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Newton and scholastic philosophy

  • DMITRI LEVITIN (a1)
Abstract

This article examines Isaac Newton's engagement with scholastic natural philosophy. In doing so, it makes two major historiographical interventions. First of all, the recent claim that Newton's use of the concepts of analysis and synthesis was derived from the Aristotelian regressus tradition is challenged on the basis of bibliographical, palaeographical and intellectual evidence. Consequently, a new, contextual explanation is offered for Newton's use of these concepts. Second, it will be shown that some of Newton's most famous pronouncements – from the General Scholium appended to the second edition of the Principia (1713) and from elsewhere – are simply incomprehensible without an understanding of specific scholastic terminology and its later reception, and that this impacts in quite significant ways on how we understand Newton's natural philosophy more generally. Contrary to the recent historiographical near-consensus, Newton did not hold an elaborate metaphysics, and his seemingly ‘metaphysical’ statements were in fact anti-scholastic polemical salvoes. The whole investigation will permit us a brief reconsideration of the relationship between the self-proclaimed ‘new’ natural philosophy and its scholastic predecessors.

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1 For an accurate recent definition of ‘scholasticism’ see Richard Serjeantson, ‘Becoming a philosopher in seventeenth-century Britain’, in Peter Anstey (ed.), The Oxford Handbook of British Philosophy in the Seventeenth Century, Oxford: Oxford University Press, 2013, pp. 9–38, 14.

2 Denis des Chene, Physiologia: Natural Philosophy in Late Aristotelian and Cartesian Thought, Ithaca, NY: Cornell University Press, 1996; Roger Ariew, Descartes and the Last Scholastics, Ithaca, NY: Cornell University Press, 1999; Cees Leijenhorst, The Mechanization of Aristotelianism: The Late Aristotelian Setting of Thomas Hobbes' Natural Philosophy, Leiden: Brill, 2002; an extremely useful overview appears in Edwards, Michael, ‘Aristotelianism, Descartes, and Hobbes’, Historical Journal (2005), 50, pp. 449–64. I do not cite here the myriad of works that have shaped our understanding of early modern Aristotelianism: the key introduction remains Charles B. Schmitt, Aristotle and the Renaissance, Cambridge, MA: Harvard University Press, 1983.

3 Some recent studies have implicitly argued the contrary. Their claims are questioned below.

4 The key study remains that by Mordechai Feingold, ‘The mathematical sciences and the new philosophies’, in N. Tyacke (ed.), The History of the University of Oxford, vol. 4: 17th-Century Oxford, Oxford: Oxford University Press, 1997, pp. 359–448; see also James Hannam, ‘Teaching natural philosophy and mathematics at Oxford and Cambridge, 1500–1700’, PhD thesis, University of Cambridge, 2008. More specifically see below.

5 CUL MS Add. 3996, fols. 3r–10v, 16r–26v, 43r–71v. A very high-quality reproduction is available at http://cudl.lib.cam.ac.uk/view/MS-ADD-03996/1. The much-cited modern edition is J.E. McGuire and M. Tamny (eds.), Certain Philosophical Questions: Newton's Trinity Notebook, Cambridge: Cambridge University Press, 1983.

6 W.W. Wallace, ‘Newton's early writings: beginning of a new direction’, in G.V. Coyne, SJ, M. Heller and J. Źyciński (eds.), Newton and the New Direction in Science, Vatican City: Specola Vaticana, 1988, pp. 23–44, 30, 34–35 and passim.

7 Jed Buchwald and Mordechai Feingold, Newton and the Origin of Civilization, Princeton, NJ: Princeton University Press, 2013, p. 15.

8 See Willughby's commonplace book, Nottingham University Library, MS Mi LM 15/1, p. 572. The discovery of this evidence is entirely that of Richard Serjeantson, who was kind enough to share it with me, and whose broader findings on this score will appear as ‘The education of Francis Willughby’, an early version of which I have been fortunate to benefit from.

9 Patrick's copy is CUL, shelfmark Peterborough 2.2, inscribed on the title page, ‘Ex libris Iohannis Patricke Reginalensis. Iuly: 1. 1650’ – Patrick took his BA from Queens’ in 1650, MA in 1654. J.A. Venn, Alumni Cantabrigienses, 10 vols., Cambridge: Cambridge University Press, 1922–53, vol. 3, p. 318.

