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    Rejecting the induction step of the sorites paradox does ... — Carmelics
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    Rejecting the induction step of the sorites paradox does not dissolve the paradox but merely transforms it into a different problem.

    Philosophy of Language
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    2 reasons for
    1 reason against

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Epistemicists like Williamson accept sharp thresholds while locating the paradox in our ignorance of where they fall, not in their existence.
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    • 2.If the 'new problem' (unknowable thresholds) is epistemological rather than semantic, rejecting induction merely relocates the paradox without dissolving it.
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    • 3.A genuine dissolution must eliminate paradox at every level; trading a semantic puzzle for an equally intractable epistemic one constitutes transformation, not resolution.
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    Reason for 2 of 2
    ?
    • 1.Supervaluationism denies the induction step by making 'there exists a last child' neither true nor false, yet still cannot assign a determinate boundary under any admissible precisification.
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    • 2.Fine's supervaluationist framework generates 'higher-order vagueness': vagueness about which precisifications are admissible reintroduces a structurally identical sorites at the metalinguistic level.
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    • 3.When rejecting the induction step produces a regress of higher-order vagueness, as Fara and Williamson argue, the paradox has been transformed into an infinite hierarchy of problems rather than resolved.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.The negation of the induction step entails the existence of a sharp threshold for vague predicates such as 'child'.
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    • 2.Positing a sharp threshold for childhood is itself paradoxical or counterintuitive.
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    • 3.A solution that generates an equally problematic consequence has not resolved the original paradox.
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    Related

    A genuine dissolution must eliminate paradox at every level; trading a semantic ...A solution that generates an equally problematic consequence has not resolved th...Epistemicists like Williamson accept sharp thresholds while locating the paradox...Fine's supervaluationist framework generates 'higher-order vagueness': vagueness...
    +5 moreShow less
    If the 'new problem' (unknowable thresholds) is epistemological rather than sema...Positing a sharp threshold for childhood is itself paradoxical or counterintuiti...Supervaluationism denies the induction step by making 'there exists a last child...The negation of the induction step entails the existence of a sharp threshold fo...When rejecting the induction step produces a regress of higher-order vagueness, ...

    Similar

    PA^F restricts the induction schema to formulas not containing F(x), b...74%A solution that generates an equally problematic consequence has not r...73%If self-predication is banished, Russell's paradox cannot even be form...70%Curry's paradox derives triviality (as shown in the entry on Curry's p...69%

    Source

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    SEP: vagueness
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    Guided by Boolos’ firm hand, logic students drive a second stake into the heart of the induction step (the entailment of preposterous conditionals). Yet the paradox seems far from dead. The hitch is that death for the induction step is life for its negation. The negation of the second premise classically implies a sharp threshold for childhood. For the falsehood of the induction step implies the existential generalization that there is a number \(n\) such that an \(n\) day old human being is a c
    Extraction notes

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

    Details

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