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    Carmelics

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    Home/Original/inverse
    See Original
    Inverse View

    It is not the case that Although actual infinites can have an ideal existence, they cannot really exist.

    ?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.The 'absurdities' in Hilbert's Hotel and similar cases are merely counterintuitive results of transfinite arithmetic, not logical contradictions.
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      Think about whether this reason is strong or weak

    • 2.Cantor's set theory rigorously demonstrates that a proper subset of an infinite set can have the same cardinality as the whole, which is a provable theorem, not an absurdity.
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      Think about whether this reason is strong or weak

    • 3.An inference from 'violates finite intuitions' to 'cannot really exist' conflates psychological surprise with metaphysical impossibility.
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      Think about whether this reason is strong or weak

    Reason for 2 of 2
    ?
    • 1.The argument illicitly assumes that operations governing finite collections, such as subtraction and part-whole relations, must govern infinite collections in the same way.
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      Think about whether this reason is strong or weak

    • 2.Georg Cantor and contemporary set theorists like Quine and Maddy have shown that denying the part-whole axiom for infinite sets yields a consistent, well-developed mathematics that maps onto physical theories.
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      Think about whether this reason is strong or weak

    • 3.If actual infinities are ruled out by Craig's reasoning, the continuous spacetime manifolds and infinite-dimensional Hilbert spaces employed in modern physics would also be metaphysically impossible, an implausible conclusion.
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      Think about whether this reason is strong or weak

    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.If actual infinites that neither increase nor decrease in the number of members they contain were to really exist, absurd consequences would result.
      ?

      Think about whether this reason is strong or weak

    • 2.In a library with an actually infinite number of books containing an infinite number of red and an infinite number of black books, the library would contain as many red books as the total books in its collection and as many red books as red and black books combined. But in reality the subset cannot be equivalent to the entire set.
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      Think about whether this reason is strong or weak

    • 3.In a real library, removing a certain number of books reduces the overall collection. But if infinites are actual, a library with an infinite number of books would not be reduced in size at all by removal of a specific number of books, such as all the red books or those with even catalogue numbers.
      ?

      Think about whether this reason is strong or weak

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    Strongest counterpoint
    Explore the most compelling reason on the other side.