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    Carmelics

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

    It is not the case that Bolzano anticipated Gentzen's Hauptsatz in a certain sense

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    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Bolzano's criterion operates at the semantic level of conceptual containment between propositions-in-themselves, not at the level of proof syntax.
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    • 2.Gentzen's Hauptsatz (Cut-Elimination) is a syntactic, proof-theoretic result about the eliminability of the cut rule from formal derivations.
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    • 3.Structural parallelism between a semantic constraint and a syntactic theorem does not constitute anticipation without shared proof-theoretic mechanism or intent.
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    Reason for 2 of 2
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    • 1.Bolzano's notion of Abfolge concerns the objective grounding relations among truths, not the normalization of formal inference procedures.
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    • 2.Gentzen's motivation was to establish consistency and the subformula property within a formal calculus, a project unintelligible in Bolzano's pre-formalist framework.
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    • 3.Attributing anticipation conflates Bolzano's metaphysics of grounding with Gentzen's proof-theoretic program, obscuring genuinely distinct intellectual projects.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.Bolzano's semantic notion of entailment requires that from the smallest number of premises the largest number of conclusions follow, none of which has simple components not also contained in the premises
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    • 2.Gentzen's characterization of normal proofs holds that they do not make a detour and do not introduce concepts not contained in the final result
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    • 3.Bolzano's and Gentzen's criteria are structurally parallel: both require that inferential steps not introduce extraneous conceptual content
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