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    Carmelics

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    Made withinDC&Austin
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    Home/Original/inverse
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    Inverse View

    It is not the case that Infinite mathematical objects, such as the completed set of all natural numbers and arbitrary irrational numbers represented by Dedekind cuts, do not exist.

    ?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.Dedekind cuts and the set of natural numbers are presupposed by classical analysis, which underwrites physical theories whose predictive success we have no rival explanation for.
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      Think about whether this reason is strong or weak

    • 2.Quine and Putnam's indispensability argument holds that ontological commitment is owed to any entity whose posit is ineliminable from our best confirmed scientific theories.
      ?

      Think about whether this reason is strong or weak

    • 3.The finitist's restriction to finite objects cannot recover the full continuum required by differential equations, leaving a systematic explanatory gap the claim does not resolve.
      ?

      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.Cantor's transfinite arithmetic demonstrates that completed infinities obey consistent, non-contradictory formal laws, satisfying the existence criterion Hilbert called 'consistency entails existence'.
      ?

      Think about whether this reason is strong or weak

    • 2.If a mathematical structure is internally consistent and theoretically indispensable, denying its existence requires a stricter criterion of existence that the finitist has not independently justified.
      ?

      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Only finite mathematical objects (like numbers and sentences) exist in whatever sense mathematical objects exist.
      ?

      Think about whether this reason is strong or weak

    • 2.Completed infinities are not finite objects.
      ?

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