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

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

    Reasons For

    1 perspective
    Reason for
    ?
    • 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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    Reasons Against

    1 perspective
    Reason against
    ?
    • 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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