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    Carmelics

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

    It is not the case that Non-standard real analysis can prove results in real analysis that were not first proven by standard real analysis methods.

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Historical priority of discovery does not establish logical or mathematical independence of the method used.
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    • 2.Robinson's 1966 non-standard proofs of results like the Bernstein-Robinson theorem were rapidly given standard reformulations by Halmos and others.
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    • 3.A result 'first proven' by non-standard means but immediately translatable into standard means reveals a sociological fact, not a mathematical one about the claim's provability.
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    Reason for 2 of 2
    ?
    • 1.Any theorem provable via non-standard analysis is provable via standard analysis by the transfer principle (Łoś's theorem).
      ?

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    • 2.If standard proofs always exist for every non-standard result, non-standard methods yield no genuinely novel theorems, only novel proofs.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • There are cases of results in real analysis that were first proven using non-standard real analysis.
      ?

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