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    It is not the case that The cardinal number of the power set of the set of space-time points (at least ℵ₂) is the largest cardinal.

    ?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.Scientific theories are revisable, and set-theoretic commitments of current physics cannot constrain what cardinalities exist independently of theory.
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    • 2.Large cardinal axioms (inaccessible, Mahlo, measurable cardinals) are mathematically consistent extensions of ZFC that posit sets far exceeding the power set of spacetime points.
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    • 3.A naturalist who defers to mathematics as a science must acknowledge that mathematical practice itself demands cardinals beyond any fixed bound.
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    Reason for 2 of 2
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    • 1.Quine-Putnam indispensability arguments license only those mathematical entities indispensable to best science, but Maddy's objections show actual scientific practice does not uniformly quantify over all posited mathematical objects.
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    • 2.The inference from 'physics requires no set larger than P(spacetime)' to 'no larger cardinal exists' commits a modal fallacy, conflating epistemic and ontological limitations.
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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.A philosopher with positivistic or naturalistic leanings should posit transfinite cardinals of only those sizes required by prevailing scientific theories.
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      Think about whether this reason is strong or weak

    • 2.The prevailing theory of the space-time continuum in physics is committed to the existence of infinite sets which have the cardinality of the set of space-time points (at least ℵ₁).
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    • 3.This scientific theory is also committed to the existence of the power set of the set of space-time points, needed to accommodate continuous and discontinuous linear paths.
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