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    The belief that PH ≠ PSPACE is itself unproven, making an... — Carmelics
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    Challenges→PH is expected to lack complete problems, unlike PSPACE

    The belief that PH ≠ PSPACE is itself unproven, making any inference from it to claims about completeness epistemically circular.

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    1 reason for
    1 reason against

    Reasons For

    1 perspective
    Reason for
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    • 1.Unproven conjectures cannot serve as reliable foundations for derivative claims without introducing circular reasoning into the epistemic chain.
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    • 2.We systematically reject circular inferences in other domains; consistency demands we apply the same standard to complexity theory claims.
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    • 3.If P ≠ NP could be false, then conclusions about NP-completeness rest on an unvalidated assumption, undermining their justificatory status.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Conditional reasoning (if P ≠ NP, then X follows) avoids circularity even when the antecedent is unproven; mathematical logic permits this structure.
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    • 2.Completeness definitions are proven *relative to* the P ≠ NP assumption, not *derived from* it; no circularity exists in conditional mathematical results.
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    • 3.All foundational mathematical frameworks rest on unproven axioms; accepting conditional inferences despite this is standard, not epistemically defective.
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    Modality & Possibility1 linkedSkepticism1 linked

    Related

    All foundational mathematical frameworks rest on unproven axioms; accepting cond...Completeness definitions are proven *relative to* the P ≠ NP assumption, not *de...Conditional reasoning (if P ≠ NP, then X follows) avoids circularity even when t...If P ≠ NP could be false, then conclusions about NP-completeness rest on an unva...
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    PH is expected to lack complete problems, unlike PSPACEUnproven conjectures cannot serve as reliable foundations for derivative claims ...We systematically reject circular inferences in other domains; consistency deman...

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    claim
    Perspectives
    2 (1 for, 1 against)
    Edits
    1 edit