The Composition of Space, Time and Matter According to Isaac Newton and John Keill

Palmerino, Carla Rita

doi:10.1007/978-94-007-4345-8_5

The Composition of Space, Time and Matter According to Isaac Newton and John Keill

Carla Rita Palmerino³

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First Online: 01 January 2012

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Part of the book series: Boston Studies in the Philosophy and History of Science ((BSPS,volume 282))

Abstract

In his Mathematical Lectures, read at the University of Cambridge between 1664 and 1666, Isaac Barrow, Lucasian professor of mathematics, criticized “those who would have magnitude constituted of a finite number of indivisibles,” an opinion which he considered repugnant to the laws of mathematics. Barrow argued in favor of the infinite divisibility of all extended quantities, including material bodies:The young Newton, who was to become Barrow’s follower as Lucasian professor of mathematics, held a view diametrically opposed to that of his master. In the Quaestiones quaedam philosophicae, a set of notes redacted between 1664 and 1665 and contained in the Trinity College Notebook, he asserted that all extended magnitudes were composed out of a finite number of extended, but partless minima.

Research for this article was made possible through the financial support of the project Visualizing the Invisible. Representations of Matter and Motion since the Renaissance, sponsored by the Netherlands Organization for Scientific Research (NWO). I wish to thank the editors for their valuable comments on earlier drafts of this article.