10 Ducheyne, Steffen, ‘Newton's training in the Aristotelian textbook tradition: from effects to causes and back’, History of Science (2005), 43, pp. 217–37; Ducheyne, The Main Business of Natural Philosophy: Isaac Newton's Natural-Philosophical Methodology, Dordrecht: Springer, 2012, pp. 3–36. The classic studies of regressus are J.H. Randall, The School of Padua and the Emergence of Modern Science, Padua: Editrice Antenore, 1961; Jardine, Nicholas, ‘Galileo's road to truth and the demonstrative regress’, Studies in History and Philosophy of Science (1976), 7, pp. 277318 and very many since; for England see now Marco Sgarbi, The Aristotelian Tradition and the Rise of British Empiricism: Logic and Epistemology in the British Isles (1570–1689), Dordrecht: Springer, 2013.

11 Newton, The Opticks, New York: Dover, 1952 (based on the 1730 edn), pp. 404–405. The passage first appears in Optice, London, 1706, p. 347. The transcription in Ducheyne, The Main Business of Natural Philosophy, op. cit. (10), p. 19, contains a misleading error, as the last ‘Analysis’ is replaced with ‘Synthesis’.

12 Other key loci include Principia, pp. 382, 943 (the latter is from the General Scholium); Math. Papers, vol. 7, pp. 212–216 (a draft for a tract on ‘Analysis Geometrica’, c.1691), 249–251 (a draft preface to ‘Geometriae Libri tres’, early 1690s); vol. 8, 442–459 (= Principia, pp. 49–54) (drafts for a new preface to the Principia, 1710s); the drafts for the above Opticks passage in CUL Add. 3970, fols. 242v–243r, 480v; that adduced in Pelseneer, Jean, ‘Une opinion inédite de Newton sur l'analyse des anciens’ à propos de l’Analysis Geometrica de Hugo de Omerique’, Isis (1930), 14, pp. 155165. The most important studies are Shapiro, Alan, ‘Newton's “experimental philosophy”’, Early Science and Medicine (2004), 9, pp. 185217; and Niccoló Guicciardini, Isaac Newton on Mathematical Certainty and Method, Cambridge, MA: MIT Press, 2009, pp. 309–327.

13 E.g. Peter Dear, Discipline and Experience: The Mathematical Way in the Scientific Revolution, Chicago: The University of Chicago Press, 1995, p. 240.

14 Ducheyne, The Main Business of Natural Philosophy, op. cit. (10), p. 8.

15 Ducheyne, The Main Business of Natural Philosophy, op. cit. (10), p. 18.

16 Ducheyne, The Main Business of Natural Philosophy, op. cit. (10), p. 16.

17 Ducheyne, The Main Business of Natural Philosophy, op. cit. (10), p. 16.

18 Ducheyne, The Main Business of Natural Philosophy, op. cit. (10), p. 16 n. 74.

19 Scott Mandelbrote, personal communication. I am very grateful to him for informing me of his findings on this matter, findings which he intends to publish in due course.

20 See Paul Richard Blum, Studies on Early Modern Aristotelianism, Leiden: Brill, 2012, pp. 275–314 (‘God and individuals: the Porphyrian tree in seventeenth/eighteenth-century philosophy’), at pp. 284, 301–302, for Cornaeus.

21 I am very grateful to David McKitterick, my colleague at Trinity, for confirming my own judgement that the handwriting is not Newton's.

22 That he did not read it during his undergraduate days is supported by the fact that the (admittedly unclear) inscription on the inside flyleaf seems to read ‘John Parke … 1659 (1660)’, again in a hand that is without doubt not Newton's. Could this be the John Parke who matriculated at King's in 1639, securing his BA in 1643 and MA 1646, or the John Parkes who matriculated at John's in 1660? Venn, op. cit. (9), vol. 3, pp. 305, 310.

23 Ducheyne, The Main Business of Natural Philosophy, op. cit. (10), p. 18.

24 Samuel Smith, Aditus ad logicam, Oxford, 1649 (1st edn London, 1613), pp. 121 (‘Demonstrationis definitio petitur aut a fine eius ad collimat, vel a materia ex qua constituitur. Finis eius est Scientia; unde Demonstratio ab Aristotele dicitur Syllogismus, qui scientiam parit’) and 127 (‘Demonstratio est Syllogismus scientificus, qui constat ex veris, primis, immediatis, notioribus & prioribus & causis conclusionis. Prima conditio est, ut constet ex veris, seu ut alii addunt, necessario veris …’). See further Sgarbi, op. cit. (10), pp. 147–150.

