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    Carmelics

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

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    Made withinDC&Austin
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    Home/Original/inverse
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    Inverse View

    It is not the case that Both Peano's axioms and Dedekind's axioms become demonstrable

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.Russell's logical theory of cardinals relies on the axiom of reducibility, which Wittgenstein and others argued is not a logical truth but an empirical assumption.
      ?

      Think about whether this reason is strong or weak

    • 2.A derivation built on non-logical axioms does not constitute a logical demonstration in the sense required for logicism's foundational ambitions.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.Benacerraf's identification problem shows that multiple incompatible set-theoretic reductions equally satisfy Peano's axioms, undermining any claim that one derivation is canonical.
      ?

      Think about whether this reason is strong or weak

    • 2.If the axioms are demonstrable only relative to an arbitrarily chosen construction, they are not demonstrated in an absolute logical sense but merely shown to be consistent within one model.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • The logical theory of cardinals provides a foundation from which both Peano's axioms and Dedekind's axioms can be derived
      ?

      Think about whether this reason is strong or weak

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    Based on where you are in your exploration

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