The idea of formal systems and Godel's incompleteness theorems comes to mind. 

A formal system is defined by axioms. We try to treat science (and by proxy, the natural world) with an assumption of nature itself being a formal system -> start with axioms and explore the space from there. Axioms and derived theorems then create the boundaries for the environment you're working with. 

Mathematical proofs show you absolute truth in the axiomatic system you are working with. They will also show the absolute falshoods of the system. The space is fractal, endlessly deep, you only can work with the knowledge you have of system you are working with.

The problem is that nature is mind-bogglingly entangled. 

You think CS dependencies are tough? Biological processes seemingly have not only unenumerable dependencies, but dependencies that well eventually circle back to the process itself. At that point, you'd expect a computer to be in deadlock, but it gets worse. There there are not only multiple different clock-cycles, but its a gradient everywhere you go. In biology, it is often said that there are always contradictions to rules being stated and that whatever "rules" we come up with are more guidelines, so we can't even make the assumption that biology and nature is a formal system.

 What are the implications of that? 
A real strangely looped rabbit hole for you 🕳️🔄🐇

From Godel Escher Bach ch 3, a visualization of this process with some defined formal system. Godel's Incompleteness Theorem proved that any formal system will  have statements about it that cannot be proved from within said system. For example, where in the system of language rules do you get meaning from? You're not going to derive semantics from syntax.

https://i.nostr.build/AaXlL.jpg

So if formal systems can't even be fully explicated , what does that imply for non-formal systems? Damned if nature is formal, damned even more if its not.

Now for a sleight shift.
Humans, we live outside many axiomatic systems, but use them to frame our understanding of the world. Ever work on a problem for such a long time, and then stop and do something else? Thats because we aren't bound by said box/axiomatic system and can move outside it. This feature itself allows us to reenter the system from different angles, or just say "Stop, its not worth it."

The capacity for humans to exit systems is a core part that separates us from computers. Wisdom incorperates restraint of application as a consequence from viewing the system wholistically.

The real questions now: What kind of boxes are we living in, be they foundational or self constructed? Are we  agents taxing towards new provable theorems contained in some system we can't exit from? What are the generating functions for this system? Are we the system itself? 

This gives me hope on the unknowable truths and falshoods. Spiritual experience is the experience of The Other, whatever that may be.

Not formally religious, but there is strong appreciation and a wistfulness toward it.