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    Carmelics

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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
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    Perspectives
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    Home/Original/inverse
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    Inverse View

    It is not the case that The second premise of the induction argument must be rejected

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

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.A 100 year old man is clearly not a child
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    • 2.The base step of the argument is plainly true
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    • 3.The argument is valid by mathematical induction
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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 1.Epistemicism (Williamson 1994) holds that vague predicates have sharp but unknowable boundaries, making the inductive step false even if unprovable.
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    • 2.If there exists a precise cutoff n where 'child' applies to n-year-olds but not (n+1)-year-olds, the universal generalization in premise two is straightforwardly false.
      ?

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    • 3.Our inability to identify which instance of the inductive step fails is an epistemic limitation, not evidence of the step's truth.
      ?

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    Reason against 2 of 2
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    • 1.Degree-theoretic semantics (Zadeh, Fine 1975) assigns truth values in [0,1], so the inductive premise is not fully true even if no single step is fully false.
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    • 2.A premise with truth value strictly less than 1 can be rejected as failing to meet the standard required for sound deductive inference.
      ?

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    • 3.Rejecting the second premise on degree-theoretic grounds is consistent with the sorites appearing compelling, since each step is nearly but not fully true.
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