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    Holmes's own reconstruction of T in NFU requires auxiliar... — Carmelics
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    Challenges→The operation T on ordinal numbers can be defined in NFU

    Holmes's own reconstruction of T in NFU requires auxiliary lemmas about type-raising that are not part of the original classical definition, making the claim equivocal.

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    Reasons For

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    • 1.Holmes's type-raising lemmas go beyond Quine's original NFU axioms, introducing non-standard machinery not explicitly defined in the classical system.
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    • 2.When reconstruction requires auxiliary principles absent from original definitions, the equivalence claim becomes ambiguous about what is actually being proven.
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    • 3.Type-raising lemmas function as hidden assumptions that change the logical structure, making the reconstruction non-trivial in ways the classical definition doesn't acknowledge.
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    Reasons Against

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    Reason against
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    • 1.Auxiliary lemmas in formal systems are standard practice; they prove theorems within the system without making the original definition equivocal or false.
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    • 2.Holmes's reconstruction remains faithful to NFU's core principles even if it requires intermediate steps; the target theorem's truth is independent of proof method.
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    • 3.Classical definitions often require constructive techniques to instantiate them; technical machinery doesn't undermine equivalence if it's internally consistent with the system.
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    Related

    Auxiliary lemmas in formal systems are standard practice; they prove theorems wi...Classical definitions often require constructive techniques to instantiate them;...Holmes's reconstruction remains faithful to NFU's core principles even if it req...Holmes's type-raising lemmas go beyond Quine's original NFU axioms, introducing ...
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    The operation T on ordinal numbers can be defined in NFUType-raising lemmas function as hidden assumptions that change the logical struc...When reconstruction requires auxiliary principles absent from original definitio...

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