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    If no reduction of natural numbers to sets succeeds, then... — Carmelics
    Home/Modality & Possibility
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    Challenges→Natural numbers are not sets.

    If no reduction of natural numbers to sets succeeds, then natural numbers are not sets.

    Modality & PossibilityTruth & Knowledge
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    Related propositions within the same area of thought.
    Account I and Account II are both incorrect reductions of natural numbers to set...Natural numbers are not sets.Similar considerations emerge from comparing other reasonable-looking attempts t...

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    Natural numbers are not sets, as established by the failure of all rea...90%Natural numbers are not sets.84%A similar argument to the one against reducing natural numbers to sets...83%Rational numbers and real numbers are not sets.82%

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    The proper conclusion to draw from this conundrum appears to be that neither account I nor account II is correct. Since similar considerations would emerge from comparing other reasonable-looking attempts to reduce natural numbers to sets, it appears that natural numbers are not sets after all. It is clear, moreover, that a similar argument can be formulated for the rational numbers, the real numbers… Benacerraf concludes that they, too, are not sets at all.

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