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    Carmelics

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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 Craig's usage of 'actual infinite' and 'potential infinite' differs from the traditional Aristotelian usage.

    ?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.Cantor's transfinite arithmetic, which Craig explicitly adopts, redefines 'actual infinite' as a completed set with determinate cardinality, superseding Aristotle's framework.
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    • 2.Craig consistently signals he is working within post-Cantorian set theory, so measuring his usage against Aristotelian standards conflates two distinct mathematical traditions.
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    • 3.The relevant question is whether Craig's usage is internally coherent within its own framework, not whether it maps onto Aristotle's pre-Cantorian distinctions.
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    Reason for 2 of 2
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    • 1.Aristotle himself treated the past as a determinate, completed sequence of events that no longer admits addition, which aligns structurally with Craig's criterion for actual infinites.
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    • 2.If Aristotle's own account of the past shares the 'no further addition' property Craig attributes to actual infinites, the divergence between their usages is narrower than the supporting arguments assert.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.For Aristotle, all elements in an actual infinite exist simultaneously, whereas a potential infinite is realized over time by addition or division.
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    • 2.For Aristotle, the temporal series of events, formed by successively adding new events, is a potential infinite, not an actual infinite.
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    • 3.For Craig, an actual infinite is a timeless totality that cannot be added to or reduced, and past events qualify as an actual infinite because they are determinate and can be collected into a totality.
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