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    Home/Original/inverse
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    Inverse View

    It is not the case that 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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    Reasons For

    1 perspective
    Reason for
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    • 1.Bolzano's own criterion for valid inference relies on truth-preservation across possible substitutions—a semantic criterion implemented through logical operations.
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    • 2.Any account of conceptual containment must ultimately answer which inferences are valid, forcing implicit appeals to proof-theoretic structure regardless of level.
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    • 3.The claim conflates Bolzano's rejection of syntacticism with a rejection of formal structure; containment relations still require determining valid transitions.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.Bolzano explicitly distinguishes propositions-in-themselves from linguistic expressions, treating them as abstract semantic entities independent of notation.
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    • 2.Conceptual containment (Bolzano's Merkmal relation) operates on the intrinsic content of concepts, not on derivability rules that depend on formal systems.
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    • 3.Proof syntax is system-relative and can vary; semantic containment is invariant across different formal representations of the same proposition.
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