‘The Twin-Brother of Space’: Spatial Analogy in the Emergence of Absolute Time

Abstract

Seventeenth-century authors frequently infer the attributes of time by analogy from already established features of space. The rationale for this can be traced back to Aristotle's analysis of time as ‘the number of movement’, where movement requires a prior understanding of spatial magnitude. Although these authors are anti-Aristotelian, they were concerned, contra Aristotle, to establish the existence of ‘empty space’, and a notion of absolute space which fit this idea. Although they had no independent rationale for the existence of absolute time, it seemed to go with absolute space, and they drew on a long tradition of space-time parallelism in securing this.

Notes

¹ N. Jolley, ‘Metaphysics’, in Cambridge Companion to Early Modern Philosophy, edited by D. Rutherford (Cambridge: Cambridge University Press, 2006), 95–135 (128). J.J. McIntosh made the same point in more colorful language: ‘Like fish and chips, philosophical discussions of space usually consort with discussions of time’; J.J. McIntosh, ‘Berkeley's Views on Time’ in New Essays on Rationalism and Empiricism, edited by C.E. Jarrett, J. King-Farlow and F.J. Pelletier, Canadian Journal of Philosophy, Supplementary Volume 4 (1978), 153–163 (153).

² I. Newton, The Principia: Mathematical Principles of Natural Philosophy, edited and translated by I.B. Cohen and A. Whitman (Berkeley, CA: University of California Press, 1990), 408.

³ N. Jolley, ‘Metaphysics’, 128–129. See also W. Von Leyden, Seventeenth Century Metaphysics (New York, NY: Barnes and Noble, 1968), 259; and M. Čapek, The Concepts of Space and Time (Dordrecht: D. Reidel, 1976), xv.

⁴ W. Charleton, Physiologia Epicuro-Gassendo-Charltoniana (New York, NY: Johnson Reprint Col, 1966), Bk I, Ch. vii, Sect 2, art 1; 75.

⁵ J. Locke, Essay Concerning Human Understanding, edited by P.H. Nidditch (Oxford: Oxford University Press, 1975), II, xv, 12; 204.

⁶ Aristotle, Complete Works, edited by J. Barnes, 2 vols (Oxford: Oxford University Press, 1984), 218a1–2; 370. On the reality of time for Aristotle, see M. Inwood, ‘Aristotle on the reality of Time’ in Aristotle's Physics: A Collection of Essays, edited by L. Judson (Oxford: Clarendon, 1995), 151–178.

⁷ Aristotle, Complete Works I, 220a24; 373.

⁸ Aristotle, Complete Works I, 219a10–11; 371.

⁹ Aristotle, Complete Works I, 219a11–12; 371.

¹⁰ Aristotle, Complete Works I, 219a17–18; 371. ‘Since then “before” and “after” hold in magnitude they must also hold in movement, these corresponding to those. But also in time the distinction between “before” and “after” must hold, for time and movement always correspond with each other’, Aristotle, Complete Works I, 219a 15–19; 371. His view seems to be not merely that magnitude induces a linear ordering on events, but also (rather surprisingly) that the ‘before’ and ‘after' in magnitude explains the direction of time. This seems to generate a vicious circularity in his account: for how can we identify a spatial trajectory as from A to B, rather than vice-versa, without presupposing the temporal notions of earlier and later? See G.E.L. Owen, ‘Aristotle on Time’ in Motion and Time, Space and Matter, edited by P. Machamer and R. Turnball (Columbus, OH: Ohio State University Press, 1976), 3–27; U. Coope, Time for Aristotle (Oxford: Oxford University Press, 2005), chapter 3.

¹¹ Aristotle, Complete Works I, 220a5–21; 372–373.

¹² Aristotle, Complete Works I, 220a14; 373. The now is like a point on a body which is the same so long as the body is at rest but different while moving, since it is ‘at one time here and at another time there’, Aristotle, Complete Works I, 219b 23–4; 372.

