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Inverse View
It is not the case that Epistemic consensus about complexity separations lacks the deductive warrant required to ground modal claims about mathematical structure.
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Reasons For
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Reason for
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1.
Consensus reflects convergence on strong evidence and rigorous partial results, which provides rational warrant even without complete deduction.
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2.
Modal facts about mathematical structures may themselves be epistemically dependent; knowing what's necessary requires reliable epistemic access.
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3.
Distinguishing 'grounding' from 'justification' is problematic—consensus can justify modal claims even if it doesn't metaphysically ground them.
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Reasons Against
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Reason against
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1.
Consensus about P vs NP remains unproven after 50+ years despite intense effort, suggesting empirical agreement alone cannot establish necessity.
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2.
Modal claims (about what must or could be true) require logical necessity, not statistical agreement among expert opinion.
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3.
Mathematical structures exist mind-independently; their properties cannot be grounded in human epistemic states or collective beliefs.
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