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. The algorithmic nature of thought is not proven, nor is it disproven by virtue of Turing excercises.