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    Craig's usage of 'actual infinite' and 'potential infinit... — Carmelics
    Home/Natural Theology
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    Craig's usage of 'actual infinite' and 'potential infinite' differs from the traditional Aristotelian usage.

    Natural Theology
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    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
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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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    Reasons Against

    2 perspectives
    Reason against 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 against 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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    Natural Theology

    Related

    Aristotle himself treated the past as a determinate, completed sequence of event...Cantor's transfinite arithmetic, which Craig explicitly adopts, redefines 'actua...Craig consistently signals he is working within post-Cantorian set theory, so me...For Aristotle, all elements in an actual infinite exist simultaneously, whereas ...
    +4 moreShow less
    For Aristotle, the temporal series of events, formed by successively adding new ...For Craig, an actual infinite is a timeless totality that cannot be added to or ...If Aristotle's own account of the past shares the 'no further addition' property...The relevant question is whether Craig's usage is internally coherent within its...

    Similar

    There can be no such thing as an actual infinite.84%God is infinite83%The future is a potential infinite, not an actual infinite.82%For Aristotle, the temporal series of events, formed by successively a...81%

    Source

    AI-extracted2/3 agreementValid
    SEP: cosmological-argument
    Craig and Sinclair 2009: 115
    View source passageHide passage
    Craig is well aware of the fact that he is using actual and potential infinite in a way that differs from the traditional usage in Aristotle and Aquinas [Craig and Sinclair 2009: 115. For Aristotle, all the elements in an actual infinite exist simultaneously, whereas a potential infinite is realized over time by addition or division. Hence, the temporal series of events, as formed by successively adding new events, was a potential, not an actual, infinite (Aristotle, Physics, III, 6)]. For Craig, however, an actual infinite is a timeless totality that cannot be added to or reduced. “Since past...
    Extraction notes

    The premises establish a clear contrast: Aristotle would classify the temporal series of past events as a potential infinite (Premises 1-2), whereas Craig classifies past events as an actual infinite (Premise 3), thereby demonstrating that their usages of these terms differ.

    Validity:

    Confidence: High confidence — the contrast is explicitly drawn in the text.

    Details

    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit