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    Carmelics

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

    It is not the case that The term 'irrational number' should be extended to include lawless and pseudo-irrationals

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
    ?
    • 1.Mathematical terms gain their meaning from the rules and techniques governing their use, not from phenomenological similarity to other objects.
      ?

      Think about whether this reason is strong or weak

    • 2.Lawless sequences, lacking any rule of extension, cannot be the subject of proofs or calculations in the way rule-governed irrationals can.
      ?

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    • 3.Extending 'irrational number' to cover lawless sequences conflates a grammatical category with a mere analogy, producing conceptual confusion rather than mathematical insight.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.Brouwer and the intuitionists argued that mathematical objects exist only insofar as they are constructible by finite mental operations.
      ?

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    • 2.A 'lawless' sequence is by definition not constructible through any specifiable procedure, making it mathematically unintelligible on constructivist grounds.
      ?

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    • 3.Extending a defined mathematical term to cover entities that violate the constructive basis of that definition undermines the integrity of the original definition.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Lawless and pseudo-irrationals are needed for the mathematical continuum
      ?

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    • 2.Lawless and pseudo-irrationals are more like rule-governed irrationals than like rationals
      ?

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    • 3.Mathematical terms may be extended to cover conceivable numbers that fit more naturally within an existing category than outside it
      ?

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