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    Stoic syllogistic is best understood as a substructural b... — Carmelics
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    Stoic syllogistic is best understood as a substructural backwards-working Gentzen-style natural-deduction system

    Philosophy of Language
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    2 reasons against

    Reasons For

    1 perspective
    Reason for
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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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    Reasons Against

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    Reason against 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 against 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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    Related

    An argument is a syllogism if and only if it either is an indemonstrable or can ...Imposing Gentzen's structural framework retroactively distorts the Stoic distinc...Stoic syllogistic consists of five kinds of axiomatic arguments called indemonst...Stoic syllogistic consists of four inference rules called themata
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    Stoic syllogistic operates with a forward-directed proof search aligned with Chr...Susanne Bobzien's scholarship demonstrates that Stoic syllogistic is better unde...The 'substructural' characterization presupposes a contraction/weakening framewo...The themata function as meta-rules for argument reduction, not as introduction/e...

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    In terms of contemporary logic, Stoic syllogistic is best understood as a substructural backwards-working Gentzen-style natural-deduction system that consists of five kinds of axiomatic arguments (the indemonstrables) and four inference rules, called themata. An argument is a syllogism precisely if it either is an indemonstrable or can be reduced to one by means of the themata (D. L. 7.78). Thus syllogisms are certain kinds of formally valid arguments. The Stoics explicitly acknowledged that the
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    Perspectives
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