What makes math more than an extremely useful language? It's
   self-consistency; it's a self-supporting structure, unlike other
   languages, that has safeguards against uncertainty by having no
   room for a middle way.

   It's practical; while it's not necessary to use mathematics in
   engineering, it's shown itself to be quite effective at
   providing a perfected form (on paper, computer, whatever) that
   can then be constructed out of materials that are... less than
   perfect.

   But that's the pragmatism of it. In an ultimate sense, *can* it
   describe everything that is? Possibly, but unlikely. Until it
   can embrace uncertainty about its own validity within its own
   system, it will never be entirely complete at a language that
   can describe everything that is. It needs room for fiction, for
   lies, for awkward things for contradictions and the like -
   things that we're quite familiar with in the everyday world.

   It's not a flaw per-se; but an incompleteness inherent deep in
   the system itself, in my opinion. A system robust enough to *be*
   the entire territory as well as a map simultaneously ought to
   include things like "oughts" and "ought not", 'mights",
   paradoxes, etc. At the same time, I don't know of any other
   system that *is* that robust just yet, because it would have to
   include all of the other systems as well, plus the indescribable
   things.