¹³ Aristotle, Complete Works I, 208a220–24; 354.

¹⁴ Aristotle, Complete Works I, 206b11–3; 351.The reason is that the parts of time and movement do not exist all at once, but only successively, while the parts of a spatial magnitude ‘persist’. Finally, Aristotle holds that time would not exist without the soul: ‘for if there cannot be someone to count there cannot be anything that can be counted either, so that evidently there cannot be number’, Arisotle, Complete Works I, 223a 23–25; 377. His view seems to be that countable movement depends on the soul, since he goes on to say that ‘that of which time is an attribute’ might exist without souls, but only ‘if movement can exist without soul’, Aristotle, Complete Works I, 223a 27; 377). But there is no indication that spatial magnitude depends in any way on movement or the soul.

¹⁵ Although there are other similarities which Aristotle seems to regard as self-evident – the ‘now’ is not a part of time any more than the point is a part of the line (Aristotle, Complete Works I, 220a 20-22); everything ‘in time’ is contained by time, just as everything ‘in place’ are contained by place (Aristotle, Complete Works I, 221a 26–28) – his most interesting ampliative inferences from space to time are based on the close association between time and motion.

¹⁶ Aristotle, Complete Works I, 223b 12–23; 378.

¹⁷ Aristotle, Complete Works I, 223a 33; 377. Though in On Generation and Corruption, he says that time is the number ‘of the circular movement’, Aristotle, Complete Works I, 337b 25; 552.

¹⁸ Averroes, Aristotelis de Physico Auditu IV (Frankfurt: Minerva, 1962), t.c. 132, fol. 203. Si autem posuerimus quod dispositio eius cum motu uno […] dissolvitur questio. For discussion, see Trifogli, Oxford Physics in the Thirteenth Century (Leiden: Brill, 2000), chapter 4; and ‘Averroes’ Doctrine of Time and Its Reception in the Scholastic Debate' in The Medieval Concept of Time, edited by Pasquale Porro (Leiden: Brill, 2001), 57–82 (64).

¹⁹ Aquinas, Summa Theoligica, translated by Fathers of the English Dominican Province, in Great Books of the Western World, vols 19 and 20 edited by Mortimer J. Adler et al, (Chicago, IL: Encyclopedia Britannica Inc., 1953), Part 1a, quest. 10, art. 1. In eo autem quod caret motu, et semper eodem modo se habet, non est accipere prius et posterius.

²⁰ Aquinas, Commentary on Aristotle's Physics, translated by Richard Blackwell (South Bend, IN: St. Augustine's Press, 1999), Bk. IV, lec. 17, sec. 576; 258. Non autem tempus mensuratur secundum quantitatem cuiuscumque motus, quia tardum movetur secundum paucum spatium in multo tempore, velox autem e converso; sed solum quantitatem primi motus sequitur tempus.

²¹ P. Duhem, Medieval Cosmology: Theories of Infinity, Place, Time, Void and the Plurality of Worlds, translated by R. Ariew (Chicago, IL: University of Chicago Press, 1985), 297. Even Suárez asserts that ‘absolutely speaking […] the first motion [motu primi mobilis] is, simply speaking, time’, F. Suárez, Disputationes Metaphysicae (DM), in Opera Omnia, edited by D. Andre and C. Breton (Paris: Vives, 1866), Disp.50, Sec. 11, 5; See also Disp. 50, Sec. 10, 11.

