...because formal languages do not use implicit terms and implicit terms are the first application of proto semantics. Perhaps the semantics of explicit natural language is equivalent to that of formal language. But then that leaves out most of what is interesting in language.
A Google search for "language" and "mathematics" turns up many links to math being treated as a language but very few about using math to analyze natural language. The one I am looking at right now "The mathematics of Language" by Marcus Kracht assumes natural language and formal languages are equivalent.
May I be snarky in my own blog? When you assume natural language is equivalent to formal language you are really saying natural language is like math. I cannot see how anyone would confuse this with what is natural. You want to do math about math and call that language? Don't!
[What I mean: if you exclude language like "don't", you miss out on an a great deal of what makes language interesting and makes language work.]
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