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Notes

1.
Barrow, The Usefulness of Mathematical Learning explained and demonstrated, pp. 151, 162.
2.
Palmerino, “The Isomorphism of Space, Time and Matter in Seventeenth-Century Natural Philosophy.”
3.
Newton, Opticks, pp. 389, 403.
4.
Janiak, “Space, Atoms and Mathematical Divisibility in Newton.”
5.
Newton, Certain Philosophical Questions, pp. 352–354.
6.
More, The Immortality of the Soul, Preface.
7.
Ibid., book I, chap. 6, p. 31.
8.
Ibid.
9.
Janiak, “Space, Atoms and Mathematical Divisibility in Newton,” p. 206.
10.
Newton, Certain Philosophical Questions, p. 341.
11.
Ibid., p. 353.
12.
Charleton, Physiologia, pp. 88, 90–93.
13.
Ibid., p. 84.
14.
Ibid., p. 97.
15.
Newton, Certain Philosophical Questions, p. 339. For Charleton’s view, see Physiologia, pp. 251–254.
16.
See Fromondus, Labyrinthus, pp. 76–97.
17.
“In omni motu tardo pausas et morulas quasdam interiiciunt quibus mobile quiescat, quae in motu celeriori complentur,” ibid., p. 62.
18.
Arriaga, Cursus philosophicus, pp. 428–432.
19.
“Declaratum certe est quoque iam ante & infinitatem illam partium in continuo, & insectilitatem Mathematicam in rerum natura non esse, sed Mathematicorum hypothesin esse, atque idcirco non oportere argumentari in Physica ex iis, quae natura non novit,” Gassendi, Opera omnia, I, p. 341b.
20.
“Ut se habet spatium reale, ita & motus realis, sed in spatio reali sunt atomi, ergo et in motu erunt atomi, sed atomi motus non possunt fingi animo, quin intelligatur totae simul, ergo datur motus totus simul, qui tamen erit successivus in connotatione seu extrinsece penes spatium mathematicum,” Magnen, Democritus reviviscens, p. 234.
21.
“Respondeo ad tertium ad sensum dari posse motum unifromiter difformem non autem stricte loquendo, quia est semper aliquod spatium per quod motus est aequalis, & uniformis idq; necessario atomorum naturam sequitur,” ibid., p. 236.
22.
“Atomus est omni figurae capax, ergo occupare potest maiorem, & maiorem locum in infinitum: cum enim figurae regulares in isoperimetris sint magis collectae minoremque locum occupent, sequitur quod quo irregularior erit figura eo maiorem occupabit locum, at non potest dari, ita irregularis, quin magis irregularis esse possit, ergo etiam maioris loci capax,” ibid., p. 247.
23.
“dantur instantia Physica; quia datur actio, per quam res est,” Fabri, Metaphysica demonstrativa, p. 371. For Fabri’s theory of matter and motion, see Palmerino, “Two Aristotelian Responses to Galilei’s Science of Motion.”
24.
Fabri, Metaphysica demonstrativa, p. 371.
25.
Ibid., p. 413.
26.
Ibid., p. 375.
27.
“nam equidem fateor instanti mathematico nihil esse posse minus; secus vero instanti physico, quod est divisibile potentia, ut dicemus alias,” Fabri, Tractatus physicus, p. 110.
28.
“Facile iuxta hanc hypothesim, omnia quae pertinent ad quantitatem explicantur; Primo motus velocitas et tarditas…. Secundo rarefactio, condensatio, compressio, dilatatio; quia quodlibet punctum potest habere, modo maiorem, modo minorem extensionem,” Fabri, Metaphysica demonstrativa, p. 414.
29.
“Si aër constat ex punctis mathematicis, non potest explicari, quomodo rarescat, vel densetur, vel comprimatur, contra post. Nec enim punctum mathematicum potest esse maius, vel minus: nec est quod Arriaga explicet condensationem per extrusionem corpusculorum, & rarefactionem per intrusionem, quippe hoc manifestae experientiae repugnat,” ibid., p. 397. Arriaga’s explanation of rarefaction and condensation is criticized also in ibid., p. 424.
30.
Ibid., p. 395.
31.
Fromondus, Labyrinthus, pp. 57f.
32.
Ibid., p. 55.
33.
Galilei, Two New Sciences, 157. For a discussion of the relation between Galileo’s theory of matter and his theory of motion, see Palmerino, “Una nuova scienza della materia per la scienza nova del moto. La discussione dei paradossi dell’infinito nella prima giornata dei Discorsi galileiani”; Ead., “Galileo’s and Gassendi’s Solutions to the Rota Aristotelis Paradox. A Bridge between Matter and Motion Theories.”
34.
Galilei, Two New Sciences, p. 54 (= Galilei, Opere, VIII, p. 93).
35.
“Subtiliores, inter eos qui continuum ex atomis struxerunt, ex infinitis potius quam finitis composuisse,” Fromondus, Labyrinthus, p. 9. For the possible influence of Fromondus on Galileo, see Redondi, “Atomi, indivisibili e dogma,” pp. 555–557.
36.
Fromondus, Labyrinthus, pp. 97–99 (Caput XXXI, Frustra quidam conati inter Aristotelem & Epicurum medij incedere, negando ullas esse in continuo partes, aut asserendo infinitas, sed indivisibiles).
37.
“Si spatij quod pertransitur magnitudo habet partes proportionales infinitas, quarum una prior est, altera posterior, igitur corpus quod sine replicatione per tale spatium movetur, debet infinitas partes transire, unam post alteram, partesque in eo motu successivae erunt etima infinitae: nam unicuique parti spatij permanentis, sua pars motus successivi respondet,” ibid., p. 137.
