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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 The claim conflates potential infinity (always being able to add another digit) with actual representability, a distinction Aristotle and later Cantor took to be philosophically significant.

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

    Reasons For

    1 perspective
    Reason for
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    • 1.Modern set theory successfully treats infinite sets as complete objects; their mathematical utility demonstrates actual infinity is representable abstractly.
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    • 2.The distinction assumes representation requires finite specification, but mathematics works with infinite objects defined by properties (e.g., 'all natural numbers').
      ?

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    • 3.Decimal expansions like 0.333... are standardly written and manipulated; mathematical notation treats them as unified entities, not mere processes.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.Potential infinity describes a process (adding digits indefinitely), while actual infinity describes a completed totality—these are ontologically distinct.
      ?

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    • 2.Representing a number requires specifying it completely; an endless process cannot constitute a finished representation in any finite system.
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    • 3.Aristotle's rejection of actual infinity in mathematics proved mathematically sound; potential infinity suffices for classical geometric and arithmetic reasoning.
      ?

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