25 William Harvey, Exercitationes de generatione animalium, London, 1651, ‘Praefatio’, esp. sig. [B4]r–v (manipulating An. Post., 99b26–100a9). See Charles B. Schmitt, ‘William Harvey and Renaissance Aristotelianism: a consideration of the Praefatio to “De generatione animalium” (1651)’, in G. Keil and R. Schmitz (eds.), Humanismus und Medizin, Weinheim: Acta Humaniora, 1984, pp. 117–138, esp. 129–132; Roger French, William Harvey's Natural Philosophy, Cambridge: Cambridge University Press, 1994, pp. 313–315; Sgarbi, op. cit. (10), pp. 180–184.

26 Ducheyne, The Main Business of Natural Philosophy, op. cit. (10), pp. 7–8 (see also the quotation keyed to n. 14 above).

27 Key studies are Paolo Mancosu, Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century, Oxford: Oxford University Press, 1996, pp. 10–33; Rivka Feldhay, ‘The use and abuse of mathematical entities: Galileo and the Jesuits revisited’, in P. Machamer (ed.), The Cambridge Companion to Galileo, Cambridge: Cambridge University Press, 1998, pp. 80–145; for the wider sociological dimension see Biagioli, Mario, ‘The social status of Italian mathematicians, 1450–1600’, History of Science (1989), 27, pp. 4195.

28 Guicciardini, op. cit. (12), pp. 291–328; Mary Domski, ‘Newton as historically minded philosopher’, in M. Dickson and M. Domski (eds.), Discourse on a New Method: Reinvigorating the Marriage of History and Philosophy of Science, Chicago: OpenCourt, 2010, pp. 65–90; Garrison, James W., ‘Newton and the relation of mathematics to natural philosophy’, Journal of the History of Ideas (1987), 48, pp. 609627; Dear, op. cit. (13), pp. 210–244.

29 On the role of mechanics see further Alan Gabbey, ‘The Principia: a treatise on “Mechanics”?’, in P.M. Harman and A.E. Shapiro, eds., The Investigation of Difficult Things: Essays on Newton and the History of the Exact Sciences, Cambridge: Cambridge University Press, 1992, pp. 305–322.

30 Guicciardini, op. cit. (12), p. 313.

31 Isaac Barrow, Lectiones mathematicae XXIII, London, 1685, pp. 5–75. For the full details of Barrow's history of mathematics see Dmitri Levitin, Ancient Wisdom in the Age of the New Science: Histories of Philosophy in England, c.1640–1700, Cambridge: Cambridge University Press, 2015, pp. 315–321.

32 Barrow cites De caelo, iii.7, 306a18–21 and Met. ii.3, 995a15–17; the translation from the latter is that of W.D. Ross, Aristotle's Metaphysics, Oxford, 1953, p. 52 (‘τὴν δ᾿ ἀκριβολογίαν τὴν μαθηματικὴν οὐκ ἐν ἅπασιν ἀπαιτητέον, ἀλλ᾿ ἐν τοĩς μὴ ἔχουσιν ὕλην’), my emphasis.

33 See Katherine Neal, From Discrete to Continuous: The Broadening of Number Concepts in Early Modern England, Dordrecht: Kluwer, 2002, pp. 12–27 (the ancient sources), 121–122 (on Barrow, although given his use of Archytas it is not quite correct to say that ‘he could … cite no examples of a classical source that agreed with his point of view’).

34 Barrow, Lectiones, op. cit. (31), pp. 33–34. The source is Nicomachus, Introduction to Arithmetic, i.3.4 (= Introduction to Arithmetic, trans. M.L. D'Ooge, London: Macmillan, 1926, pp. 184–185). Barrow cites fr. 1 (‘ταῦτα γὰρ τὰ μαθήματα δοκοῦντι ἔμμεναι ἀδελφεά’), but Archytas' real belief is given in fr. 4 (‘καὶ δοκεῖ ἁ λογιστικὰ [‘logistics’, i.e. arithmetic] ποτὶ τὰν σοφίαν τῶν μὲν ἀλλᾶν τεχνῶν καὶ πολὺ διαφέρειν, ἀτὰρ καὶ τᾶς γεωμετρικᾶς ἐναργεστέρω πραγματεύεσθαι ἃ θέλει’). The Archytas fragments were published by Henri Estienne in an edition of Aristotle and Theophrastus (1557), and they appeared in the many popular collections of Pythagorean fragments published in the sixteenth and seventeenth centuries. See J. Hankins and A. Palmer, The Recovery of Ancient Philosophy in the Renaissance, Florence: Olschki, 2008, p. 51.

