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    Carmelics

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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 A naturalist who defers to mathematics as a science must acknowledge that mathematical practice itself demands cardinals beyond any fixed bound.

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

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Mathematical practice can be conducted in finitist or predicativist frameworks without invoking large cardinals.
      ?

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    • 2.Using large cardinals in proofs doesn't require belief in their existence—they may be merely useful formal devices.
      ?

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    • 3.Naturalism requires only that mathematics be empirically adequate, not that all its theoretical posits are ontologically real.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Mathematical practice regularly quantifies over arbitrarily large cardinals (e.g., in set theory, category theory, proof theory).
      ?

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    • 2.Naturalism commits us to accepting what our best scientific theories require; mathematics is indispensable to science.
      ?

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    • 3.There is no principled bound where mathematical practice stops; each supposedly 'final' cardinal admits further constructions.
      ?

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