>>13209139>Godel proved that we can never actually know if a mathematical statement is true or falseThis is literally not what Godel proved. Why do people like you always make threads where the premise is entirely founded on your misreading of a wikipedia page?
Godel proved that, in any consistent formal system, *there exist* mathematical statements which are true, but this truth cannot be proved by the axioms of that formal system.
Your understanding is wrong on two levels. One, it's not about any arbitrary mathematical statement -- it's about a specific one, the so-called "Godel sentence". It's rather abstract and is defined to refer to itself (albeit indirectly) to explicitly demonstrate the incompleteness theorem.
Two, it's not about not knowing whether the statement is true or false. The Godel is sentence is true -- by definition. There is no question about its truth. The formal system simply doesn't have enough tools to demonstrate this veracity. In order to do so, we (humans) have to extend beyond that formal system to prove its veracity (or posit it as an axiom). But in doing so we create another formal system, and if it is also consistent, then we have inadvertently generated a new, different Godel sentence for this new formal system. And so on and so forth.
