"No math = no physics"

I would say that as a practical matter, this is true, because often, many theories make the same qualitative prediction, but different quantitative ones. The effect of gravity on light for instance. In Newtonian gravity, light affected the same as matter, but in General Relativity, the effect is larger. Another example would be flat-Earth theory gravity versus Newtonian. Flat-Earthers would say that the Earth is constantly accelerating upwards at 9.8 m/s^2. To a high level of precision, this matches the idea that objects are attracted by G M/ R^2. Difference becomes large at high altitudes (large R), where it is quantitatively different, but qualitatively the same.

One could probably get by setting up experiments where the only possible results are (same, different), but that's really the same as defining numbers of terms of what they lie between; i.e., calculating sqrt(2) by calculating the largest number < sqrt(2) and the smallest number > sqrt(2).

The rate of scientific progress jumped enormously after Newton, as people began thinking more and more quantitatively, and developed tools accordingly. This is not an accident.

"The amazing thing is that this is a scientifically productive rule - finding a new representation that gets rid of epiphenomenal distinctions, often means a substantially different theory of physics with experimental consequences!"

Yeah, I never understood this. The fact that switching two electrons should have no experimental consequences has dramatic experimental consequences. The fact that the phase of a wavefunction doesn't matter matters a great deal.

Physics shouldn't have logical contradictions.