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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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    Home/Original/inverse
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    Inverse View

    It is not the case that It is not necessary to conjure up the picture of the infinite (of the enormously big) in mathematical reasoning.

    ?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.Gödel's incompleteness theorems were discovered through reasoning about the totality of all provable sentences, an explicitly infinite domain.
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      Think about whether this reason is strong or weak

    • 2.Mathematical reasoning that produces genuine results via infinite pictures cannot be dismissed as mere psychological scaffolding without mathematical content.
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      Think about whether this reason is strong or weak

    • 3.Wittgenstein's finitist criterion for mathematical meaningfulness would, if applied consistently, eliminate large portions of classical number theory.
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      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.Cantor's transfinite arithmetic generates theorems (e.g., |ℕ| < |ℝ|) that are unintelligible without a picture of completed infinite totalities.
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      Think about whether this reason is strong or weak

    • 2.If a mathematical calculus generates results that require infinite structures for their interpretation, then pictures of the infinite are mathematically indispensable.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.The calculus contains nothing infinite.
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    • 2.Once we see that the calculus contains nothing infinite, there is no mathematical deficit that requires supplementation by a picture of the infinite.
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