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    Carmelics

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    Made withinDC&Austin
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    Perspectives
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    Topics
    42
    Home/Original/inverse
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    Inverse View

    It is not the case that A choice function exists in constructive mathematics

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.Diaconescu's theorem shows that the Axiom of Choice implies the Law of Excluded Middle in intuitionistic set theory (IZF).
      ?

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    • 2.Constructive mathematics explicitly rejects the Law of Excluded Middle as a valid logical principle.
      ?

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    • 3.Therefore, unrestricted choice functions in constructive mathematics generate a contradiction with its foundational logical commitments.
      ?

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    Reason for 2 of 2
    ?
    • 1.Bishop-style constructivism permits only dependent choice and countable choice, not full AC over arbitrary sets.
      ?

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    • 2.A general choice function over all non-empty sets requires selecting from collections with no computable or definable structure.
      ?

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    • 3.Possessing a witness-producing procedure for existence claims does not guarantee a uniform procedure across infinitely many arbitrary sets simultaneously.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.A choice is implied by the very meaning of existence in constructive mathematics
      ?

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    • 2.To constructively assert existence is to possess a procedure that produces a witness
      ?

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