35 For the recognition that the ancients had made arithmetic prior to geometry, using some of the standard sources, see e.g. John Wallis, Mathesis Universalis [1657], in Wallis, Opera mathematica, 3 vols., London, 1693–1699, vol. 1, p. 53.

36 McGuire and M. Tamny, op. cit. (5), pp. 26–42, 336–338.

37 Walter Charleton, The immortality of the human soul, London, 1657, pp. 63–65.

38 An early modern commonplace: see e.g. René Descartes, Regulae ad directionem ingenii, in Oeuvres de Descartes, ed. Charles Adam and Paul Tannery, 12 vols., Paris: Léopold Cerf, 1897–1910, vol. 10, pp. 376–377; John Wallis to Gerard Langbaine et al., 20 December 1656, in The Correspondence of John Wallis, ed. P. Beeley and C.J. Scriba, 3 vols., Oxford: Oxford University Press, 2003–2012, vol. 1, p. 265; Fermat to Digby, February 1657, The Correspondence of John Wallis, pp. 275–276; John Wallis, A treatise of algebra, London, 1685, pp. 1, 3–4. This belief was reinforced by Fermat's new edition of Diophantus (1670): see e.g. John Collins to John Gregory, 25 March 1671, in S. Jordan Rigaud (ed.), The Correspondence of Scientific Men of the Seventeenth Century, 2 vols., Oxford: Oxford University Press, 1846, vol. 2, p. 218.

39 For the place of the soul in early modern taxonomies of knowledge see Richard Serjeantson, ‘The soul’, in D.M. Clarke and C. Wilson (eds.), The Oxford Handbook of Philosophy in Early Modern Europe, Oxford: Oxford University Press, 2011, pp. 119–141.

40 McGuire and Tamny, op. cit. (5), pp. 219–121, thus strongly insisted that Hobbes was Newton's direct source, an insistence that seems rather over-eager. For Hobbes, Douglas Jesseph, Squaring the Circle: The War Between Hobbes and Wallis, Chicago: The University of Chicago Press, 1999, pp. 189–246, supplies all the key loci, so I do not give them here.

41 J.W.N. Watkins, Hobbes's System of Ideas: A Study in the Political Significance of Philosophical Theories, London: Hutchinson, 1965, pp. 47–65; Aldo Gargani, Hobbes e la scienza, Turin: Einaudi, 1971, pp. 32–96.

42 See the very astute points made in Prins, J., ‘Hobbes and the school of Padua: two incompatible approaches of science’, Archiv für Geschichte der Philosophie (1990), 72, pp. 2646, esp. 30, 40; also Jesseph, op. cit. (40), pp. 238–240; Talaska, Richard A., ‘Analytic and synthetic method according to Hobbes’, Journal of the History of Philosophy (1988), 26, pp. 207237, esp. 236.

43 Noel Malcolm, Aspects of Hobbes, Oxford: Oxford University Press, 2002, pp. 146–155 (‘Hobbes's science of politics and his theory of science’), 153. See also the similar conclusion applied more generally in Hans-Jürgen Engfer, Philosophie als Analysis: Studien zur Entwicklung philosophischer Analysiskonzeptionen unter dem Einfluss mathematischer Methodenmodelle im 17. und frühen 18. Jahrhundert, Stuttgart: Frommann-Holzboog, 1982, p. 71 (‘Die Verwechslung und Vermischung dieser verschiedenen mathematischen Methodenmodelle führt zu erheblichen Komplikationen auch in der sich an ihnen orientierenden philosophischen Methodendiskussion, die nicht zuletzt dadurch zustande kommen, daß in den zugrunde liegenden mathematischen Modellen dieselben methodologischen Schlüsselbegriffe verwendet werden. Insbesondere gilt dies für die noch bei Kant zentralen Begriffe “analytisch” und “synthetisch” bzw. “resolutio” und “compositio”, die in den verschiedenen Konzeptionen unterschiedliche Funktionen übernehmen und sich dementsprechend schon in der Methodologie des 17. Jahrhunderts durch die Vieldeutigkeit ihrer Verwendung auszeichnen’).

44 Engfer, op. cit. (43), p. 69 (‘Die Rezeption dieser mathematischen Methodenschriften im 16. Jahrhundert wird zunächst durch ihre wirkliche oder vermutete Kompatibilität mit dem aristotelischen Wissenschaftsideal’).

