Well, the friend had counterexamples to "math as a basis for society is good". I sort of skipped over that. They mentioned those who rationalized bad things like racism, and also Engels. (We both agree that communism is not a successful philosophy.) Counterexamples aren't really enough to dismiss an idea unless they're stronger than the evidence that the idea is good, but I couldn't think of such evidence at the time, and I still can't think of anything particularly convincing. There's no successful society to point at that derived all of its laws and givernment axiomatically.