> conception here is that one's layered abstractions is basically an informal mathematics... which is formally structured... which is a formal grammar. It's your internal language, using internal symbols instead of English names

Unless we're getting metaphysical to the point of describing quantum systems as possessig a language, there are various continuous analog systems that can compute without a formal grammar. The language system could be the one that thinks in discrete 'tokens'; the conscious system something more complex.