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Definition of axioms in English English dictionary
propositions selected as the foundations of a field - classically geometry - which, together with methods of proof, allow other propositions to be proved in an ordered way The axiomatic method has powerfully influenced philosophy, although each feature of the method has been criticized as inappropriate for philosophy
Wffs that are stipulated as unproved premises for the proof of other wffs inside a formal system
a maxim widely accepted on its intrinsic merit; a statement accepted as true as the basis for argument or inference; an established rule or principle or a self-evident truth
A fundamental theorem that serves as a basis for deduction of other theorems. E.g., "A point has no mass; a line has no width. A plane is a flat surface with no mass and contains an infinity of points and lines"
A self-evident and necessary truth; a proposition which it is necessary to take for granted; a proposition whose truth is so evident that no reasoning or demonstration can make it plainer
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 self-evident and necessary truth; a proposition which it is necessary to take for granted; a proposition whose truth is so evident that no reasoning or demonstration can make it plainer. For example, "The whole is greater than a part
A symbolic algebra system, featuring a high level graphical user interface in front of a knowledge based core A complete hypertext users' guide is included; from Numerical Algorithms Group
Strictly speaking, an axiom is one of a set of fundamental formulas that one starts with to prove theorems by deduction In CYC®, the axioms are those formulas that have been locally asserted into the CYC® KB CYC® axioms are well-formed CYC® formulas, since the system won't let you add formulas to CYC® that are not well-formed However, not all well-formed CYC® formulas are axioms, since not all of them are actually in the KB And some of the formulas in the KB are not, strictly speaking, axioms, since they were added to the KB via inference, instead of being locally asserted In informal usage, though, Cyclists don't always adhere to the strict meaning of axiom, and may refer to a formula they are considering adding to the KB or have recently removed from the KB as an axiom Axiom is also the name of one of the internal KB data structure types
A statement which is accepted as a basis for further logical argument Generally axioms are self-evident truths or principles which are basic enough that there are no principles more basic from which to prove them
(postulate) In a mathematical or logical system, an initial proposition or statement that is accepted as true without proof and from which further statements, or theorems, can be derived In a mathematical proof, the axioms are often well-known formulae for which the proof has already been established
Logical condition constraining the behaviour of an object May be expressed as an invariant, or as a precondition or postcondition on one of the object's methods
A proposition formally accepted without demonstration, proof, or evidence as one of the starting-points for the systematic derivation of an organized body of knowledge Also see OCP, BGHT, ColE, noesis, and MacE
Axioms are the limits placed on a reality They can range from 0 to 33 When trying to do something from a higher axiom in a reality that cannot support it, then a contradiction is caused Axioms come in four categories: Technological, Social, Magic, and Spiritual
A basic assumption about a mathematical system from which theorems can be deduced For example, the system could be the points and lines in the plane Then an axiom would be that given any two distinct points in the plane, there is a unique line through them
An axiom is a statement or idea which people accept as being true. the long-held axiom that education leads to higher income. = principle. a rule or principle that is generally considered to be true (axioma, from , , from axios ). 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