Ten things all languages have in common
blog.duolingo.com
blog.duolingo.com
Turning machines are only complete on a self-referential way, within the limited scope of computation.
Human language is far more complex than a Turing Machine language or any other computational language.
Or to relate it with computing terminology:
Language is digital but existence is analog.
And not all languages can communicate all ideas. Piraha is a famous example of a language without counting, and which also lacks abstract words.