting Peano) simple arithmetic including addition can be defined and many theorems proven by assuming
1 + 2 = 1 + inc(1) Expansion of abbreviation (2 = inc(1))Any fact that we can derive from the axioms need not be an axiom. Anything that we cannot derive from the axioms and for which we also cannot derive the negation might reasonably added as an axiom.1 + 2 = inc(1) + 1 Axiom 4
1 + 2 = 2 + 1 Abbreviation (2 = inc(1))
1 + 2 = 2 + inc(0) Expansion of abbreviation (1 = inc(0))
1 + 2 = inc(2) + 0 Axiom 4
1 + 2 = 3 Axiom 3 and Use of abbreviation (inc(2) = 3)
Probably the most famous very early set of axiom are the 4+1 postulates of Euclid. These turn out to be fairly incomplete, actually, and many more postulates are necessary to completely characterize his geometry (Hilbert used 23).
I say 4+1 since the 5th postulate (through a point outside a line there is exactly one parallel) was suspected to be derivable from the first 4 for nearly two millennia. Ultimately, the fifth postulate was found to be independent of the first four. Indeed, one can assume that no parallels through a point outside a line exist, that exactly one exists, or that infinitely many exist. These choices give us alternative forms of geometry in which the interior angles of a triangle add up to less than, exactly or more than a straight line respectively and are known as elliptic, Euclidean and hyperbolic geometries. The general theory of relativity is essentially a claim that mass gives space hyperbolic geometry.
The fact that alternative forms of geometry might exist was very troubling to mathematicians of the 19th century and in similar developments, say Boolean Algebra, there were generally elaborate efforts taken to derive the system from normal arithmetic systems. Galois showed just before his untimely death that these efforts were largely wasted but that the grand parallels between axiomatic systems could be put to good use as he algebraicly solved many classical geometrical problems. Ultimately, the abstract parallels between algebraic systems were seen to be more important than the details and modern algebra was born.
In the twentieth century, Gödel's Incompleteness Theorem showed that no explicit (i.e. recursive) set of axioms sufficiently large for ordinary mathematics could be both (1) complete (i.e. every statement can be either proved or disproved) and (2) consistent (i.e. no statement can be both proved and disproved).
See also:
Source: adapted by the editor from Wikipedia, the free encyclopedia under a copyleft GNU Free Documentation License (GFDL) from the article "Axiom."
Synonym: AxiomSynonym: maxim (n). (additional references) |
| Context | Synonyms within Context (source: adapted from Roget's Thesaurus). |
Maxim | Axiom, theorem, scholium, truism, postulate. |
| Source: adapted from Roget's Thesaurus. | |
Crosswords: Axiom |
| English words defined with "axiom": Murphy's Law ♦ posit, position, postulate. (references) |
| Specialty definitions using "axiom": Axiom of Choice, Axiom of Comprehension, AXIOM* ♦ Banach-Tarski paradox ♦ Cogito ergo sum ♦ Extended Self-containing Prolog ♦ Gilderoy's Kite ♦ infinite set ♦ Nail in One's Coffin ♦ Plowden ♦ Russell's Attic, Russell's Paradox ♦ Scratchpad II ♦ Zermelo Fränkel set theory, Zermelo set theory. (references) |
| Etymologies containing "axiom": maxim. (references) |
| Non-English Usage: "Axiom" is also a word in the following languages with English translations in parentheses. Czech (axiom), German (axiom), Swedish (axiom, axioms). |
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Source: compiled by the editor from various references; see credits. | |||
| Title | Author | Quote |
Sylvie and Bruno Concluded | Carroll, Lewis | An Axiom, you know, is a thing that you accept without contradiction. |
Source: compiled by the editor from various references. | ||
| "Axiom" is generally used as a noun (singular) -- approximately 97.56% of the time. "Axiom" is used about 82 times out of a sample of 100 million words spoken or written in English. Its rank is based on over 700,000 words used in the English language. Some parts-of-speech are not covered due to the samples used by the British National Corpus. (note: percents less than one-hundredth of one percent have been omitted) |
| Parts of Speech | Percent | Usage per 100 Million Words | Rank in English |
| Noun (singular) | 97.56% | 80 | 37,112 |
| Lexical Verb (infinitive) | 1.22% | 1 | 339,140 |
| Noun (common) | 1.22% | 1 | 339,140 |
| Total | 100.00% | 82 | N/A |
Source: compiled by the editor from several corpora; see credits.
| Country | Name |
| Australia | Axiom Properties Ltd. |
| (more examples...) |
Source: compiled by the editor from Icon Group International, Inc.