45 He used it twice in MS. First, in the unpublished preface to the Principia of the 1710s: Principia, pp. 53–54. Ducheyne, The Main Business of Natural Philosophy, op. cit. (10), p. 22, makes a great deal of this passage, but apart from it remaining unpublished, we should also note that it is not clear from it that Newton thinks that in his own work he has ever moved towards the discovery of causes (proximate or otherwise), only that that is a desirable aim. As he said again and again, he had not discovered the cause of gravity. Just as importantly, it appears to be connected – like all his causal talk – to the rhetoric of philosophy revealing the ‘first cause’ (God): see the use in CUL MS Add. 3965, fol. 359v (a draft for the General Scholium). See further below.

46 Ducheyne, The Main Business of Natural Philosophy, op. cit. (10), p. 24.

47 See, respectively, the unpublished preface to the Principia (CUL MS Add. 3968, fol. 109, c. 1710), in Principia, pp. 50–51, 52, 53; ‘Preface’, Principia, p. 53; Scholium on Book I, Section 11, Principia, p. 588. See further Principia, p. 408 (‘I use interchangeably and indiscriminately words signifying attraction, impulse, or any sort of propensity toward a center, considering these forces not from a physical but only from a mathematical point of view’). See also the discussion in George E. Smith, ‘The Methodology of the Principia’, in I.B. Cohen and G.E. Smith, The Cambridge Companion to Newton, Cambridge: Cambridge University Press, 2002, pp. 138–173, 143 (‘In Newton's hands force is a flagrantly theoretical quantity’), 148–149, 151. Ducheyne, The Main Business of Natural Philosophy, op. cit. (10), p. 26, attempts to negate this by claiming that what Newton is saying is that ‘while an account of the remote cause of celestial and terrestrial motions is explicitly absent from the Principia, it is nowhere implied thereby that Newton also avoided an account of their proximate cause’, but then why do none of these Newton loci refer to anything like ‘proximate causes’? (Of course, given that we now know that there is no evidence of Newton reading the scholastic works in which such a concept is to be found, this is not particularly surprising.)

48 CUL MS Add. 3970, fol. 480v. On this text see McGuire, J.E., ‘Newton's “Principles of Philosophy”: an intended preface for the 1704 Opticks and a related draft fragment’, BJHS (1970), 5, pp. 178186.

49 As well as the very many drafts in CUL MS Add. 3970, see CUL Add. MS 3968.39, fol. 586v, quoted at Ducheyne, The Main Business of Natural Philosophy, op. cit. (10), p. 22.

50 Newton, Opticks, op. cit. (11), pp. 401–402.

51 Newton, Opticks, op. cit. (11), p. 405.

52 Newton to Oldenburg, 19 June 1672, in Correspondence, vol. 1, p. 164. The first sentence of the Opticks repeats the claim that Newton is searching for ‘Properties of Light’ (p. 1). I was rather proud of spotting this repeated usage, only then to realize that it had also been spotted much earlier than me, and explained in illuminating detail, in A.E. Shapiro, Fits, Passions, and Paroxysms: Physics, Method, and Chemistry and Newton's Theories of Colored Bodies and Fits of Easy Reflection, Cambridge: Cambridge University Press, 1993, pp. 13–23 (tracing the continuous use of the concept from the Optical Papers through to Newton's later works).

53 See e.g. CUL MS Add. 3970, fol. 243r (draft for Query 23/31): ‘<The business of Experimental Philosophy is only to find out by experience & Observation <not how things were created but> what is the> present frame of nature … This inquiry must proceed first by Analysis in arguing from effects to causes & from compositions to components <ingredients>. And when we have found <the principles> [the causes <& ingredients of things we may> proceed by <Synthesis> from those Principles’. No regressus theorist would ever have used ‘causes’ interchangeably with ‘ingredients’.

54 This much seems to be admitted in Ducheyne, ‘Newton's training’, op. cit. (10), p. 228: ‘Newton introduced a new causal entity, “Universal Gravitation”, which was completely different from the Aristotelian notion of cause’. But if it is not to be understood in the Aristotelian sense, then why not simply adopt the phenomenological reading? The conclusion in Guicciardini, op. cit. (12), pp. 323–324, seems far more likely (it accounts for the differences between the various mathematical passages and the more causal-sounding passages in the Queries to the Opticks), as long as ‘Aristotelian’ is taken in a very wide rhetorical sense, not the precise sense meant by Ducheyne.

