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    Aristotle's geometric arguments against the existence of ... — Carmelics
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    Aristotle's geometric arguments against the existence of an infinite dimension are invalid

    Modality & Possibility
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    2 reasons for
    1 reason against

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Aristotle's geometric arguments assume that any magnitude composed of infinite parts must itself be traversable only by infinite successive steps.
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    • 2.Cantorian set theory demonstrates that infinite sets can be placed in bijection with proper subsets, undermining the Aristotelian assumption that infinite extension entails unmeasurable magnitude.
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    • 3.If the mathematical structure of infinity is coherent and does not generate the contradictions Aristotle alleges, his reductio ad absurdum arguments lose their logical force entirely.
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    Reason for 2 of 2
    ?
    • 1.Aristotle's arguments rely on the potential/actual infinity distinction, treating actual infinite dimensions as geometrically self-contradictory.
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    • 2.Crescas, following in the tradition of atomist and Neoplatonic cosmology, argues that an actually infinite dimension need not permit the construction of the absurd proportional relationships Aristotle projects onto it.
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    • 3.If the geometric contradictions Aristotle derives depend on treating infinite magnitudes as though they behave like arbitrarily large finite ones, the arguments are category errors, not valid reductions.
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    Reasons Against

    1 perspective
    Reason against
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    • 1.Even if a dimension is infinite, all real points within that dimension are a finite distance from one another
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    • 2.Aristotle's arguments against the infinite are based on the distances between different points
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    • 3.If all real points in an infinite dimension are finitely distant from one another, Aristotle's distance-based arguments are cancelled
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    Related

    Aristotle's arguments against the infinite are based on the distances between di...Aristotle's arguments rely on the potential/actual infinity distinction, treatin...Aristotle's geometric arguments assume that any magnitude composed of infinite p...Cantorian set theory demonstrates that infinite sets can be placed in bijection ...
    +5 moreShow less
    Crescas, following in the tradition of atomist and Neoplatonic cosmology, argues...Even if a dimension is infinite, all real points within that dimension are a fin...If all real points in an infinite dimension are finitely distant from one anothe...If the geometric contradictions Aristotle derives depend on treating infinite ma...If the mathematical structure of infinity is coherent and does not generate the ...

    Similar

    Aristotle's arguments against the infinite are based on the distances ...80%Riemannian geometry satisfies Weyl's fundamental principle of infinite...78%If all real points in an infinite dimension are finitely distant from ...77%Sextus's argument assumes the particulars are always infinite and inde...75%

    Source

    AI-extracted1/3 agreementValid
    SEP: crescas
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    Another original definition of infinite in the thought of Crescas is his utilization of the difference between the infinite in practice and the infinite in potential. One of Aristotle’s methods of affirming the non-existence of the infinite was to claim that the existence of an infinite dimension forbids some of the laws of geometry. Crescas refutes this kind of argument by the differentiation between the infinite in practice versus the infinite in potential. The argument goes thus: Even if I ha
    Extraction notes

    Validity: Extracted via Max plan + API grounding/validity checks

    Details

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