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    Carmelics

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    Home/Original/inverse
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    Inverse View

    It is not the case that Ordinal identity guarantees structural isomorphism but not cardinality equivalence when cardinal and ordinal number theories are defined independently.

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

    Reasons For

    1 perspective
    Reason for
    ?
    • 1.Ordinal identity intrinsically depends on cardinality; two sequences differ ordinally if they assign different sizes to their elements or domains.
      ?

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    • 2.The claim conflates notational or formal independence with metaphysical independence; definitions being separate doesn't prevent ordinal facts from constraining cardinality facts.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Ordinal structure (successor relations, ordering) can be preserved across systems while cardinality (set size) varies if definitions operate independently.
      ?

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    • 2.The natural numbers exemplify this: ordinal sequence (1,2,3...) remains identical under different set-theoretic constructions with different cardinality criteria.
      ?

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    • 3.Independent axiomatic systems can define identity conditions separately, making structural isomorphism sufficient for ordinal equivalence without requiring cardinality matching.
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