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    Therefore, the claimed correspondence presupposes a compl... — Carmelics
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    Challenges→The integers can be placed in a one-to-one correspondence with the natural numbers.

    Therefore, the claimed correspondence presupposes a completed infinite totality, which strict finitists and intuitionists like Brouwer deny is mathematically legitimate.

    ?Rate how convincing each reason is below to see the overall strength.
    1 reason for
    1 reason against

    Reasons For

    1 perspective
    Reason for
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    • 1.Completed infinities require us to treat infinite collections as finished wholes, but we can only ever construct finite initial segments.
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    • 2.Intuitionistic mathematics successfully formalizes constructive reasoning without invoking completed infinities, showing they're not necessary.
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    • 3.The law of excluded middle fails for infinite propositions; accepting completed infinities forces us to assume it holds universally.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Classical mathematics produces consistent, empirically adequate formal systems without requiring actual construction of infinite objects.
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    • 2.Rejecting completed infinities eliminates useful theorems in analysis, topology, and set theory that have deep mathematical significance.
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    • 3.The distinction between 'potentially infinite' and 'completed infinite' may be epistemological, not ontological; legitimacy depends on coherence, not constructibility.
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    Truth & Knowledge1 linkedModality & Possibility1 linked

    Related

    Classical mathematics produces consistent, empirically adequate formal systems w...Completed infinities require us to treat infinite collections as finished wholes...Intuitionistic mathematics successfully formalizes constructive reasoning withou...Rejecting completed infinities eliminates useful theorems in analysis, topology,...
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    The distinction between 'potentially infinite' and 'completed infinite' may be e...The integers can be placed in a one-to-one correspondence with the natural numbe...The law of excluded middle fails for infinite propositions; accepting completed ...

    Details

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