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Vladimir_Nesov comments on What independence between ZFC and P vs NP would imply - Less Wrong Discussion
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If you suppose "interpretation" to be a distinction that can't be settled by observation, and simultaneously that any distinction must be settled by observation, then it's not clear what you're objecting to. These posts seem relevant: Belief in the Implied Invisible, You're Entitled to Arguments, But Not (That Particular) Proof.