²² DM, Disp. 50, Sec. 9, 1. See also Coimbra Commentators: ‘tempus non distingui re a motu’, Coimbra Commentators, Commentarii Collegii Conimbrincensis, Physicorum Aristotelis (Coimbra: 1602), IV: Ch. xiv, q. 2, art. 1; 106. See also Eustachius à Sancto Paulo: ‘tempus internum ne differat realiter a motu’, Eustachius à Sancto Paulo, Summa, Summa Philosophiae Quadripartita, Part I (Physica), Treatise 3, disputation 3, question 2 (Paris, 1640), 159. I don't mean to suggest that the seventeenth-century scholastic accounts are crudely reductionistic. Thus, Suarez develops a distinction between ‘extrinsic time’ and ‘intrinsic duration’. Extrinsic time is the single universal measure of duration; intrinsic duration is the successive existence of individual movements, thus Suárez's observation that there are as many intrinsic durations as distinct movements, DM, Disp. 50, Sec. 10, 11. For discussion, see S. Daniel, ‘Seventeenth Century Scholastic Treatments of Time’ The Journal of the History of Ideas, 42 (1981): 587–606; C. Esposito, ‘The Concept of Time in the Metaphysics of Suarez’ in Medieval Concept of Time: Studies on the Scholastic Debate and its Reception in Early Modern Philosophy, edited by P. Porro (Leiden: Brill Academic Publishers, 2001), 283–298; and E. Bexley, ‘Quasi-absolute time in Francisco Suárez's Metaphysical Disputations’, this issue.

²³ S. Hutton, ‘Some Renaissance Critiques of Aristotle's Theory of Time’, Annals of Science, 34 (1977): 344–363 (350). See also R. Ariew and A. Gabbey, ‘The Scholastic Background’ in Cambridge History of Seventeenth Century Philosophy, edited by D. Garber and M. Ayers, 2 vols (Cambridge: Cambridge University Press, 1998), 425–453 (436–440).

²⁴ Owing again to Aristotle's authority, space was generally conceived as the combined material places of the cosmos, with no possible void either within or beyond its finite celestial boundaries. See for example Aquinas, Commentary on Aristotle's Physics, Bk. IV, lec. 14, sec. 543; 244.

²⁵ Scotus: ‘the vacuum that is assumed in this article to be possible to God is not a space with positive dimensions, but all that is there is the possibility of having such together with a lack of any dimensions in actuality’, Scotus, Quaestiones Quodlibetales, ed. Felix Alluntis. (Madrid: Biblioteca de Autores Cristianos, 1963), 11, 2, n. 21. For detailed discussion of Scotus on space and time, see R. Cross, The Physics of Duns Scotus (Oxford: Oxford University Press, 1998), chapters 11–13; and N. Lewis, ‘Space and Time’ in The Cambridge Companion to Duns Scotus, edited by T. Williams (Cambridge: Cambridge University Press, 2002), 69–99. Nicole Oresme argues against Aristotle that if all the bodies within the sphere of the heavens were destroyed while the heavens remained intact, ‘it would necessarily follow that in this concavity there would be a great expanse and empty space’, N. Oresme, Le livre du ciel et du monde, edited by A. Menut and A. Ednomy (Madison, WI: University of Wisconsin Press, 1968), Bk. I, Ch. 24, fol. 39a; 177. But, like Scotus, he refuses to grant this empty space – which he associates with the immensity of God's presence – the geometrical structure of corporeal extension: ‘this space of which we are talking is infinite and indivisible and is the immensity of God’ (N. Oresme, Le livre du ciel, Bk. I, Ch. 24, fol. 39a; 177).

²⁶ Nevertheless, we imagine it as having spatial dimensions ‘in a certain relation corresponding to the real and positive dimensions of bodies’, Coimbra Commentators, Physicorum Aristotelis, Bk VIII, Ch. x, q. 2, Art 4; 370. For detailed discussion of the ontological status of imaginary space, and its relation to God, see E. Grant, Much Ado About Nothing: Theories of Space and Vacuum from the Middle Ages to the Scientific Revolution (Cambridge: Cambridge University Press, 1981), Ch. 6; C. Leijenhorst, ‘Jesuit Concepts of Spatium Imaginarium and Thomas Hobbes’, Doctrine of Space, Early Science and Medicine, 3 (1996): 355–380; D. Des Chene, Physiologia: Natural Philosophy in Late Aristotelian and Cartesian Thought (Ithaca, NY: Cornell University Press, 1996), 385–387.

