Science is “empirically complete” when it is well funded, all unknowns are constrained in scope, and (n+1) generations of scientists produce no breakthroughs of any kind.

If a hypothetical entity could encompass every aspect of science into reasoning and ground that understanding in every aspect of the events in question, free from bias, what is this epistemological theory?

I’ve been reading wiki articles on epistemology all afternoon and feel no closer to the answer in the word salad in this space. It appears my favorite LLM’s responses reflect a similar understanding. Maybe someone here has a better grasp on the subject?

Gödel’s incompleteness theorem would like a word…

Not really, that theorem says there are true things that cannot be proven, whereas this question is more about running out of proofs that you can make.

Really this question has little to do with mathematical proof, because the basis of science is deductive, statistical knowledge.

In any specific axiomatic system. Other more powerful systems may still answer the questions. (Sometimes in opposite ways depending on your choice, it turns out)How axiomatic systems relate to the real world and what math even is remain in the realm of philosophy.