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    Therefore, unrestricted choice functions in constructive ... — Carmelics
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    Challenges→A choice function exists in constructive mathematics

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

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    1 reason for
    1 reason against

    Reasons For

    1 perspective
    Reason for
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    • 1.Constructive mathematics requires computational witnesses for existence claims, but unrestricted choice provides non-computable selections.
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    • 2.The axiom of choice implies excluded middle in intuitionistic logic, directly contradicting constructivism's rejection of classical principles.
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    • 3.Unrestricted choice over infinite sets violates the finite Church-Turing thesis that grounds constructive computation.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Restricted choice functions (dependent products) are compatible with constructivism and handle most mathematical practice.
      ?

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    • 2.The contradiction claim conflates unrestricted classical choice with any use of choice; constructive choice principles exist consistently.
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    • 3.Intuitionistic type theory incorporates choice without generating contradictions, suggesting the problem is overstated.
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    Truth & Knowledge1 linkedPhilosophy of Language1 linked

    Related

    A choice function exists in constructive mathematicsConstructive mathematics requires computational witnesses for existence claims, ...Intuitionistic type theory incorporates choice without generating contradictions...Restricted choice functions (dependent products) are compatible with constructiv...
    +3 moreShow less
    The axiom of choice implies excluded middle in intuitionistic logic, directly co...The contradiction claim conflates unrestricted classical choice with any use of ...Unrestricted choice over infinite sets violates the finite Church-Turing thesis ...

    Details

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