²⁷ Scotus, Quaestiones Quodlibetales, 11, 4, n. 24.Also Lewis, ‘Space and Time’, 92. Oresme is clear that geometrical notions no more apply to the duration of void space than to the space itself: ‘this space of which we are talking is infinite and indivisible and the immensity of God, and God himself, just as the duration of God called eternity is infinite, indivisible and God himself’, Oresme, Le livre du ciel, Bk. I, Ch. 24, fol. 39b; 177. See also Oresme, Le livre du ciel, Bk. II, Ch. 1fol. 6c; 273 and Bk. II, Ch. 2, fol 69c–70a; 285. For discussion of Oresme on space, see Grant, Much Ado About Nothing, 119–20 and Duhem, Medieval Cosmology, 263–267; on time, see S. Carhoti, ‘Time and modi rerum in Nicole Oresme's Physics commentary’ in Medieval Concept of Time, 319–349.

²⁸ MD Disp. 50, Sec. 9, 1. See also MD Disp. 54, 4, 7, in F. Suarez, Beings of Reason: Metaphysical Disputation 54, translated by J.P. Doyle (Milwaukee, WI: Marquette University Press, 1995). See also Commentary on the Metaphysics, translated by J.P. Doyle (Milwaukee, WI: Marquette University Press, 2004), Bk XII, Ch. 6, q.1; 209. Although time is not ‘in reality’ distinct from motion, we can imagine an absolute time in order to explain the sense in which it cannot be repeated, even though motions can be. Imaginary time also allows us to conceive a time for the motion of the outermost sphere, just as imaginary space allows us to speak of a place for the outermost sphere. As Suárez says, if we ‘distinguish between the interval or imaginary successive extension, which we conceive of as necessarily flowing from all eternity, and the real duration of motion we call real and true time’, we will understand that no part of this imagined ‘flowing and successive extension’ is identical with any other, DM, Disp. 50, Sec. 9, 15. See also Coimbra Commentators, Physicorum Aristotelis, IV, Ch. xiv, q. 1, art. 2; 102; Eustachius, Physica, Part I, Treatise 3, Disp. 3, q. 2; 159.

²⁹ Patrizi, in B. Brickman, ‘On Physical Space’, Journal of the History of Ideas, 4 (1943): 224–245 (236). He infers that the space which actually holds the world is similar to the surrounding void space it might come to occupy: ‘Neither of these two spaces is a body. Each is capable of receiving a body. Each gives way to a body. Each is three-dimensional. Each can penetrate the dimensions of bodies.’ (Brickman, ‘On Physical Space’, 238, 231). Also see Grant, Much Ado about Nothing, 199–206; and Jammer, Concepts of Space: The History of Theories of Space in Physics, second edition (Cambridge, MA: Harvard University Press, 1969), 85–90. Telesio conceived of space and body as distinct things, capable of complete interpenetration. Although he does not say so explicitly, this seems to imply that space is three-dimensional in its own right, as Grant observes (Grant, Much Ado about Nothing, 193).

³⁰ The cosmologies of Bruno and Campanella include an eternal and infinite incorporeal space possessing dimensions independently of bodies (though they are less welcoming of absolute void). See for example Bruno, ‘On the Infinite Universe and Worlds’ in Bruno: His Life and Thought, edited by D. Singer (New York, NY: Henry Schuman, Inc., 1950), 273. For discussion of Campanella on space, see Grant, Much Ado about Nothing, 194–199.

³¹ N. Copernicus, De Revolutionibus (Nuremberg, 1643), Bk. 1, Ch 8; 5.

³² Neil Lewis observes that, in Scotus time (late thirteenth century), ‘Although many philosophers have been prepared to grant, against Aristotle, the possibility of extra- or intracosmic void, very few have been willing to dispute Aristotle's rejection of the possibility of time without motion’, Lewis, Space and Time, 89–90.

