you need to define real
he seems to think that math is the language of the universe or some idealism like that, and that therefore real numbers (more precisely, irrationals) can't be real since they contradict with his vision of reality
except math was never the language of the universe, it's a language that can model the universe, it can also model other things, just like other languages
math is real in the sense that it exists in our head, that we recognize collectively that it exists, it is not real in the sense that it’s reality itself
so real number aren't any less real than natural number, and, they are logically sound from the axioms we use