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    Carmelics

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    Home/Original/inverse
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    Inverse View

    It is not the case that Aristotle's geometric arguments against the existence of an infinite dimension are invalid

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    Reasons For

    1 perspective
    Reason for
    ?
    • 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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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 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 against 2 of 2
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    • 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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