Here, a video series explores Godel’s incompleteness results:
The core point is that Hilbert’s scheme collapsed, nicely summarised. The Godel incompleteness results and the Turing machine halting challenge made Mathematics irreducibly complex. So, Mathematics, too, is a venture of knowledge as warranted, credibly true (so reliable) belief, which must be open to correction.
An exercise of rational, responsible faith, not utter certainty on the whole, once a sufficiently complex system is on the table. (Yes, first duties of reason obtain . . . here, there be dragons that love chick peas [Cicero . . .].)
The defeasible [= defeat-able] framework for understanding knowledge extends to Mathematics. A fortiori to Computer Science and Physics, then onward across the spectrum of disciplines and praxis.
We walk by faith, and not by sight. The question, then — given the Agrippa trilemma —
. . . is the worldviews question: which core first plausibles, why. END