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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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    Perspectives
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    42
    Home/Original/inverse
    See Original
    Inverse View

    It is not the case that A genuine number must measure in and of itself

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.Real numbers like √2 are defined by Dedekind cuts, which partition the rationals without requiring any independent measuring capacity.
      ?

      Think about whether this reason is strong or weak

    • 2.A number's legitimacy derives from its structural role in a complete ordered field, not from autonomous metric function.
      ?

      Think about whether this reason is strong or weak

    • 3.Completeness of ℝ—filling every gap in the rationals—is itself a mathematically productive property Wittgenstein's criterion cannot capture.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.Frege argued in Grundgesetze that numbers are logical objects whose validity is grounded in consistent formal definition, not operational utility.
      ?

      Think about whether this reason is strong or weak

    • 2.Excluding irrational numbers for failing to 'measure in themselves' would eliminate π and e, crippling analysis and physics without principled justification.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • If a purported 'number' leaves the task of measuring to the rationals, then we have no need of it as a distinct number
      ?

      Think about whether this reason is strong or weak

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