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    Carmelics

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

    It is not the case that π' is not a genuine irrational number.

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.The distinction between base-notation systems is a feature of representation, not of mathematical objects themselves.
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    • 2.If π' has a well-defined decimal expansion and satisfies the algebraic definition of irrationality, it qualifies as irrational by standard criteria.
      ?

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    • 3.Wittgenstein's criterion conflates epistemic accessibility across notations with ontological status, a category error Frege warned against in Grundlagen.
      ?

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    Reason for 2 of 2
    ?
    • 1.Benacerraf's insight that mathematical identity cannot depend on representational accidents applies directly: no number essentially belongs to one notation.
      ?

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    • 2.π' can be systematically translated into any positional base, meaning its confinement to one notation reflects our current knowledge, not an intrinsic property.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.π belongs to all base-notational systems, while π' belongs only to one.
      ?

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    • 2.There can't be irrational numbers of different types.
      ?

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