Strange that you didn't correct what I said to Aurino...
I've taken a number of physics classes and a number of math classes. I've also read a good deal of physics. I'm not a physicist and don't pretend to be. But, I know when someone is making statements that are obviously false or misleading.
In any case, Aurino did not ask to define acceleration. What he said was: "why is it that you can't possibly run any experiment to prove that the definition of acceleration does not properly describe the motion of bodies in space?"
Now, there's two reasons why someone would ask that question, either that they don't know that you can measure acceleration that is properly described by dv/dt if measured against certain fixed positions along the path of the object, or they are questioning the whole issue of absolute position.
The second interpretation is more likely since Aurino's point in his first post was to substantiate his earlier question: "Since you acknowledge that the problem [that physical theories are not absolute but change over time] exists, how do you know that the 'mathematically valid' solutions of today won't turn out to be invalid as we gather more empirical knowledge?" What Aurino, I believe, sought to prove is that there is no absolute basis for acceleration (which if I'm not mistaken he should have used velocity) then what is the basis of physical law.
Dummy me I gave away the store by anticipating his questioning to that of reference frame and thereby gave him an opportunity to bail out of the dilemma he wished to pose (instead he could act as if he were asking me a simple physics equation out of the blue). Oh well, I'm not a physicist (let me repeat it, I'm not a physicist), so to anyone out there who would like an excuse to waive off my arguments for that reason, then here's your free pass. Of course, I myself would be concerned by something that Dick Feynman used to say quite often "the easiest person to fool is yourself". If you think discounting someone's argument should be based on status in a field and not the content of the argument, then you should feel very comfortable fooling yourself.
Regarding the internet posts (LANL, Rice university, Gödel's proof, etc) these are called references. I know, silly me for thinking that someone out to provide support or text which better describes what is being communicated.
Warm regards, Harv