Axiom (nonfiction)

An axiom or postulate is a premise or starting point of reasoning.

As classically conceived, an axiom is a premise so evident as to be accepted as true without controversy.

As used in modern logic, an axiom is simply a premise or starting point for reasoning.

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.

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.

The word comes from the Greek axíōma (ἀξίωμα) 'that which is thought worthy or fit' or 'that which commends itself as evident.'

Fiction cross-reference

• Axiom Antics

Nonfiction cross-reference

• Lemma (nonfiction)

External links:

• Axiom @ Wikipedia