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    If a strategy for resolving paradox lacks principled gene... — Carmelics
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    Supports→Denying a property corresponds to the predicate 'does not exemplify itself' is ad hoc and a poor strategy for resolving Russell's paradox

    If a strategy for resolving paradox lacks principled generalizability to analogous cases (e.g., the Burali-Forti paradox), it fails as a theoretical solution rather than a patch.

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    Reasons For

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    Reason for
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    • 1.Theoretical coherence requires solutions to apply consistently across structurally similar problems, not just isolated cases.
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    • 2.Ad-hoc fixes that work for Russell's paradox but fail for Burali-Forti suggest deep conceptual gaps rather than genuine understanding.
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    • 3.Science and mathematics progress through unifying principles; particularistic solutions regress toward mere technical workarounds.
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    Reasons Against

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    Reason against
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    • 1.Not all paradoxes have identical logical structures; solutions may legitimately differ based on the specific principles each violates.
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    • 2.Generalizability across cases can be a theoretical virtue that conflicts with other virtues like simplicity, intuitive appeal, or empirical adequacy.
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    • 3.A solution's inability to generalize may reflect the domain's genuine complexity rather than the solution's theoretical inadequacy.
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    Truth & Knowledge1 linkedPhilosophy of Language1 linked

    Related

    A solution's inability to generalize may reflect the domain's genuine complexity...Ad-hoc fixes that work for Russell's paradox but fail for Burali-Forti suggest d...Denying a property corresponds to the predicate 'does not exemplify itself' is a...Generalizability across cases can be a theoretical virtue that conflicts with ot...
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    Not all paradoxes have identical logical structures; solutions may legitimately ...Science and mathematics progress through unifying principles; particularistic so...Theoretical coherence requires solutions to apply consistently across structural...

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