55 Principia, p. 943, my emphasis.

56 Prominent examples include the collected essays in J.E. McGuire, Tradition and Innovation: Newton's Metaphysics of Nature, Dordrecht: Kluwer 1995; Howard Stein, ‘Newton's metaphysics’, in Cohen and Smith, op. cit. (47), pp. 256–307; Domski, Mary, ‘Newton's empiricism and metaphysics’, Philosophy Compass (2010) 5, pp. 525534; Andrew Janiak, Newton as Philosopher, Cambridge: Cambridge University Press, 2008; Eric Schliesser, ‘Without God: gravity as a relational quality of matter in Newton’, in D. Jalobeanu and P. Anstey (eds.), Vanishing Matter and the Laws of Motion: Descartes and Beyond, London: Routledge 2011, pp. 80–102, esp. 95 (and other essays); Kochiras, Hylarie, ‘Gravity and Newton's substance counting problem’, Studies in History and Philosophy of Science (2009) 40, pp. 267280, esp. 270 (and other essays).

57 Dmitri Levitin, ‘The historical assumptions behind the General Scholium’, in S. Ducheyne, S. Mandelbrote and S. Snobelen, eds., Newton's General Scholium after 300 Years (forthcoming) – the following discussion expands significantly on the final section of this chapter. I would go as far as to say that no major natural philosopher between 1500 and 1800 said more often than Newton that they were not doing metaphysics.

58 CUL MS Add. 9597.2.11, fol. 2r: ‘Quod in Metafysica docetur <& si a revelatione deducitur religio esse>, si a Phaenomenis per sensus quinque externos, a Physicam pertinent, si a cognitione actionum internarum mentis nostrae per sensum reflexionis, philosophia est de sola mente humana & ejus ideis <tanquam Phaenomenes internas> & ad Physicam <item> pertinent. De Idearum objectis disputare nisi quatenus sunt phaenomena <somnium est>. In omni Philosophia incipere debemus a Phaenomenis, & nulla admittere <rerum> principia nullas causas nullas explicationes nisi quae per phaenomena stabiliuntur’. This text is not published in the Newton Project, and I have consulted the original in CUL. The translation is that offered in I.B. Cohen, ‘A guide to Newton's Principia’, in Principia, p. 54.

59 Stein, op. cit. (56), p. 256. It should be added that a non-anachronistic history of metaphysics in seventeenth-century Europe is a major desideratum.

60 The key loci are Met. iv, 1003a21 and vi, 1026a19–20. For the early modern reception the key study remains Reiner, Hans, ‘Die Entstehung der Lehre vom bibliothekarischen Ursprung des Namens Metaphysik: Geschichte einer Wissenschaftslegende’, Zeitschrift für philosophische Forschung (1955), 9, pp. 7799, at 79–80, supplemented in many very useful ways by Leijenhorst, op. cit. (2), pp. 17–55.

61 See Ian Hunter, ‘The university philosopher in early modern Germany’, in C. Condren, S. Gaukroger and I. Hunter (eds.), The Philosopher in Early Modern Europe, Cambridge: Cambridge University Press, 2006, pp. 35–65, 62–63. On the importance of Scheibler's work in seventeenth-century Oxford (the first Oxford edition was published in 1637, with additions by the young Thomas Barlow) see Richard Serjeantson, ‘Hobbes, the universities and the history of philosophy’, in Condren, Gaukroger and Hunter, op. cit., pp. 113–140, 131. For a very late English manifestation of this definition of metaphysics see also [Daniel Whitby?], Brevissimum metaphysicae compendium, secundum mentem nominalium, Oxford, 1690, pp. 1–2 (I adopt the speculative attribution to Whitby from the ESTC, but I have been unable to find any evidence for it – the work may as well be treated as anonymous).

62 Charles Lohr, ‘Metaphysics’, in E. Kessler and Q. Skinner (eds.), The Cambridge History of Renaissance Philosophy, Cambridge: Cambridge University Press, 1988, pp. 537–638, 631–632; J.A. van Ruler, ‘Franco Petri Burgersdijk and the case of Calvinism within the neo-scholastic tradition’, in R.P. Bos and H.A. Krop (eds.), Franco Burgersdijk (1590–1635), Amsterdam: Rodopi, 1993, pp. 37–65, 41. For More see Enchiridion metaphysicum, sive de rebus incorporeis, London, 1671, 1–42, esp. 1 (‘Metaphysicaest Ars recte contemplandi res Incorporeas quatenus e Lumine Naturae Facultatibus nostris innotescunt. Itaque Metaphysica Theologia quasi quaedam Naturalis est’).

