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    Carmelics

    A reasoning platform. Break down any belief into clear reasons, explore both sides, and weigh the evidence honestly.

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    LoyalLoyalJusticeJustice
    Made withinDC&Austin
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Home/Original/inverse
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    Inverse View

    It is not the case that There must be gaps between the rational numbers that require filling with irrational numbers to account for continuous motion.

    ?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.Continuous motion is a physical phenomenon whose mathematical description is a modeling choice, not a metaphysical necessity.
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      Think about whether this reason is strong or weak

    • 2.A model using only rational-valued coordinates can approximate any physical trajectory to within any finite precision demanded by measurement.
      ?

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    • 3.The alleged 'gaps' are artifacts of conflating the mathematical real line with physical space, not discovered features of motion itself.
      ?

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    Reason for 2 of 2
    ?
    • 1.Wittgenstein argued that irrational numbers are not discovered by revealing pre-existing gaps but are constructed through extending mathematical grammar via new rules.
      ?

      Think about whether this reason is strong or weak

    • 2.The supporting argument illicitly treats the density-of-rationals as a spatial deficiency rather than a feature of how we apply number concepts to extension.
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      Think about whether this reason is strong or weak

    • 3.No physical experiment can detect a trajectory passing through an irrational rather than a nearby rational coordinate, undermining the causal-explanatory claim.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.If an object moves continuously from A to B, it traverses all distances along that path.
      ?

      Think about whether this reason is strong or weak

    • 2.The rational numbers are only dense, not continuous — an object traveling only rational distances would skip some intervals.
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    • 3.Continuous motion therefore traverses distances that cannot be commensurately measured by rational numbers alone.
      ?

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    Next step

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    Strongest counterpoint
    Explore the most compelling reason on the other side.