The New Shorter Oxford English Dictionary gives three definitions.

1) a) An established or generally accepted principle;
b) a maxim;
c) a rule.

2) Logic. A proposition (true or false).

3) Math.
a) A self-evident truth;
b) a proposition on which an abstractly defined structure
is based.

Rand:axiom is 3a;
McCullough:axiom is 3b;
Ontolog Forum:axiom is ?;

 
Dick McCullough
Context Knowledge Systems
Name your propositions !

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