38.
“Deus tamen materiam illam sine forma, aut cum ipsa contra naturam conservata, potest sine fine rarefacere. Quod etiam exemplo tarditatis in motu possumus declarare: tarditats enim in successivis est quaedam partium laxitas, simillima raritati in permanentibus.… Veluti autem ex tarditate motus infinita rarefactionem posse sine fine procedere ostenditur; ita ex velocitate motus, quae etiam in infinitum increscere potest (cur enim Deus caelestes sphaeras ampliores & ampliores sine fine creare nequeat, quae omnes 24 horarum spatio revolvantur?) ostendere possumus, condensationem, si ad virtutem divinam comparemus, nullum habere finem,” ibid., pp. 191–193.
39.
Newton, Certain Philosophical Questions, p. 40.
40.
Ibid., pp. 46f., 78f., 87.
41.
Cohen, “Newton’s Concept of Force and Mass, with Notes on the Laws of Motion,” p. 74. Newton speaks about “particles of time,” which he describes as “infinitely small” or “minimally small” in The Principia. Mathematical Principles of Natural Philosophy, pp. 316, 652f., 673f.
42.
Newton, Unpublished Scientific Papers, p. 272.
43.
Blay, “Force, Continuity, and the Mathematization of Motion at the End of the Seventeenth Century,” pp. 225f.
44.
Newton, Papers and Letters on Natural Philosophy, p. 251.
45.
Ibid., p. 253.
46.
Newton, Unpublished Scientific Papers, pp. 149–50.
47.
Ibid., p. 148.
48.
Ibid., pp. 149f.
49.
Ibid., p. 150.
50.
Ibid., p. 151.
51.
Ibid., pp. 151f.
52.
Charleton, Physiologia, p. 89.
53.
Newton, Certain Philosophical Questions, p. 45.
54.
Newton, Unpublished Scientific Papers, p. 145.
55.
Ibid., p. 137.
56.
More, Manual of Metaphysics: A Translation of the Enchiridium Metaphysicum (1679), p. 58. For an analysis of the influence of More’s Enchiridium on Newton’s De gravitatione, see Slowik, “Newton’s Metaphysics of Space”; id. “Newton, the Parts of Space, and the Holism of Spatial Ontology”.
57.
McGuire, “Newton on Place, Time and God,” p. 117.
58.
Alexander (ed.), The Leibniz-Clarke Correspondence, pp. 25, 31f.
59.
Ibid., p. 38.
60.
Ibid., p. 48. Alexander wrongly replaced the term “indiscerpible,” used by Clarke in his original letter, with “indiscernible.” See Janiak, “Space, Atoms and Mathematical Divisibility in Newton,” p. 225.
61.
Ibid.
62.
Newton, The Principia. Mathematical Principles of Natural Philosophy, p. 795.
63.
Ibid., pp. 795–796. I follow here the corrected translation found in Janiak, “Space, Time and Mathematical Divisibility in Newton,” p. 215.
64.
Janiak, Newton as Philosopher, p. 109.
65.
Newton, Unpublished Scientific Papers, p. 312.
66.
Newton, Opticks, pp. 403f.
67.
Janiak, “Space, Atoms and Mathematical Divisibility,” pp. 226f.
68.
Newton, Certain Philosophical Questions, p. 336.
69.
Keill, An Introduction to Natural Philosophy, p. viii.
70.
For an analysis of Keill’s theory of the composition of the continuum, see Thijssen, “David Hume and John Keill and the Structure of the Continua.” Thijssen focuses on lectures 2 and 3 of Keill’s Introduction.
71.
Keill, An Introduction to Natural Philosophy, pp. 13–15.
72.
Ibid., p. 20.
73.
Ibid., p. 26.
74.
Ibid., pp. 26–30.
75.
Ibid., pp. 30f.
76.
Ibid., pp. 31f.
77.
Ibid., p. 31.
78.
Ibid., pp. 32–45.
79.
Ibid., p. 35.
80.
Ibid., pp. 33–37.
81.
Ibid., pp. 38f.
82.
Ibid., p. 39.
83.
Descartes, Œuvres, vol. VIII, p. 51. In the letter to Gibieuf, Descartes wrote: “Ainsi, nous pouvons dire qu’il implique contradiction, qu’il y ait des atomes ou des parties de matière qui aient l’extension et toutefois soient indivisibles, à cause qu’on ne peut avoir l’idée d’une chose étendue qu’on puisse avoir aussi celle de sa moitié, ou de son tiers, ni, par conséquent, sans qu’on la conçoive divisible en 2 ou en 3. Car, de cela seul que je considère les deux moitiés d’une partie de matière, tant petite qu’elle puisse être, comme deux substances complètes, & quarum ideae non redduntur a me inadequatae per abstractionem intellectus, je conclus certainement qu’elles sont réellement divisibles,” ibid., vol. III, p. 477. For Descartes’ rejection of indivisibles, see Roux, “Descartes atomiste?”
84.
Keill, An Introduction to Natural Philosophy, p. 41.
85.
Ibid., pp. 43f.
86.
Ibid., p. 45.
87.
Ibid., p. 46.
88.
Ibid., p. 48.
89.
Ibid., p. 59.
90.
Ibid., p. 64.
91.
Ibid., p. 73.
92.
Galilei, Dialogue, p. 229 (= Galilei, Opere, VII, p. 248).
93.
Keill, An Introduction to Natural Philosophy, p. 144.
94.
Newton, Unpublished Scientific Papers, p. 151.
95.
Keill, An Introduction to Natural Philosophy, p. 39.
96.
Ibid.
97.
Ibid., p. 21.

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Palmerino, C.R. (2013). The Composition of Space, Time and Matter According to Isaac Newton and John Keill. In: GARBER, D. (eds) The Mechanization of Natural Philosophy. Boston Studies in the Philosophy and History of Science, vol 282. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4345-8_5

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