What is "axiom"

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 Agent, a.]

1. (Logic & Math.) A self-evident and necessary truth, or a proposition whose truth is so evident as first sight that no reasoning or demonstration can make it plainer; a proposition which it is necessary to take for granted; as, ``The whole is greater than a part;'' ``A thing can not, at the same time, be and not be.''

2. An established principle in some art or science, which, though not a necessary truth, is universally received; as, the axioms of political economy.

   Syn: Axiom, Maxim, Aphorism, Adage.

   Usage: An axiom is a self-evident truth which is taken for granted as the basis of reasoning. A maxim is a guiding principle sanctioned by experience, and relating especially to the practical concerns of life. An aphorism is a short sentence pithily expressing some valuable and general truth or sentiment. An adage is a saying of long-established authority and of universal application.

late 15c., from Middle French axiome, from Latin axioma, from Greek axioma "authority," literally "that which is thought worthy or fit," from axioun "to think worthy," from axios "worthy, worth, of like value, weighing as much," from PIE adjective *ag-ty-o- "weighty," from root *ag- "to drive, draw, move" (see act (n.)).\n\nAxioms in philosophy are not axioms until they are proved upon our pulses. [Keats, letter, May 3, 1818]

n. 1 (context philosophy English) A seemingly (l/en: self-evident) or necessary (l/en: truth) which is based on (l/en: assumption); a (l/en: principle) or (l/en: proposition) which cannot actually be proved or disproved. 2 (context mathematics logic proof theory English) A fundamental (l/en: assumption) that serves as a basis for (l/en: deduction) of theorems. Examples: "Through a pair of distinct points there passes exactly one straight line", "All right angles are congruent". 3 An established principle in some artistic practice or science that is universally received.

1. n. a saying that widely accepted on its own merits [syn: maxim]

2. (logic) a proposition that is not susceptible of proof or disproof; its truth is assumed to be self-evident

An axiom or postulate as defined in classic philosophy, is a statement (in mathematics often shown in symbolic form) that is so evident or well-established, that it is accepted without controversy or question. Thus, the axiom can be used as the premise or starting point for further reasoning or arguments, usually in logic or in mathematics. The word comes from the Greek axíōma 'that which is thought worthy or fit' or 'that which commends itself as evident.'

As used in modern logic, an axiom is simply a premise or starting point for reasoning. Whether it is meaningful (and, if so, what it means) for an axiom, or any mathematical statement, to be "true" is a central question in the philosophy of mathematics, with modern mathematicians holding a multitude of different opinions.

As used in mathematics, the term axiom is used in two related but distinguishable senses: "logical axioms" and "non-logical axioms". Logical axioms are usually statements that are taken to be true within the system of logic they define (e.g., (A and B) implies A), while non-logical axioms (e.g., ) are actually substantive assertions about the elements of the domain of a specific mathematical theory (such as arithmetic). When used in the latter sense, "axiom", "postulate", and "assumption" may be used interchangeably. In general, a non-logical axiom is not a self-evident truth, but rather a formal logical expression used in deduction to build a mathematical theory. As modern mathematics admits multiple, equally "true" systems of logic, precisely the same thing must be said for logical axioms - they both define and are specific to the particular system of logic that is being invoked. To axiomatize a system of knowledge is to show that its claims can be derived from a small, well-understood set of sentences (the axioms). There are typically multiple ways to axiomatize a given mathematical domain.

In both senses, an axiom is any mathematical statement that serves as a starting point from which other statements are logically derived. Within the system they define, axioms (unless redundant) cannot be derived by principles of deduction, nor are they demonstrable by mathematical proofs, simply because they are starting points; there is nothing else from which they logically follow otherwise they would be classified as theorems. However, an axiom in one system may be a theorem in another, and vice versa.

Axiom is a free, general-purpose computer algebra system. It consists of an interpreter environment, a compiler and a library, which defines a strongly typed, mathematically (mostly) correct type hierarchy.

Axiom were a rock band formed in Melbourne in 1969 and included musicians Glenn Shorrock and Brian Cadd.

An axiom is a proposition in mathematics and epistemology that is taken to be self-evident.

Axiom may also refer to:

Axiom is the ninth studio album by the London-based trip hop band Archive. It was released in May 2014.

AXIOM is an open hardware and free software digital cinema camera family of devices being developed by a DIY community around the apertus° project.

Axiom was a record label founded by musician Bill Laswell in 1989, with the support of Chris Blackwell, founder of Island Records. Axiom was an independent subdivision of Blackwell's Island Records, with Laswell being afforded a budget for a certain number of albums each year, basically of his own choosing. The freedom Blackwell gave Laswell gave rise to a number of studio albums and field recordings that otherwise would likely not have been made within the confines of a normal major label structure.

In 1989, Chris Blackwell sold Island Records to PolyGram, which, in 2000, became a subsidiary of the Universal Music Group—with Blackwell staying on as CEO. In 1997, Blackwell resigned from PolyGram after struggling with what he saw as restrictive oversight of his management. Axiom was (at that moment) shuttered as well, with most of the catalog falling out of print since then. When Blackwell started up his new venture, Palm Pictures, Laswell and the Axiom imprint were once again reactivated. Unfortunately, Palm since scaled back its involvement in the recorded-music field, effectively making Axiom dormant once again. A rumored play to buy the Axiom catalog from Universal Music also fizzled.

Under Island's aegis, Axiom released Sonny Sharrock's Ask the Ages and Henry Threadgill's Too Much Sugar for a Dime, as well as records by Laswell projects such as Praxis and Material. A series of stellar world-music titles were also released by Axiom, including Simon Shaheen's tribute to Mohammed Abdel Wahab, Shankar's Soul Searcher and pristine field recordings of Gnawa musicians in Morocco, Mandinka & Fulani Music in the Gambia and the famed Master Musicians of Jajouka in the Rif Mountains of Morocco. The major-label backing that Blackwell gave allowed Laswell to trek to these far out regions with modern equipment and make what are arguably the most pristine recordings of these ancient musics to date in their home environments.

After moving to Palm Pictures, Axiom released only a handful of albums, notably by Material and the group Tabla Beat Science, which included Zakir Hussain, Ustad Sultan Khan, Bill Laswell, Karsh Kale, and others.