Comment by pavas
1 day ago
I think the nuance they are pointing towards is that we cannot with any certainty say one way or another, as this is an unsolved problem in mathematics, and may possibly remain unsolved forever.
Your opinion is a possibility but it is not grounded by any proof, as such it is nothing more than an assumption. I think the more intellectually healthy approach is to list out the possibilities and figure out what they entail, rather than to throw all your eggs in one basket blindly, which amounts to a leap of faith or a retreat to commitment.
But that's just my two cents, take it or leave it.
Can you be more explicit?
I absolutely do not understand what are you talking about.
The question whether the tautologies exists regardless of whether we know about them or not is absolutely not a problem that is studied by mathematics and can be proven by mathematics.
Correct, these questions lie outside the internal practice of mathematics. If you want to see where that computational mindset breaks down, read Carnap's "Empiricism, Semantics, and Ontology" regarding internal versus external frameworks (or have an LLM summarize it...), or look into Brouwer's Intuitionism, or better yet into Lawvere and Topos theory, where the "underlying tautologies" literally change depending on the categorical environment you construct (but this may take some time to wrap your mind around so don't expect to understand much right away). Or, given the thread topic, you can just prompt an LLM to interactively walk you through how classical logic fails in a constructivist topos, or if you have interests outside of applied math or mathematics itself, you can ask it about foundational questions in science and mathematics, which unlike the prevailing opinion in many tech circles, aren't resolved.