It seems to me that when I say "every Hilbert space is convex", I'm not saying something in math; I'm saying something about math, in English. Yes, I might talk about the world by saying "the world has the structure of a Hilbert space". But then I might talk about blog commenters (not the ones here at OB) by saying they are like a horde of poo-throwing chimpanzees, and yet that doesn't make primatology a language.