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Principle vs Axiom vs Fundamental vs Law vs Theorem

Principle, axiomfundamentallawtheorem are comparable when they denote a proposition or other formulation stating a fact or a generalization accepted as true and basic.

Principle applies to a generalization that provides a basis for reasoning or a guide for conduct or procedure.

Axiom can apply to a principle that is not open to dispute because self-evident and is usually one upon which a structure of reasoning is or may be erected. Perhaps more frequently the term implies a principle universally accepted or regarded as worthy of acceptance rather than one necessarily true.

Fundamental usually applies to a principle, but sometimes a fact, so essential to a philosophy, religion, science, or art that its rejection would destroy the intellectual structure resting upon it.

Law applies to a formulation stating an order or relation of phenomena which is regarded as always holding good.

Theorem applies to a proposition that admits of rational proof and, usually, is logically necessary to succeeding logical steps in a structure of reasoning.