This much is good. Gödel has proven that some truths live outside of logic and that we can’t get there from here.
Not precisely what Godel proved, actually. He showed that in any first order recursive theory that is complicated enough to model the natural numbers, there are statements that can neither be proved nor disproved.
In any particular model, there will be truths that cannot be proven. But you have to have a model *first* for this to work. Different models will have different unreachable truths. And the truths common to all models will be exactly those that can be proved.
Furthermore, these results *fail* for second order models (as opposed to first order models). For example, there is only one second order models of the natural numbers and infinitely many first order models.
However, the missing information will be about the self, the subject. Scientific method can help us study objects of mind-senses but cannot help us know the self, the subject.
IMO, Planck’s observation, as noted in the first post of the thread, is most significant It is not about petty arguments.
OK, now that is precisely wrong. The Godel results are about systems that are complicated enough to have self-reference. But the *statements* that cannot be decided are NOT necessarily those that involve self-reference directly.
For example, the Axiom of Choice, the Continuum Hypothesis, Martin's Axiom, etc. None of these have anything to do with self-reference.
In the case of the laws of physics, I disagree that they would be purely mathematical (and thereby not a deductive system). There are *two* parts to any physical theory: the mathematical aspect and the correspondence between that math and observations (reality). Most of the questions that arise in the math will have NO correspondence with observation. So those are irrelevant to the physics.
In other words, most of the undecidable questions in the math will have no bearing on anything observable, and hence will be irrelevant to understanding the universe.