[fghorow]

As a working scientist, I read the OP with great interest (no pun intended).

In essence from my perspective, the axiomatic approach is like "theory" and the operational approach is like "experiment" or "observation" in the sciences.

There's a very good reason why experiment/observation trumps theory in the scientific method.

[dalbasal]

Good point. That said, the more distance from hard science you have, the likelier this is to go wrong.

If you're dealing with psychology, economics or such experimental observations can have the exact same problem. They're true in this case, at this level of abstraction or otherwise "not really wrong but not — but not as useful or as powerful as some other framing".

Framing is the key point here. What's in model or not. What questions are your trying to answer. etc. The harder the science, the less flexibility scientists have in framing.