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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 Hilbert's distinction between ideal and real mathematics shows that relaxing consistency standards undermines the foundational role formal systems are meant to play.

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

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Paraconsistent logics tolerate contradictions without trivializing all theorems, suggesting consistency isn't strictly necessary for foundations.
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    • 2.Many formal systems already contain inconsistencies (e.g., Frege's system) yet contributed substantively before their contradictions were discovered.
      ?

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    • 3.The foundational role of formal systems could be pragmatic utility rather than absolute consistency—usefulness doesn't require perfect coherence.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Formal systems serve foundational purposes by guaranteeing we can't derive contradictions, which consistency standards directly protect.
      ?

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    • 2.Relaxing consistency allows contradictions, making it impossible to use formal systems for reliable deduction or mathematical certainty.
      ?

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    • 3.Hilbert's ideal/real distinction shows real mathematics needs consistency to avoid trivializing all propositions via explosion.
      ?

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