³³ Hutton, ‘Some Renaissance Critiques’, 359.

³⁴ Bruno, ‘Camoeracensis Acrotismus’ in Čapek, Concepts of Space and Time. See also Bruno, ‘On the Infinite Universe and Worlds’ (Fifth Dialogue; 363). For discussion of Bruno on time see Hutton, ‘Some Renaissance Critiques’ and Granada, ‘The Concept of Time in Giordano Bruno’ in Medieval Concept of Time, 477–505. Indeed, although space is the same everywhere, ‘time is understood as flowing most rapidly in those things which move very fast, and at a slower rate in things which change more slowly’, Bruno, ‘Camoeracensis Acrotismus’ in Čapek Concepts of Space and Time. On the lack of succession in Bruno's universal duration see Granada, ‘The Concept of Time’, 505.

³⁵ Sometimes Campanella endorses the traditional reduction of time in general to celestial motion: ‘tempus universale est ipse coeli motus’, Campanella, Metafisica, edited by G. Di Napoli (Bologna: Zanicehlli, 1967) II, 8, 3, 1; 158. While space has its own unchanging existence analogous to the ‘aeviternal’ existence of angels, time is the successive duration of changing things, Compendium Physiologicae, edited by G. Ernst and P. Ponzio (Milan: Rusconi, 1999) IV, 40. See Ponzio, ‘Tempus, Aevum, Aetertnitas in the Philosophy of Tommaso Campanella’ in The Medieval Concept of Time, 506–18 (510). See also B. Bonansea, Tommaso Campanella: Renaissance Pioneer of Modern Thought (Washington, DC: Catholic University of America Press, 1969), 189–195.

³⁶ Copernicus, ‘Letter Against Werner’ in Three Copernican Treatises, edited by E. Rosen (New York, NY: Columbia University Press, 1939), 79. For more detailed discussions of celestial reductionism, and its challengers, in the late medieval and early modern periods, see Ariotti, ‘Toward Absolute Time: The Undermining and Refutation of the Aristotelian Conception of Time in the Sixteenth and Seventeenth Centuries’, Annals of Science, 30 (1973): 31–50.

³⁷ Proposition 49, in A Source Book in Medieval Science, edited by E. Grant (Cambridge, MA: Harvard University Press, 1974), 48.

³⁸ Proposition 79: Si caelum staret, ignis in stupam non ageret quia nec tempus esset, in Duhem, Medieval Cosmology, 299.

³⁹ Čapek, ‘The Conflict between the Absolutist and the Relationist Theory of Time before Newton’, Journal of the History of Ideas, 48 (1987): 595–608 (596). See also Von Leyden, Seventeenth Century Metaphysics, 259; M. Futch, Leibniz's Metaphysics of Time and Space (New York, NY: Springer Science, 2008), 9–10.

⁴⁰ See Hutton, ‘Some Renaissance Critiques’, and C. Steel, ‘The Neoplatonic Doctrine of Time and its Influence on Medieval Philosophy’ in The Medieval Concept of Time, 3–32.

⁴¹ On this connection, see Koyré, From the Closed World to the Infinite Universe (New York, NY: Harper, 1958); and E. Grant, Planets, Stars and Orbs: The Medieval Cosmos 1200-1687 (Cambridge: Cambridge University Press, 1996).

⁴² See S. Daniel, ‘Seventeenth Century Scholastic Treatments of Time’ and P. Ariotti, ‘Toward Absolute Time’.

⁴³ Simplicius, On Aristotle's Physics 3, translated by J.O. Urmson (Ithaca, NY: Cornell University Press, 2002), 87.

