Skip to content
Carmelics
TopicsThinkersChangesContributorsLoading account…

    Carmelics

    A reasoning platform. Break down any belief into clear reasons, explore both sides, and weigh the evidence honestly.

    Navigate

    • Topics
    • Search
    • Recent Changes
    • Contribute
    • How It Works
    • Glossary
    • Thinkers
    • Contributors
    • About
    • Statistics
    • Terms
    • Privacy

    Database

    Statements
    —
    Perspectives
    —
    Topics
    —

    Press ? for keyboard shortcuts

    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    The second premise of the induction argument must be reje... — Carmelics
    Home/Philosophy of Language
    HistoryEditSee Inverse

    The second premise of the induction argument must be rejected

    Philosophy of Language
    ?Rate how convincing each reason is below to see the overall strength.
    2 reasons for
    1 reason against

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.Epistemicism (Williamson 1994) holds that vague predicates have sharp but unknowable boundaries, making the inductive step false even if unprovable.
      ?

      Think about whether this reason is strong or weak

    • 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.
      ?

      Think about whether this reason is strong or weak

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

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 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.
      ?

      Think about whether this reason is strong or weak

    • 2.A premise with truth value strictly less than 1 can be rejected as failing to meet the standard required for sound deductive inference.
      ?

      Think about whether this reason is strong or weak

    • 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.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.A 100 year old man is clearly not a child
      ?

      Think about whether this reason is strong or weak

    • 2.The base step of the argument is plainly true
      ?

      Think about whether this reason is strong or weak

    • 3.The argument is valid by mathematical induction
      ?

      Think about whether this reason is strong or weak

    Sign in or register to share your perspective on this statement.

    Next step

    Based on where you are in your exploration

    Strongest counterpoint
    Explore the most compelling reason on the other side.

    Topics

    Philosophy of Language

    Related

    A 100 year old man is clearly not a childA premise with truth value strictly less than 1 can be rejected as failing to me...Degree-theoretic semantics (Zadeh, Fine 1975) assigns truth values in [0,1], so ...Epistemicism (Williamson 1994) holds that vague predicates have sharp but unknow...
    +6 moreShow less
    If the conclusion is false and the argument is valid and the base step is true, ...If there exists a precise cutoff n where 'child' applies to n-year-olds but not ...Our inability to identify which instance of the inductive step fails is an epist...Rejecting the second premise on degree-theoretic grounds is consistent with the ...The argument is valid by mathematical inductionThe base step of the argument is plainly true

    Similar

    Mathematical induction does not function as an inference that derives ...76%If the conclusion is false and the argument is valid and the base step...76%Single-case induction becomes one means among others for establishing ...76%If inductive arguments are unclear, the fault lies with induction itse...76%

    Source

    AI-extracted1/3 agreementValid
    SEP: vagueness
    View source passageHide passage
    The conclusion is false because a 100 year old man is clearly a non-child. Since the base step of the argument is also plainly true and the argument is valid by mathematical induction, we seem to have no choice but to reject the second premise.
    Extraction notes

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

    Details

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