63 Meditationes de prima philosophia in qua Dei existentia et animae immortalitas demonstratur, Paris, 1641. There are some very interesting comments on Descartes as part of the tradition of making God and immaterial substances the subject of metaphysics in Joël Biard, ‘God as first principle and metaphysics as a science’, in R.L. Driedman and L.O. Nielsen (eds.), The Medieval Heritage in Early Modern Metaphysics and Modal Theory, 1400–1700, Dordrecht: Kluwer, 2003, pp. 75–97, esp. 92–94.

64 See e.g. CUL MS Add. 3970.3, fol. 249r; CUL MS Add. 95972.14, fol. 4r; CUL MS Add. 3970.3, fols. 621v–622r, discussed further in Levitin, op. cit. (57).

65 CUL MS Add. 3970.3, fol. 620v. I have heavily normalized and modernized this text. A full discussion appears in Levitin, op. cit. (57).

66 Of course, Newton also speculated on natural-philosophical explanations for gravity, e.g. the electrical spirit of the end of the General Scholium. For the methodological status of such speculations – of which the Queries to the Opticks are archetypal  see Shapiro, op. cit. (12), p. 188.

67 Newton, Principia, p. 941.

68 Newton, ‘De gravitatione’, in Newton, Philosophical Writings, ed. Andrew Janiak, Cambridge: Cambridge University Press, 2004, pp. 21, 25, 26.

69 Pedro Hurtado de Mendoza, Universa philosophia … nova editio, Lyon, 1624 (1st edn 1617), pp. 343–345 (‘Expenditur doctrina de virtuali punctorum extensio’), concluding on p. 343b: ‘Virtualem item extensionem admitto in substantia spirituali: at in materiali recuso’. For body and soul see p. 344b.

70 Pedro da Fonseca, Commentariorum Petri Fonsecae … in Metaphysicorum Aristotelis Stagiritae libros, 3 vols., Cologne, 1599–1604 (this was the first edition to contain the full three volumes), vol. 3, p. 379a: ‘Hanc autem virtualem extensionem dari a forma incorporea, & inextensa nullum est incommodum: praesertim cum omnis forma, quae in se una est, det substantiae quam constituit virtualem potentiarum multitudinem, quae ex essentia a se composita quasi nascuntur’. See the valuable discussion in Dennis Des Chene, Life's Form: Late Aristotelian Conceptions of the Soul, Ithaca, NY: Cornell University Press, 2000, pp. 90–91. Luis de Ribas, Summa theologica, Lyon, 1643, pp. 82–83 (the chapter is entitled ‘Quid sit Immensitas, & an soli Deo conueniat’).

71 Descartes to Henry More, 15 April 1649, in Oeuvres de Descartes, op. cit. (38), vol. 5, p. 342: ‘Quantum autem ad me, nullam intelligo nec in Deo nec in Angelis vel mente nostra extensionem substantiae, sed potentiae duntaxat; ita scilicet ut possit Angelus potentiam suam exerere nunc in maiorem, nunc in minorem substantiae corporeae partem; nam, si nullum esset corpus, nullum etiam spatium intelligerem, cui Angelus vel Deus esset coextensus’.

72 Louis de la Forge, Traitté de l'esprit de l'homme, de ses facultez et fonctions, et de son union avec le corps, Paris, 1666 (1st edn 1664), p. 187: ‘Ils disent pour éviter cette difficulté que l'Esprit n'est pas estendu réellement, mais virtuellement, & que cette estenduë virtuelle suffit pour ester coestendu (permettez-moi ce mot) & present localement à un Corps qui a une extension réelle. Je ne les accuserai pas ici de n'entendre pas ce qu'ils veulent dire, quoi qu'il y ait lieu de croire que cela leur arrive assez souvent, lorsqu'ils allèguent de belles paroles auxquelles aucune idée qu'ils puissant expliquer ne répond dans leur esprit; mais accordons-leur qu'ils comprennet fort clairement ce que c'est qu'une étendue virtuelle, il faut aussi qu'ils m'accordent qu'on ne saurait concevoir aucune sorte d'extension, sans concevoir en meme temps plusieurs parties, dont l'une soit hors de l'autre; or dès qu'on aperçoit qu'une partie est hors d'une autre, on voit par meme moyen que ce sont deux parties dont l'une peut être conçue sans l'autre, et par conséquent exister séparément; et ainsi c'est une extension réelle, et ce sont des parties réelles qu'ils attribuent à l'esprit, lorsqu'ils pensent ne lui donner qu'une étendue et des parties virtuelles. Il est donc impossible de comprendre l'union de l'esprit et du corps selon les principes de la philsoophie de l'Ecole’.

