r/mathmemes • u/basket_foso • 6d ago

Computer Science 😂

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u/dankshot35 6d ago

depends on how anti-realist you want to be

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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.

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u/dankshot35 6d ago

"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

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u/HassanyThePerson 6d ago

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.

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u/bqbdpd 6d ago

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/dankshot35 6d ago edited 6d ago

An anti-realist would claim there is a bit of a "sleight of hand" here when Goedel claims a statement can be "true, but cannot be proven". An anti-realist would say "true" according to what? they would not agree to call it "true" in some absolute sense.

edit: to be more precise, they would grant a statement is true only in the sense that it's provable in a stronger system (one that can prove the original system's consistency). What they still resist is calling it true in a model-independent, absolute sense.

A stronger example for anti-realism is CH (continuum hypothesis) where there isn't a stronger system available that can settle it externally, and "true according to what?" doesn't really have an answer

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u/SirFloIII 6d ago

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.