What you miss is that this was the central message of Descartes about science and reality. "Deconstruction" is a cool word I guess, but the proper conversation is that human neural computation is a predication engine with essentially infinite expressibility, and science will always have more questions that can be asked and answered by empirical observation replicated by others.

You are right that this comes with the axioms -- what you can directly observe as true in some predication context. Near his death, Descartes was asked what is true, and he rightly said, anything you can deduce, assuming the axioms from which you make the deduction are all true. Recall, his seminal understanding in science was in geometry and came from Euclid's proofs.

You are onto something much much more profound and fundamental than shallow ideas like "deconstruction."

Predication is the fundamental computation in what neurons do for a living as revealed by natural language. And, it is there and there alone where the limits of our (scientific) knowledge are quite strictly, unlimited.

What reality is underneath this is what Descartes called the "perfection of God" and he asserted we would never necessarily know that, or need to know that since humans would never be able to necessarily know, or certainly, communicate it in natural language (or any known system of logic except computational logic by definition that require no axioms).

This was 50 years before Newton, by the father of the Age of Reason. Our brains are statistical engines of a form that nothing we have ever been able to build can yet reach, but building a brain computation engine is, unlike absolute truth, within our grasp.

So it isn't a question. Science, on any subject, will forever be asking more questions and getting answers that people can agree are true, in the predication context of the questions which is essentially never exhausted. We see this in human lying. (Not telling the truth is as informative as telling the truth...if not more informative if you care to study it.)

The proof that computational cognitive neuroscience has known this fundamental limitation in brain computation for over 40 years is a reference at this end of this article on the topic at hand:

https://medium.com/liecatcher/how-your-brain-computes-41ebe7428ff9

Physicists should stick with physics or at least become more knowledgeable about other sciences before misleading people about what is known in other sciences even though they make the best liars. Math is good, but in some situations, computational modelling is the right answer.

https://medium.com/liecatcher/physicists-are-the-best-liars-c8e9ccfcf6b4