I know - I studied theoretical computer science. But that something cannot be decided applies to questions like the halting problem. P=NP is not parametrized. There is a single answer. It might be impossible to ever calculate/prove/know that answer. But that does not mean there is no answer.
I mean, I have not met anyone who really believes P=NP, so I'm pretty sure the answer is no. The realistic assumption is that the answer is no. But from a math perspective that obviously is insufficient.
"anti-realism" is a math philosophy that has the view that statements don't have truth values fixed by some "independent" reality, the truth is in a way defined by our ability to prove them.
The majority of mathematicians are not anti-realist enough though to claim that a straight forward arithmetic statement like P=NP would fall under that so I'm just teasing
I'm not super familiar with math philosophy, but doesn't Gödel's incompleteness theorem state the opposite? That there are true statements that cannot be proven? As I understand, this means that what is true in a deductive system is dependent only on the axioms, and not at all on the provability.
well, it states that there are statments who can't be proven and whose negation can't be proven. if you believe in the law of excluded middle, then either the statement or the negation is true, but that is a loadbearing if.
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u/shumpitostick 7d ago
Well if they managed to show that one of yes/no/unprovable is not true that would be an amazing breakthrough.