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    Carmelics

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

    It is not the case that Wittgenstein's rule-following considerations suggest that what counts as a 'valid axiom' depends on communal practice, not intrinsic formal properties.

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

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Some axioms (e.g., non-contradiction) are universally adopted across radically different communities, suggesting intrinsic formal properties matter.
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    • 2.A community can be *wrong* about axioms; validity cannot reduce to consensus if consensus is answerable to mathematical reality.
      ?

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    • 3.Wittgenstein's remarks on rules show how practice constrains interpretation, but don't entail that validity is *constituted by* rather than *discovered through* practice.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Rule-following requires interpretation, and interpretations are only constrained by what a community recognizes as correct applications.
      ?

      Think about whether this reason is strong or weak

    • 2.Axioms in non-Euclidean geometry were rejected then accepted, showing validity shifts with communal mathematical practice, not formal properties.
      ?

      Think about whether this reason is strong or weak

    • 3.No formal system can bootstrap itself into justification without external appeal to shared understanding and agreement.
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      Think about whether this reason is strong or weak

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