Abstract
In an early treatise, now entitled De Gravitatione et aequipondio fluidorum (c. 1668), Newton attacks Descartes’ doctrine of material extension. The occasion for the attack occurs in a discussion of the nature and existence of space, in which Newton argues that the extension of space is uncreated, eternal, immutable, and endowed with an autonomous geometrical structure.1 Not surprisingly, the proposition on which Newton concentrates is his posi- tive claim that “Space everywhere extends to infinity. [Spatium in infinitum usque omnifariam extenditur] ” (De Grav. p. 101).
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Notes
A. Rupert Hall and Maria Boas Hall, Unpublished Scientific Papers of Isaac Newton, Cambridge University Press, 1962, De Gravitatione, pp. 99, 100-101, and 110. Subsequent page references to De Grav. will be in the text.
U. L. C. MS. Add. 3996. folio 83r−v. Subsequent references to the Questiones will be in the text. Professor Martin Tanny and I are completing a critical edition of Questiones which will be published by the Cambridge University Press. In all passages quoted from the Questiones spelling has been modernized.
John Locke, An Essay Concerning Human Understanding, London, Everyman’s Library, 1972, Vol. I, Bk. II, Chapters XVI and XVII. Subsequent references are to this edition will be in the text.
J. E. McGuire, ‘Existence, Actuality and Necessity: Newton on Space and Time’, Annals of Science 35 (1978), 463–509.
London, 1687, Part XIII, Chapter 11, p. 858.
Diogenes Laertius, De Vitis Dogmatis et Apophthegmatis — Libri X, London, 1664. Epicurus Lib. X, p. 276. This page is dog-eared by Newton, as indeed are many pages in the edition having to do with the infinity of the world.
London, 1654, Bk. I, Chapter 11, Section 11, 9-15. There are many late 16th century and early 17th century copies of Lucretius’ poem in the Trinity College Library. There is no evidence, however, that Newton used them. Nevertheless, it seems improbable that he did not know of Lucretius.
Nicolas de Cusa, Opera Omnia. Heidelberg Academy Edition, ed. Ernest Hoffmann & Raymund Klibansky, Lipsig, 1932, Vol. I, De Docta Ignorantia, Chapter XVII, p. 33. Since nothing determinate can be infinite, Cusanus never affirms the infinity of the world, as Descartes mistakenly claims he does (AT. V. 50, To Chanut, 6, June 1647). D. W. Singer, Giordano Bruno, His Life and Thought, New York: Abelard-Schuman, 1950. On the Infinite Universe and the Worlds. First Dialogue, p. 257. Gottfried Liebniz, New Essays Concerning Human Understanding, the Open Court Company, Chicago, 1916, the critique of Bk. II of Locke’s Essay, Chapter XVII, pp. 161-164.
Ibid., Chapter XV, pp. 158-159 and Chapter XVII, pp. 169-174. Leibniz’s approach to infinity must be understood in the context of his claim that ostensibly extended phenomena are not true unities in the manner of indivisibles whose unity and being are one.
U. L. C. MS. Add. 3995. folios 9r−v-18r.
Folio 83r−v. Both folios are copiously filled with citations from, and page references to, Descartes’ Meditations and the Objections and Replies. In every case Newton’s citations and page references are to the Opera Philosophica, 3rd edition, Amsterdam, 1656, which includes Descartes’ complete works. The exact citations and references to this edition leave no doubt that Newton had read Descartes’ philosophical writings carefully.
Oeuvres de Descartes, Charles Adam and Paul Tannery (eds.), Libraire Philosophique J. Urin, Paris, 1973. Meditation II, pp. 28-29, Vol. VU. In the future, all references will be in the text as (AT. VII. 28-29).
John Wallis, Operum Mathematicorum Pars Altera, Oxford, 1656, Arithmetica Infinitorum in pars altera, propositions 34 and 40.
For a useful discussion of Descartes’ distinction between the ‘indefinite’ and the infinite, see John Cottingham (ed. and transl., Descartes’ Conversations with Barman. Clarendon Press, Oxford, 1976), Commentary, p. 101.
Ibid., See Cottingham’s discussion of the notion of adequate knowledge in Descartes, p. 65.
In his reply to my paper at the Montreal meeting of the Union of the History and Philosophy of Science, pp. 18-19.
J. E. McGuire, ‘Newton on Place, Time, and God: An Unpublished Source’, British Journal for the History of Science, II, (1978), 114–129, p. 119.
Ibid., pp. 119 and 121.
Op. Cit., note 4. See Section Three entitled ‘Existence and natures’, pp. 474-487.
Op. Cit., note 17.
Ibid.
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© 1983 D. Reidel Publishing Company, Dordrecht, Holland
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McGuire, J.E. (1983). Space, Geometrical Objects and Infinity: Newton and Descartes on Extension. In: Shea, W.R. (eds) Nature Mathematized. The University of Western Ontario Series in Philosophy of Science, vol 20. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-6957-5_5
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