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    Poincaré and Weyl both argued that classical transfinite ... — Carmelics
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    Challenges→Two infinite well-ordered sets with the same ordinal number have the same cardinal number.

    Poincaré and Weyl both argued that classical transfinite arithmetic conflates structural correspondence with genuine numerical equality, making the entailment from same ordinal to same cardinal non-trivial.

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    Key Terms

    Non-trivial(philosophy of mind and epistemology)
    Something that is meaningful, substantial, or not obvious—the opposite of a trivial or pointless explanation.
    Ordinal(as a mathematical structure being preserved or not)
    A type of number used in mathematics to describe the order or position of things (like 1st, 2nd, 3rd), not just how many.
    Poincaré(as the scientist whose work is being referenced)
    Henri Poincaré was a French mathematician and physicist (1854-1912) who discovered that tiny, unmeasurable changes in a system's starting conditions can lead to completely different outcomes—a key insight that helped create chaos theory.
    Structural correspondence(as what Poincaré and Weyl claim is being confused with genuine equality)
    When two things have the same pattern or structure—like two maps that show the same layout even if one is bigger than the other.

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    Transfinite arithmetic(as the subject being criticized)
    The branch of mathematics that deals with numbers and calculations involving infinity—basically, math rules that work when things are infinitely large.
    Weyl(as a historical reference in physics)
    Hermann Weyl (1885-1955) was a German mathematician and physicist who identified a mathematical problem about how to connect measurements made in different reference frames in a consistent way.
    cardinal(in mathematics and set theory)
    A number that represents the size of a set (how many things are in it), as opposed to the order they're in.
    entailment(Conceptualist framework)
    Understood in terms of truth at a world

    Connections

    2 topics

    Proof of definition segments1 linkedModality & Possibility1 linked

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    Two infinite well-ordered sets with the same ordinal number have the same cardin...

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