I also disagree with your point and your arguments. So many sentences in your response are blatantly false. You can win the Olympics of jumping to conclusions.
Let's start with CS. CS is the set of first principles that are then applied to software. This is because CS is another branch of mathematics, starting with Boolean logic and discrete mathematics.
Language relevance is shown here. We are using it right now. It is not a complete system because some ideas can't be expressed in language and some sentences in a logical system can't be proved or disproved, but the overwhelming majority of sentences are useful.
And everything I have written is based on first principles, you can read about Gödel incompleteness theorem for a start. It applies to LLMs because it applies to all uses of language. Nothing is specific to neural networks.
In fact, go and read about Gödel, because it proves that no logical system is complete, and your worldview seems to be dependent on the outdated assumption that there should be such a complete system. This includes all reasoning systems and all of mathematics.