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    The syllogism 'if As are Bs and Bs are Cs, then As are Cs... — Carmelics
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    Home/Modality & Possibility
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    The syllogism 'if As are Bs and Bs are Cs, then As are Cs' is a perfect deduction in Aristotle's sense

    Modality & PossibilityTruth & Knowledge
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    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
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    • 1.Anything taking the form 'if As are Bs and Bs are Cs, then As are Cs' is a deduction in Aristotle's sense
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    • 2.A perfect deduction is one whose validity needs no proof
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    • 3.The validity of this syllogistic form needs no proof and admits of no proof
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
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    • 1.Aristotle's 'perfect' deductions are restricted to the four categorical syllogisms of the first figure (Barbara, Celarent, Darii, Ferio).
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    • 2.The form 'if As are Bs and Bs are Cs, then As are Cs' uses relational transitivity, not Aristotelian predication of universal affirmation in Barbara.
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    • 3.Without the precise 'All A is B / All B is C / therefore All A is C' quantified structure, the argument falls outside Aristotle's formal syllogistic.
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    Reason against 2 of 2
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    • 1.Aristotle in Prior Analytics I.2 grounds perfection in self-evidence via the dictum de omni, which requires specific subject-predicate containment relations.
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    • 2.Lukasiewicz and Patzig both demonstrate that Aristotelian syllogistic is a term logic where validity depends on predication, not hypothetical transitivity.
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    • 3.A deduction involving schematic transitivity ('As are Bs') without quantified categorical form is not obviously self-evident in the dictum de omni sense, requiring additional justification.
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    Modality & PossibilityTruth & Knowledge

    Connections

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    Related

    A deduction involving schematic transitivity ('As are Bs') without quantified ca...A perfect deduction is one whose validity needs no proofAny proof of this form would ultimately rely on the intuitive validity of this s...Anything taking the form 'if As are Bs and Bs are Cs, then As are Cs' is a deduc...
    +6 moreShow less
    Aristotle in Prior Analytics I.2 grounds perfection in self-evidence via the dic...Aristotle's 'perfect' deductions are restricted to the four categorical syllogis...Lukasiewicz and Patzig both demonstrate that Aristotelian syllogistic is a term ...The form 'if As are Bs and Bs are Cs, then As are Cs' uses relational transitivi...The validity of this syllogistic form needs no proof and admits of no proofWithout the precise 'All A is B / All B is C / therefore All A is C' quantified ...

    Similar

    Anything taking the form 'if As are Bs and Bs are Cs, then As are Cs' ...89%All deductions in Aristotle's syllogistic system are valid81%A deduction is minimally a valid syllogism.79%Logic deals with syllogism, which involves the deduction of conclusion...78%

    Source

    AI-extracted1/3 agreementValid
    SEP: aristotle
    View source passageHide passage
    Accordingly, anything taking this form will be a deduction in Aristotle’s sense. Let the As, Bs, and Cs be anything at all, and if indeed the As are Bs, and the Bs Cs, then of necessity the As will be Cs. This particular deduction is perfect because its validity needs no proof, and perhaps because it admits of no proof either: any proof would seem to rely ultimately upon the intuitive validity of this sort of argument.
    Extraction notes

    Validity: Extracted via Max plan + API grounding/validity checks

    Details

    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit