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Riemann’s Scale: A Puzzle About Infinity

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Abstract

Ordinarily, the order in which some objects are attached to a scale does not affect the total weight measured by the scale. This principle is shown to fail in certain cases involving infinitely many objects. In these cases, we can produce any desired reading of the scale merely by changing the order in which a fixed collection of objects are attached to the scale. This puzzling phenomenon brings out the metaphysical significance of a theorem about infinite series that is well known by mathematicians but has so far eluded philosophical scrutiny.

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Notes

  1. As evidence that this discovery would be surprising, we need only recall a substantial body of work in metaphysics and philosophical logic that readily invokes possibilities of the sort that this discovery would rule out. See Lewis (1986), Sider (2009), and Hawthorne and Uzquiano (2011) for a representative sample.

  2. I am grateful to Karen Crowther, Casper Storm Hansen, Gabriel Uzquiano, and a referee for valuable comments on previous versions of this note.

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Funding

Funding was provided by Research Council of Norway (Grant No. 250654).

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  1. University of Oslo, Oslo, Norway

    Øystein Linnebo

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  1. Øystein Linnebo
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Correspondence to Øystein Linnebo.

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Linnebo, Ø. Riemann’s Scale: A Puzzle About Infinity. Erkenn 88, 189–191 (2023). https://doi.org/10.1007/s10670-020-00345-x

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  • DOI: https://doi.org/10.1007/s10670-020-00345-x

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