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> Motion is absolute means that all is in motion

That's not a usual use of “absolute”; “motion is universal” would be the normal way of expressing that idea.

> This is an axiom.

Well, you could have an axiomatic system in which that was an axiom, but I don't see why you would want to.

Can you give an example of a system which is not based on axioms? There is none. There may be hidden assumptions but there will always be axioms. Axioms are simply definitions that are kept constant. In your case you make the assumption that absolute rest exists. The axiom of the universality of motion is a good one because it agrees with the observations.

> In your case you make the assumption that absolute rest exists.

This is a straw man. No one is making that assumption. Something is in motion or at rest with respect to a reference frame. For some reason, you keep misinterpreting this statement and ranting about "absolute motion" and "absolute rest".

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