⁴⁴ Lucretius, De Rerum Natura, translated by C. Bailey (Oxford: Oxford University Press, 1947), Bk. I, lines 968–983; 226–227; Patrizi, ‘On Physical Space’, 236; Bruno, ‘On the Infinite Universe and Worlds’, Dialogue One; 227. See also ‘Introductory Epistle’ to ‘Infinite Universe and Worlds’, 231. Granada remarks that the same considerations of divine power and goodness that establish the infinity of worlds and spatial extension ‘are also valid in the context of time or duration’, even though Bruno does not so apply them, Granada, ‘The Concept of Time’, 479. It is noteworthy, however, that Bruno does not attempt to apply the Archytas argument to separate time from motion; indeed he remarks in the same dialogue that time exists beyond our world because ‘there is the measurement and true nature of motion, since moving bodies are there’, Bruno, ‘On the Infinite Universe and Worlds’, Fifth Dialogue; 363. Locke, Essay, II, xiii, 21; 175–176. For general discussion of Archytas, see C. Huffman, Archytas of Tarentum: Pythagorean, Philosopher and Mathematician King (Cambridge: Cambridge University Press, 2005); Grant, Much Ado About Nothing, 106–108; Jammer, Concepts of Space, 9–10.

⁴⁵ Oeuvres de Descartes, edited by C. Adam and P. Tannery, 11 vols (Paris: J. Vrin, 1996), Vol. 5, 345. See also Vol. 8A, 52.

⁴⁶ Aristotle, Complete Works I, 252a1-252b6; 420.

⁴⁷ Coimbra Commentators, Physicorum Aristotelis, Bk. VIII, Ch. x, Q ii, Art iv; 369.

⁴⁸ Patrizi, ‘On Physical Space’, 236.

⁴⁹ Bradwardine, ‘de causa Dei contra Pelagium et Du virtute causarum’ in A Source Book in Medieval Science, Bk. I, ch. 5: 557.

⁵⁰ Aquinas, Summa Theologica, Ia 25, art. 4.

⁵¹ Scotus, Quaestiones Quodlibetales, II, 11, ii.

⁵² Scotus, Quaestiones Quodlibetales, XIII, q. 3; Grant, Much Ado About Nothing, 124–125.

⁵³ See Leibniz, New Essays on the Human Understanding, edited by P. Remnant and J. Bennett (Cambridge: Cambridge University Press, 1996) II, xv; 155. See also Bennett, Kant's Analytic (Cambridge: Cambridge University Press, 1966), 174–176.

⁵⁴ Aristotle, Compete Works, 221b10–11; 375.

⁵⁵ See Grant, Much Ado about Nothing, chapter 4; and C.B. Schmitt, ‘Experimental Evidence for and against a Void: the Sixteenth-Century Arguments’, Isis, 58 (1967): 352–366.

⁵⁶ For an influential recent discussion of empty time, see S. Shoemaker, ‘Time Without Change’, Journal of Philosophy, 66 (1969): 363–381.

⁵⁷ Gassendi, ‘Syntagma Philosophicum’ in Opera Omnia in sex tomos divisa, vol. 1 (Lyon: Laurent Anisson and Jean-Baptiste Devent, 1658), Bk II, Sec. i, Ch. vii; 224–225; Čapek, Concepts of Space and Time, 199–201; Collected Works of Pierre Gassendi, edited by C. Brush (New York, NY: Johnson Reprint Co., 1972), 395–396; compare with Charleton, Physiologia, 75–78.

⁵⁸ Gassendi, ‘Syntagma Philosophicum’, Bk II, Sec. i, ch. 1; 183; Čapek, Concepts of Space and Time, 92; Collected Works of Pierre Gassendi, 387; compare with Charleton, Physiologia, 67.

⁵⁹ Gassendi, ‘Syntagma Philosophicum’, Bk II, Sec. i, ch. 1; 183; Čapek, Concepts of Space and Time, 92; Collected Works of Pierre Gassendi, 387; compare with Charleton, Physiologia, 67.

