I would say that has a physics based answer as well that is made more precise by a non-semantic answer... sliders for amount of mixing and flipping, firmness, temperature of griddle, testing for color change, etc all tie directly into physics or sensors and trying to write a "Sunny Side Up" function first, then writing an "Over Easy" function, and then writing a "Scrambled" function become much easier and more robust when those names map to setting of the physics model.
You've asserted the existence of a physics based answer, but you haven't answered what the "physics-based" criteria of an egg being "cooked" is. I assert that a straightforward short definition does not exist.