I want to know the answer to the following question:
What did Kurt Godel's theorem demonstrate about axioms and the inference rules?
All the background I'm provided with is that "It is generally accepted that Kurt Gödel's incompleteness theorem of 1931 definitively demonstrated that for any set of axioms and inference rules proposed to encapsulate mathematics, there would in fact be some truths of mathematics which could not be deduced from them, and hence that Principia Mathematica could never achieve its aims.". Is that enough to answer the question?