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    Mathematical practice across analysis, geometry, and numb... — Carmelics
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    Supports→Set theory is unnecessary for mathematics.

    Mathematical practice across analysis, geometry, and number theory proceeded rigorously for centuries without set-theoretic foundations.

    ?Rate how convincing each reason is below to see the overall strength.
    1 reason for
    1 reason against

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Euler, Gauss, and Cauchy produced theorems still considered valid today without referencing set theory or its axioms.
      ?

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    • 2.Rigorous mathematical practice requires clear definitions and logical proof structure, which existed centuries before Cantor.
      ?

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    • 3.Set-theoretic foundations were developed to formalize existing mathematics, not to enable it; the practice preceded the framework.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Historical mathematicians used implicit set-theoretic concepts (collections, domains, quantification) without formalizing them.
      ?

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    • 2.Rigor is relative to era; pre-Cauchy 'rigor' tolerated infinitesimals and divergent series now recognized as inadequately justified.
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    • 3.Set theory revealed hidden paradoxes in informal practice (like unrestricted comprehension), showing earlier foundations were incomplete.
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    Related

    Euler, Gauss, and Cauchy produced theorems still considered valid today without ...Historical mathematicians used implicit set-theoretic concepts (collections, dom...Rigor is relative to era; pre-Cauchy 'rigor' tolerated infinitesimals and diverg...Rigorous mathematical practice requires clear definitions and logical proof stru...
    +3 moreShow less
    Set theory is unnecessary for mathematics.Set theory revealed hidden paradoxes in informal practice (like unrestricted com...Set-theoretic foundations were developed to formalize existing mathematics, not ...

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    claim
    Perspectives
    2 (1 for, 1 against)