SOMETHING PROFOUND FOR AMATEUR PHILOSOPHERS OF THE GODEL: The Godel / Penrose criticism is false outside of it’s narrow claims, because of a common misunderstanding of Godel’s claims, and what we mean by ‘axioms’, ‘closure’, ‘proof’, and ‘true’.
The insight is: “The sets of Mathematical reducibility are smaller than Computational reducibility, are smaller than (Re)Combinatorial reducibility are smaller than Evolutionary reducibility(combinatorial-adversarial)”.
Language is just a system of reducibility necessary for both communication and mental disambiguation, prediction, association, reasoning, calculating, and yes, computing. Mathematics is just a very simple cardinal language of positional names. There is no reason why any language is limited (not infinite).
In fact, the problem with the various languages (systems of reducibility listed above) other than mathematics, is that expressions (sentences) become long enough to override human ability to retain context sufficient to test episodes (relations), and so we must invent stories (programs, consisting of sentences) to reduce complexity to the limits of our cognitive ability to test consistency, correspondence, and coherence.
If you grasp this, it means that there is a single rule of language we call grammar (continuous recursive disambiguation) and that ordinary language is infinite in expansion and reducibility – and only limited by the human ability to hold context, the same way GPT3 /4 is limited by context (which is why it gives clown world answers).
