So, typically, formal axiomatic systems assume that an algorithm operates on data expressed using symbols from a finite alphabet and that the data processed can be infinitely large . It is patently obvious that the alphabet human information processors make us of is not finite. We coin new words at every turn of a clause, and we use old words in novel ways at the least opportunity. Besides, it is not clear what the words mean, even when they are old and well worn. Human information processing never operates on infinitely large data.
Sentences are never infinitely long.
Clauses are never infinitely complex. In fact, it is theoretically possible to list all clauses that a human listener or reader can understand. This is ridiculous. Turing Machines are Turing Machines and brains brains. The preceding two examples show how properties of formal models can be used to prove things about original entities the models are based on.