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    Carmelics

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    It is not the case that Therefore, unrestricted choice functions in constructive mathematics generate a contradiction with its foundational logical commitments.

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

    Reasons For

    1 perspective
    Reason for
    ?
    • 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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    Reasons Against

    1 perspective
    Reason against
    ?
    • 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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