As I was browsing pornhub, I started reading articles about AI, dick still in hand, and went down the rabbit-hole (no pun intended) of self referential systems and proofs. This is something I do frequently (getting off track, not beating off, though I have been slacking recently).

Now I'm no expert but my neurotic DID personality which prompted this small reading binge DOES think it is an expert. And it got me thinking.

Godel’s second incompleteness theorem says that "no sufficiently strong proof system can prove its own consistency."

Then utilizing proof by contradiction, systems that are "sufficiently strong" should produce truth outputs that are monotonic. E.g. statements such as "this sentence is a lie."

Wouldn't monotonicity then be proof (soft or otherwise) that a proof system is 'sufficiently strong' in the sense that Godel's second theorem meant?

Edit: I WELCOME input, even if this post is utterly ignorant and vapid. I really don't know shit about formal systems or logic. Welcome any insight or feedback that could enlighten me.

I only read this because I saw the gödel tag. I don't know enough about high-level mathematics to contribute. 🙁 But I'll try anyway.

It could be that mathematics is more akin to religion in that it accurately maps to our observations of the universe because we specifically made it so. or what's much more likely is that we're only studying the secondary, tertiary, etc. effects of how the universe (and its parents/hosts, whatever they may be) actually work. Because of this, there will always be things that don't quite make sense, don't have apparent connections, or aren't even observable.

Example: if there are multiple universes (or anything losely described thereas, like segmented areas of spacetime), the constants we are used to, and therefore the effects of many laws of physics, could be drastically different. Similarly, we may be copletely unable to see some forces, interactions, etc. because of our viewpoint. We cannot easily study the outside of the box we're trapped in (or its nature) if we cannot study it -- let alone what lies beyond. At best all we can do is infer what might exist, and see if it fits our views of how physics works. but because of the above, it could quite easily be impossible to test if such theories are true or not.