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    A naturalist who defers to mathematics as a science must ... — Carmelics
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    Challenges→The cardinal number of the power set of the set of space-time points (at least ℵ₂) is the largest cardinal.

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

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    1 reason for
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    Reasons For

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    Reason for
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    • 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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    Reasons Against

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    Reason against
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    • 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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    Key Terms

    knowledge(Distinguished from mere true belief, which may be the product of indoctrination and need not exercise deliberative capacities.)
    Justified true belief — true belief that has been arrived at through the exercise of deliberative capacities, including comparison of and deliberation among alternatives.

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    Mathematical practice can be conducted in finitist or predicativist frameworks w...Mathematical practice regularly quantifies over arbitrarily large cardinals (e.g...Naturalism commits us to accepting what our best scientific theories require; ma...Naturalism requires only that mathematics be empirically adequate, not that all ...
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    The cardinal number of the power set of the set of space-time points (at least ℵ...There is no principled bound where mathematical practice stops; each supposedly ...Using large cardinals in proofs doesn't require belief in their existence—they m...

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    claim
    Perspectives
    2 (1 for, 1 against)
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    1 edit