⁶⁰ Gassendi, ‘Syntagma Philosophicum’, Bk II, Sec. i, ch. vii; 224; Čapek, Concepts of Space and Time, 199–200; Collected Works of Pierre Gassendi, 396.

⁶¹ Gassendi, ‘Syntagma Philosophicum’, Bk II, Sec. i, ch. vii; 183; Collected Works of Pierre Gassendi, 387.

⁶² Gassendi, ‘Syntagma Philosophicum’, Bk II, Sec. i, ch. vii; 225; Collected Works of Pierre Gassendi, 397; Čapek, Concepts of Space and Time, 201; Charleton, Physiologia, 78.

⁶³ Gassendi, ‘Syntagma Philosophicum’, Bk II, Sec. i, ch. vii; 225; Collected Works of Pierre Gassendi, 397; Čapek, Concepts of Space and Time, 201; Charleton, Physiologia, 78.

⁶⁴ Gassendi, ‘Syntagma Philosophicum’, Bk II, Sec. i, ch. vii; 225; Čapek, Concepts of Space and Time, 201.

⁶⁵ Gassendi, ‘Syntagma Philosophicum’, Bk II, Sec. i, ch. vii; 220; Collected Works of Pierre Gassendi, 391. On the connection between the work of Charleton (and by extension Gassendi) and Newton, see Westfall, Never at Rest (Cambridge: Cambridge University Press, 1980); J.E. McGuire, ‘Existence, Actuality and Necessity: Newton on Space and Time’, Annals of Science, 35 (1978): 463–508; R. Kroll, ‘The Question of Newton's relation to Gassendi’, Journal of the History of Ideas, 45 (1984): 339–359; and D. Jalaobenau, ‘Space, Bodies and Geometry: Some sources of Newton's Metaphysics’ in Notions of Space and Time: Early Modern Concepts and Fundamental Theories, edited by F. Lindhard and P. Eisenhardt (Frankfurt: Klosterman, 2007), 81–112.

⁶⁶ See J.T. Baker, An Historical and Critical Examination of English Space and Time Theories from Henry More to Bishop Berkeley (Bronxville, NY: Sarah Lawrence College, 1930), 15.

⁶⁷ On the dating of the lectures, see Feingold, ‘Isaac Barrow: divine, scholar, mathematician’ in The Life and Times of Isaac Barrow, edited by M. Feingold (Cambridge: Cambridge University Press, 1990), 1–104 (68).

⁶⁸ Mathematical Works of Isaac Barrow, edited by W. Whewell, 2 vols (Cambridge: Cambridge University Press, 1860), I, 155. He also invokes various other thought experiments.

⁶⁹ Mathematical Works I, 158.

⁷⁰ Mathematical Works I, 165.

⁷¹ Mathematical Works II, 161; Čapek, Concepts of Space and Time, 204.

⁷² G.J. Whitrow, The Natural Philosophy of Time (Oxford: University of Oxford Press, 1980) 184–188; E.W. Strong, ‘Barrow and Newton’, Journal of the History of Philosophy, 8 (1970): 155–170; A.R. Hall, Henry More and the Scientific Revolution (Cambridge: Cambridge University Press, 1990), 210–214; Jammer, Concepts of Space, 110–111; R. Arthur, ‘Newton's Fluxions and Equably Flowing Time’, Studies in the History and Philosophy of Science, 28 (1995): 323–351 (329–30).

⁷³ Mathematical Works I, 158–160. For discussion, see E.A. Burtt, The Metaphysical Foundations of Modern Science (New York, NY: Doubleday, 1954), 149–50; Grant, Much Ado About Nothing, 236–38; and Futch, Leibniz's Metaphysics of Time and Space, 23.

⁷⁴ Mathematical Works, II, 161; Čapek, Concepts of Space and Time, 203–204.

