Infinite Divisibility and Actual Parts in Hume’s Treatise

Hume Studies 28 (1):3-25 (2002)
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According to a standard interpretation of Hume’s argument against infinite divisibility, Hume is raising a purely formal problem for mathematical constructions of infinite divisibility, divorced from all thought of the stuffing or filling of actual physical continua. I resist this. Hume’s argument must be understood in the context of a popular early modern account of the metaphysical status of the parts of physical quantities. This interpretation disarms the standard mathematical objections to Hume’s reasoning; I also defend it on textual and contextual grounds.



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Thomas Holden
University of California at Santa Barbara

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