A conclusion I came to recently, after getting tremendously high, was that Godel’s proof shows that no axiomatic system can ever be coherent. Not Wittgenstein’s attempt at “ending philosophy” with the tractatus, the general model of physics which breaks down when you try to combine gravity and quantum physics, or Bertrand Russell’s attempt to create a “closed mathematical system”, result in anything but a system which must expand endlessly to account for all of its own contradictions.
What this tells me is anything we try to give ourselves to gain familiarity, which is really just an attempt to prove Hume’s problem of induction wrong, can ever produce “coherence” in anything systematic sense. Our own perceptions can operate on these systems in a highly local level, in that we can use small equations, and make basic metaphysical statements, like Aristotle does, but we will never grasp the whole.
I am certainly an atheist, in that calling “god” anything other than Spinoza’s deterministic whole makes no sense to me (and saying there is a deterministic whole in itself is kind of faith based, I believe in it because it seems to follow from what is demonstrable, in a sort of prima fasci way), because I’m not sure what exactly it is I’d be calling god, but I’ve become much more interested in Christian arguments like Aquinas after talking to my teacher recently who specializes in him. If the axioms we base our framework for reality on are never “proveable” in a truly systematic way, then what sort of assumptions is it possible to make and still be “consistent”? The fact that there is even a hint of doubt that religiosity doesn’t equal “unprovable” to me is fascinating in itself.
My girlfriend said very eloquently "god is the axiomatic whole". It would seem so. If one were to resolve the contradictions in these systems, they would know the nature of the universe.