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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Home/Original/inverse
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    Inverse View

    It is not the case that Under strict constructivism in the tradition of Brouwer and Bishop, a proof that not-all-are-equalities does not constructively exhibit which specific inclusion is proper, leaving the disjunction epistemically inert.

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    Reasons For

    1 perspective
    Reason for
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    • 1.Proof by contradiction of ¬(all-equal) does yield information: it eliminates the all-equal case, restricting the logical space constructively.
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    • 2.Some disjunctions gain epistemic force through constraint elimination alone; knowing what's *not* true enables bounded search and reasoning.
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    • 3.Modern constructivism (e.g., CZF) accepts some classical logical principles; dismissing all non-intuitive proofs overstates Brouwer-Bishop strictness.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Constructive proofs require explicit algorithms; negation-of-universal statements lack computational content about which case holds.
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    • 2.Epistemically inert means unusable for further reasoning; a disjunction without instantiation cannot guide mathematical construction.
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    • 3.Brouwer-Bishop tradition prioritizes intuitionistic validity where existence means constructible; abstract negations violate this principle.
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