They should take their own medicine. How would one test those three assumptions they make? As for Mathematics being selectively real, I agree with that totally

They should take their own medicine. How would one test those three assumptions they make? As for Mathematics being selectively real, I agree with that totally. Mathematics is just a language we use to describe models and their properties in a most rigorous way. That's all. Can we find a model of the universe from which we can derive all its properties? Unlikely (see Gödel), if so the model would have to be pretty "primitive" and thus too large for comprehension. But so what, we can find great models for certain aspects of reality, and I don't see a limit for how far this can be taken to get better and better models for more and more areas of reality.