Expressions using "axiom": axiom of choice ♦ axiom of Comprehension. Additional references. | |
| Source: compiled by the editor from various references; see credits. |
| The following statistics estimate the number of searches per day across the major English-language search engines as identified by various trade publications. Hyperlinks lead to commercial use of the expression at Amazon.com. |
| Language | Translations for "axiom"; alternative meanings/domain in parentheses. | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Afrikaans | aksioom, aksioma. (various references) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Albanian | aksiomë. (various references) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Arabic | مسلمة (muslim, postulate, presupposition), حقيقة مقررة, بديهية. (various references) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Bulgarian | аксиома (principle). (various references) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Chinese | 公理 (Axiomatic, truism). (various references) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Czech | axiom. (various references) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Danish | aksiom (postulate), postulat (postulate). (various references) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Dutch | axioma (postulate), grondstelling. (various references) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Esperanto | aksiomo. (various references) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Farsi | پند (Advice, Aphorism, Maxim, Moral, Motto, Precept, Rede), قضیه حقیقی , قاعده کلی (Maxim), حقیقت متعارفه , حقیقت اشکار, اندرز (Advice, Counsel, Motto, Sermon), اصل عمومی , بدیهیات . (various references) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Finnish | aksiooma (postulate), postulaatti (postulate). (various references) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
French | axiome. (various references) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
German | axiom (postulate), grundsatz (Canon, dogma, maxim, policy, precept, principle, tenet, theorem). (various references) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Greek | αξίωμα (capacity, commission, dignity, office, principle, tenet). (various references) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Hebrew | מושכל ראשון, ו"א", אמת" (truism, truth), אקסיומ". (various references) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Hungarian | axióma, alapigazság (elemental truth). (various references) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Icelandic | grundvallarregla, frumsenda, frumregla. (various references) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Indonesian | asas (basis, foundation, principle), aksioma, kaidah (method, principle, rule). (various references) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Italian | assioma (postulate). (various references) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Japanese Kanji | 自明の理 (self-evident truth, truism), 公理 (maxim, self-evident truth). (various references) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Japanese Katakana | "うり (high-interest rate, large profits, luggage, maxim, portmanteau, public official, retail, self-evident truth, utility, wicker trunk), じめいのり (self-evident truth, truism). (various references) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Korean | 통칙. (various references) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Manx | jarroo-raa (motto, shibboleth), feerid (authenticity, perfection, reality, simplicity, truth, veracity), baghtaght. (various references) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Pig Latin | axiomay axioma (maxim, postulate). (various references) axiomã. (various references) аксиома (fundamental truth). (various references) aksiom. (various references) axioma (postulate). (various references) axiom (axioms). (various references) กฎเก"ฑ์ที่ยอมรับกันทั่วไป. (various references) aksiyom (axiomatic), belit. (various references) аксіома. (various references) sự thật (truly, truth), phương ngôn (dialect), chân lý. (various references) gwireb (aphorism, truism). (various references) | ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| Language | Period | Translations |
| Greek | 700 BCE-300 CE | axioma. (various references) |
| Latin | 500 BCE-Modern | axioma. (various references) |
| Source: compiled by the editor from various references. | ||
Derivations | |
Words beginning with "axiom": axiomatic, axiomatically, axiomatisation, axiomatisations, axiomatization, axiomatizations, axiomatize, axiomatized, axiomatizes, axiomatizing, axioms. (additional references) | |
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"Axiom" is suggested in spellcheckers for the following: agion, Aimo, aion, ajion, Asicom, Asioz, axem, axeo, axie, axiem, axien, axim, axime, axio, axioe, axiol, axioma, axiome, axion, axiop, Axios, axium, axoid, axom, axum, Axxiom, azio, exigo, exio, famicom, haxhiu, maxiom, oxiom, oxion. (additional references) | |
| Source: compiled by the editor, based on several corpora (additional references). | |
| # of Phoneme Matches | Pronunciation | Word(s) rhyming with "axiom" (pronounced a"ksēum) |
| 4 | -s ē u m | calcium, lawrencium, paramecium, potassium. |
| 3 | -ē u m | alluvium, ammonium, aquarium, atrium, auditorium, bacterium, barium, beryllium, cadmium, cesium, chromium, colloquium, compendium, condominium, consortium, crematorium, delirium, deuterium, disequilibrium, emporium, equilibrium, europium, fermium, gallium, geranium, gonium, gymnasium, hafnium, harmonium, helium, Herbarium, holmium, honorarium, idiom, indium, iridium, linoleum, lithium, magnesium, medium, millennium, minium, moratorium, myocardium, nephridium, neptunium, niobium, nobelium, opium, opprobrium, osmium, palladium, pandemonium, petroleum, planetarium, Plasmodium, plutonium, podium, polonium, premium, presidium, promethium, protium, psyllium, radium, requiem, rhodium, selenium, sodium, stadium, strontium, superpremium, symposium, tedium, tellurium, thallium, thorium, titanium, tritium, uranium, vanadium, yttrium, zirconium. |
Source: compiled by the editor (additional references); see credits. | ||
Scrabble® Enable2K-Verified Anagrams | |
| Words within the letters "a-i-m-o-x" | |
-1 letter: maxi, moxa, oxim. | |
-2 letters: aim, ami, max, mix, moa. | |
-3 letters: ai, am, ax, ma, mi, mo, om, ox, xi. | |
| Words containing the letters "a-i-m-o-x" | |
+1 letter: axioms. | |
+2 letters: chamoix, mailbox, toxemia. | |
+3 letters: amphioxi, anoxemia, anoxemic, apomixes, apomixis, cacomixl, exogamic, exonumia, maxicoat, monaxial, proximal, toxaemia, toxaemic, toxemias. | |
+4 letters: amphioxus, anoxemias, axiomatic, cacomixls, exogamies, hypoxemia, mailboxes, maxicoats, myxoviral, proximate, tamoxifen, taxonomic, toxaemias. | |
+5 letters: axiomatize, axoplasmic, chemotaxis, dominatrix, exhumation, hypoxemias, proximally, tamoxifens, taxonomies, taxonomist, xenogamies. | |
| Source: compiled by the editor from various references; see credits. SCRABBLE® is a registered trademark. All intellectual property rights in and to the game are owned in the U.S.A and Canada by Hasbro Inc., and throughout the rest of the world by J.W. Spear & Sons Limited of Maidenhead, Berkshire, England, a subsidiary of Mattel Inc. Mattel and Spear are not affiliated with Hasbro. | |
| 1. Definition 2. Synonyms 3. Crosswords 4. Usage: Commercial | 5. Quotations: Fiction 6. Usage Frequency 7. Names: Company Usage 8. Expressions | 9. Expressions: Internet 10. Translations: Modern 11. Translations: Ancient 12. Derivations | 13. Rhymes 14. Anagrams 15. Bibliography |
Copyright © Philip M. Parker, INSEAD. Terms of Use.
