/ak"see euhm/, n.
1. a self-evident truth that requires no proof.
2. a universally accepted principle or rule.
3. Logic, Math. a proposition that is assumed without proof for the sake of studying the consequences that follow from it.
[1475-85; < L axioma < Gk: something worthy, equiv. to axio-, var. s. of axioûn to reckon worthy + -ma resultative n. suffix]

* * *

In mathematics or logic, an unprovable rule or first principle accepted as true because it is self-evident or particularly useful (e.g., "Nothing can both be and not be at the same time and in the same respect").

The term is often used interchangeably with postulate, though the latter term is sometimes reserved for mathematical applications (such as the postulates of Euclidean geometry). It should be contrasted with a theorem, which requires a rigorous proof.

* * *

      in logic, an indemonstrable first principle, rule, or maxim, that has found general acceptance or is thought worthy of common acceptance whether by virtue of a claim to intrinsic merit or on the basis of an appeal to self-evidence. An example would be: “Nothing can both be and not be at the same time and in the same respect.”

      In Euclid's (Euclid) Elements the first principles were listed in two categories, as postulates and as common notions. The former are principles of geometry and seem to have been thought of as required assumptions because their statement opened with “let there be demanded” (ētesthō). The common notions are evidently the same as what were termed “axioms” by Aristotle, who deemed axioms the first principles from which all demonstrative sciences must start; indeed Proclus, the last important Greek philosopher (“On the First Book of Euclid”), stated explicitly that the notion and axiom are synonymous. The principle distinguishing postulates from axioms, however, does not seem certain. Proclus debated various accounts of it, among them that postulates are peculiar to geometry whereas axioms are common either to all sciences that are concerned with quantity or to all sciences whatever.

      In modern times, mathematicians have often used the words postulate and axiom as synonyms. Some recommend that the term axiom be reserved for the axioms of logic and postulate for those assumptions or first principles beyond the principles of logic by which a particular mathematical discipline is defined. Compare theorem.

* * *

Universalium. 2010.

Игры ⚽ Нужно сделать НИР?

Look at other dictionaries:

  • Axiom — Fichier:Axiom sur les Champs Elysées.jpg Axiom sur les Champs Elysées à Paris Nom Hicham Kochman Naissance 19 janvier 1975 (1975 01 19) (36 ans) Lil …   Wikipédia en Français

  • Axiom — Тип система компьютерной алгебры Разработчик независимая группа людей Операционная система кроссплатформенное программное обеспечение Лицензия модифицированная лицензия BSD Сайт …   Википедия

  • Axiom — Saltar a navegación, búsqueda Axiom es un programa de álgebra computacional (CAS) muy útil para la investigación y el desarrollo de los algoritmos matemáticos, para los cuales define una sintaxis rigurosa, con niveles de jerarquías matemáticas… …   Wikipedia Español

  • Axiom S5 — is the distinctive axiom of the S5 modal logic and states that if necessarily possibly p , then possibly p . It also states, perhaps less intuitively and more controversially, that if possibly necessarily p , then necessarily p . The use of S5 is …   Wikipedia

  • Axiom — Ax i*om, n. [L. axioma, Gr. ? that which is thought worthy, that which is assumed, a basis of demonstration, a principle, fr. ? to think worthy, fr. ? worthy, weighing as much as; cf. ? to lead, drive, also to weigh so much: cf F. axiome. See… …   The Collaborative International Dictionary of English

  • Axiom — Sn Grundsatz erw. fach. (16. Jh., Form 18. Jh.) Entlehnung. Entlehnt aus gleichbedeutend l. axiōma, dieses aus gr. axíōma, einer Ableitung von gr. áxios würdig, wert , zunächst in lateinischer Form, dann endungslos. So benannt nach der Auffassung …   Etymologisches Wörterbuch der deutschen sprache

  • axiom — 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… …   Dictionary of sociology

  • axiom — [ak′sē əm] n. [Fr axiome < L axioma < Gr axiōma, authority, authoritative sentence < axioun, to think worthy < axios, worthy < base of agein, to weigh, orig., to lend: see ACT1] 1. a statement universally accepted as true; maxim 2 …   English World dictionary

  • Axĭom — (v. gr. Axiōma), unmittelbares, eines Beweises weder fähiges, noch bedürftiges Urtheil, Grundsatz (s.d.); daher Axiomăta hypostatĭca, in der Trinitätslehre die Merkmale, wodurch die 3 Personen der Gottheit als geschiedene kennbar werden. Daher… …   Pierer's Universal-Lexikon

  • Axiōm — (griech.), ein Satz von einleuchtender Gewißheit, der eines Beweises weder bedarf, noch fähig ist. Gäbe es nicht wirkliche Axiome, so fehlte allen Beweisen, durch die ja immer nur die Gewißheit eines Satzes auf die eines andern begründet wird,… …   Meyers Großes Konversations-Lexikon

  • Axiom — Axiom, eine Hypothese, auf der eine Wissenschaft aufgebaut wird, also z.B. in der Mechanik ein Satz, der nicht bewiesen werden kann. Alle Beweise in den mathematischen Wissenschaften sind Reduktionsmittel der Erkenntnis, d.h. sie sind Methoden,… …   Lexikon der gesamten Technik

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”