Therefore, no object can have a property that exists only when the object is at rest. Because there is no absolute rest.
What are you talking about? Motion is definitely not absolute, and only Galilean invariance is needed to see that.
An object is at rest with respect to its own reference frame.
> The academic descendants of the same academics who believed in absolute rest now call themselves physicists and make the same mistake and assume that absolute rest exists.
In other words, you think all physicists are wrong and you're right?
Motion is absolute means that all is in motion. This is an axiom. When you say motion is not absolute, can you give an example of an object which is at rest, which does not move with the earth and does not move with the galaxy? There is no such object.
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.
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".
The ship is at rest with respect to its own reference frame.
> So do you deny that the earth is moving? I assume not.
The earth is at rest with respect to its own reference frame.
It is moving with respect to other things, such as the sun, or the center of the galaxy. Motion and rest are relative. This is the key concept, and I don't understand why you're having such trouble with it.