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    Carmelics

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    Home/Original/inverse
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    Inverse View

    It is not the case that Stoic syllogistic is best understood as a substructural backwards-working Gentzen-style natural-deduction system

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Stoic syllogistic operates with a forward-directed proof search aligned with Chrysippan analysis, not the backward proof construction central to Gentzen's natural deduction.
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    • 2.The themata function as meta-rules for argument reduction, not as introduction/elimination rules operating on formula complexity in the Gentzen sense.
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    • 3.Imposing Gentzen's structural framework retroactively distorts the Stoic distinction between analysis and synthesis, which has no direct Gentzen analogue.
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    Reason for 2 of 2
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    • 1.Susanne Bobzien's scholarship demonstrates that Stoic syllogistic is better understood as a proof system governed by a specific dialectical analysis procedure with its own integrity.
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    • 2.The 'substructural' characterization presupposes a contraction/weakening framework absent from Stoic logical texts, where no such structural rules are explicitly recognized or rejected.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.Stoic syllogistic consists of five kinds of axiomatic arguments called indemonstrables
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    • 2.Stoic syllogistic consists of four inference rules called themata
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    • 3.An argument is a syllogism if and only if it either is an indemonstrable or can be reduced to one by means of the themata
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