⁷⁵ Richard Arthur suggests that Barrow infers absolute time from absolute space: ‘In order for the parts or points of space to exist in the absence of material things (either before the world was created or in the infinite space outside the world), they must be able to perdure through time in the absence of change’, Arthur, ‘Newton's Fluxions and Equably Flowing Time’. 331. However, Barrow does not say that time must exist before and outside the world because space actually persists then and there. Rather he says that ‘Time existed before the world began’ because ‘it's possible that some thing existed there’, Mathematical Works, II, 161. The claim is parallel to, not derived from, the corresponding thesis about space: ‘there was space before the world […] inasmuch as there might have been such and so many bodies’, Mathematical Works, II, 161. Time is not the duration of actually empty space; rather absolute space and time are, respectively, the dimensions and persistence of counterfactual arrangements of bodies. Indeed, as Arthur himself notes, Barrow would be ‘inconsistent’ to infer absolute time as the ‘perdurance’ of absolute space, since in his view absolute space is not an ‘actual existent’, but a mere capacity for the reception of bodily dimensions. As such, why does it need an independent and flowing time? But this uncharitable charge of inconsistency is avoided if we read Barrow, more literally, as making parallel assertions about the ontology of space and time apart from bodies.

⁷⁶ Mathematical Works, II, 161. See also Mathematical Works, I, 158.

⁷⁷ Mathematical Works, II, 161.

⁷⁸ Mathematical Works, II, 162; Čapek, Concepts of Space and Time, 204.

⁷⁹ Mathematical Works, II, 165–166; Čapek, Concepts of Space and Time, 208.

⁸³ DG, 20.

⁸⁰ On the date of composition of ‘De Gravitatione’, see B. Dobbs, Janus Face of Genius (Cambridge: Cambridge University Press, 1991), 141–146. For recent discussion of the philosophical aspects of ‘De Gravitatione’, see A. Janiak, Newton as Philosopher (Cambridge: Cambridge University Press, 2008), chapter 5; and G. Gorham, ‘How Newton Solved the Mind-Body Problem’, History of Philosophy Quarterly, 28 (2011), 21–44.

⁸¹ Descartes' ‘strict’ definition of motion: ‘the transfer of one piece of matter, or one body, from the vicinity of the other bodies that are in immediate contact with it, and which are regarded as being at rest, to the vicinity of other bodies’. (Oeuvres de Descartes. Edited by C. Adams and P. Tannery (Paris: J. Vrin, 1976), Vol 8A 53)

⁸² I. Newton, De Gravitatione (DG), in Philosophical Writings, edited by A. Janiak (Cambridge: Cambridge University Press, 2004), 12–39 (20–21).

⁸⁴DG, 22.

⁸⁵ DG, 26

⁸⁶ Newton, Principia, 408

⁸⁷ Čapek, Concepts of Space and Time, xvii.

⁸⁸ Newton, Principia, 413. For a recent, thorough discussion of this thought experiment, see R. Rynasiewicz, ‘By Their Properties, Causes and Effects: Newton's Scholium on Time, Space, Place and Motion’, Studies in History and Philosophy of Science, 26 (1995), 133–153, 295–321.

⁸⁹ See, for example, Burtt, The Metaphysical Foundations of Modern Science, 356; G.J. Whitrow, Natural Philosophy of Time (Oxford: Oxford University Press, 1980), 35.

⁹⁰ Newton, Principia, 414.

⁹¹ For discussion of this point, see P. Bricker, ‘Absolute Time vs. Absolute Motion’ in Philosophical Perspectives on Newtonian Science, edited by P. Bricker and R.I.G. Hughes (Cambridge, MA: MIT Press, 1990), 77–89; and R. DiSalle, Understanding Space-Time (Cambridge: Cambridge University Press, 2006), chapter 2.

⁹² Newton, Principia, 410.

⁹³ Newton, Principia, 410.

⁹⁴ Compare with Čapek, Concepts of Space and Time, xxxviii. See also Duhem's discussion of the ideal clock in medieval thought. Duhem, Medieval Cosmology, chapter 7.