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Infinite Divisibility and Actual Parts in Hume's Treatise

Infinite Divisibility and Actual Parts in Hume's Treatise Hume Studies Volume 28, Number 1, April 2002, pp. 3-25 Infinite Divisibility and Actual Parts in Hume's Treatise THOMAS HOLDEN I believe that the smallest portion of matter may be practically divided ad infinitum; that equal qualities taken from equal qualities, an unequal quality will remain; that two and two make seven; that the sun rules the night, the stars the day; and the moon is made of green cheese. Tobias Smollett, The History and Adventures of an Atom (1769)1 Introduction The ferocious controversy in early modern natural philosophy over the structure of continua focuses on a cluster of supposed paradoxes of infinite divisibility. According to the recent commentary, these paradoxes are straightforwardly mathematical in nature: they simply challenge mathematical constructions of infinite divisibility. So interpreted, the paradoxes are then quite easy to disarm. They rest on quaint mathematical mistakesÂ--forgivable in the early modern period, perhaps, but clear errors all the same. But this interpretation of the Enlightenment controversy will not stand scrutiny. The early modern debate depends crucially on a body of metaphysical doctrine concerning the 'filling' or 'stuffing' of actual physical continuaÂ--a body of doctrine that dominates the natural philosophy of the period and that sets http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Hume Studies Hume Society

Infinite Divisibility and Actual Parts in Hume's Treatise

Hume Studies , Volume 28 (1) – Jan 26, 2002

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Hume Society
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Abstract

Hume Studies Volume 28, Number 1, April 2002, pp. 3-25 Infinite Divisibility and Actual Parts in Hume's Treatise THOMAS HOLDEN I believe that the smallest portion of matter may be practically divided ad infinitum; that equal qualities taken from equal qualities, an unequal quality will remain; that two and two make seven; that the sun rules the night, the stars the day; and the moon is made of green cheese. Tobias Smollett, The History and Adventures of an Atom (1769)1 Introduction The ferocious controversy in early modern natural philosophy over the structure of continua focuses on a cluster of supposed paradoxes of infinite divisibility. According to the recent commentary, these paradoxes are straightforwardly mathematical in nature: they simply challenge mathematical constructions of infinite divisibility. So interpreted, the paradoxes are then quite easy to disarm. They rest on quaint mathematical mistakesÂ--forgivable in the early modern period, perhaps, but clear errors all the same. But this interpretation of the Enlightenment controversy will not stand scrutiny. The early modern debate depends crucially on a body of metaphysical doctrine concerning the 'filling' or 'stuffing' of actual physical continuaÂ--a body of doctrine that dominates the natural philosophy of the period and that sets

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Hume StudiesHume Society

Published: Jan 26, 2002

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