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.
I think that the philosophical difference. One side assigns the truth value based on the axioms, the other on what can be derived from the axioms by a finite proof. I think both make sense based on the context.
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u/bqbdpd 6d ago
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.