You seem to be assuming that philosophers are somehow restricted to using natural language only, but
* the formalization and regimentation of natural language has always been a fairly central concern in philosophy (that's where formal logic comes from);
* mathematics can be, and used to be, done in largely natural language.
What was a good definition of philosopher then is not what is a good definition now. Meaning evolves!
I invite you to think historically, and in terms of ongoing differentiation of science: the drive towards formalising/axiomatising mathematics which was started in earnest at the end of the 19th, beginning of the 20th century, has been accelerating. These days mathematics is partly verified in interactive theorem provers like Isabelle/HOL, Coq, Agda and Lean. A Fields medallist (Voevodsky) dedicated his post-Fields career towards more mechanisation of Mathematics. I predict that in 100 years from now, mathematics that is not formalised in a mechanical tool will not be publishable in reputable venues.
Philosophy is also much more formal than it was 1000 years ago (e.g. compare [1] to [2]). Indeed, the formalization of mathematics was driven by philosophers trying to put mathematical reasoning on an adequate foundation.
* the formalization and regimentation of natural language has always been a fairly central concern in philosophy (that's where formal logic comes from);
* mathematics can be, and used to be, done in largely natural language.