# Axiom

An Axiom is a Formal Statement that is assumed to be necessarily True.

**AKA:**Formal Axiom, Assumption, Formal Assumption.**Context:**- It can be a Premise.
- It can be part of an Axiomatic System.
- …

**Example(s):**- an Axiom of Choice.
- a Mathematical Axiom,
- a Distributivity Axiom.
- a Set Axiom.

**See:**Fact, Ground Fact.

## References

- WordNet.
- maxim: a saying that is widely accepted on its own merits
- (logic) a proposition that is not susceptible of proof or disproof; its truth is assumed to be self-evident

- (Wikipedia, 2009) ⇒ http://en.wikipedia.org/wiki/Axiom
- In traditional logic, an axiom or postulate is a proposition that is not proved or demonstrated but considered to be either self-evident, or ...

- http://en.wiktionary.org/wiki/axiom
- 1. (philosophy) 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.
- 2. (mathematics) An unproved 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".
- 3. An established principle in some art or science that is universally received:
*The axioms of political economy cannot be considered absolute truths.*

- http://www.logic-classroom.info/glossary.htm
- axiom is a first principle or premise.