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.

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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.

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