73 Pierre Petit, De extensione animae et rerum incorporearum natura libri II, Paris, 1665, pp. 49–50: ‘Si enim ubique totus, ubi partes? Qui igitur ita indivisibilis est, quomodo extensus dici potest? nempe virtuali extensione: ita enim respondent. At, quid est virtualis extensio, nisi Deum indivisibili essentia ita in omnibus operari, ac si revera per universum esset Orbem extensus? Ad potentiam igitur vimque agendi virtualis illa extensio recidit, quando in ipsa substantia nihil apparet, nisi simplicissimum & summe individuum, ita omnem excludens extensionem, ut nec ejus partes ullae vel mente designari possint. Caeterum, divinam potentiam ad omnia extendi loca, omnesque Mundi partes complecti nemo negat. Quin non alia est apud Theologorum praestantissimos immensitatis notio. “Deus” (inquit D. Thomas) “in omnibus est per essentiam, quia substantia ejus omnibus adest, ut causa essendi”’. Petit's marginal note is to ‘distinct. 37’, which is most likely Aquinas's commentary on Lombard's Sentences (which is divided into ‘distinctiones’), but Aquinas certainly does not say there what Petit claims he does. Some linguistic similarities can be found in Aquinas, Quaestiones disputatae de veritate, q. 10a. 11 ad 7, but there again Aquinas says something different. I am very grateful to the second of the BJHS referees for assisting me in thinking through this unsolved puzzle.

74 Samuel Haworth, Anthropologia, or, A philosophic discourse concerning man. Being the anatomy both of his soul and body, London, 1680, p. 66. This is part of the chapter defending the soul's extension (pp. 58–66). Little is known about Haworth: a skeletal introduction is available in M.S.R. Jenner, ‘Haworth, Samuel’, ODNB.

75 Isaac Newton, ‘Tempus et locus’ (CUL MS Add. 3965, early 1690s), quoted and trans. in McGuire, J.E., ‘Newton on place, time, and God: an unpublished source’, BJHS (1978), 11, pp. 114129, 121.

76 E.g. in Janiak, op. cit. (56), p. 166 n. 5.

77 Henry More, The immortality of the soul, London, 1659, pp. 32–33.

78 For the former suggestion see e.g. many of the essays in McGuire, op. cit. (56); for the latter, Schliesser, op. cit. (56), esp. p. 88.

79 Rudolph Goclenius, Lexicon Philosophicum quo tanquam clave philosophiae fores aperuntur, Frankfurt, 1613, p. 146 (entry on ‘Emanare’): ‘Emanare est immediate essentiam comitari, tamen sine respectu existentiae, & ante existentiam, & sine respectu causae externae’.

80 Franco Burgersdijk, Institutionum logicarum libri duo, Cambridge, 1637, pp. 69–70 (in Chapter 17, on efficient cause): ‘Primo, dividitur causa efficiens in activam, quae effectum causat mediante actione; & in eam, a qua res immediate emanat, ac sine ulla actione proficiscitur’. Burgersdijk then goes on to give the example of fire and heat (‘ignis est causa emanativa proprii caloris; at est causa activa caloris in alio’). For the popularity of Burgersdijk's work in seventeenth-century English pedagogy see Mordechai Feingold, ‘The humanities’, in Tyacke, op. cit. (4), pp. 211–357, 294–296.

81 Adriaan Heereboord, ΕΡΜΗΝΕΙΑ Logica: sive synopseos logicae Burgersdicianae, London, 1651, pp. 36–38. There were further English editions in 1658, 1662 and 1676 (London) and 1663, 1670 and 1680 (Cambridge). See also Heereboord, Meletemata philosophica, Amsterdam and London, 1680 (1st edn 1654), pp. 263–265.

82 For a native example, albeit one taken from the work of Bartholomäus Keckermann, see [Henry Ainsworth/Zachary Coke], Art of logick, London, 1657 (1st edn 1654), p. 54. That the work is derived from that of Keckermann was first noted in Serjeantson, Richard, ‘Testimony and proof in early modern England’, Studies in the History and Philosophy of Science (1999) 30, pp. 195236, 207 n. 63. The English abridger's identity is discussed in Measell, James S., ‘The authorship of the Art of Logick’, Journal of the History of Philosophy, 15 (1977), pp. 321324.

83 Johann Heinrich Alsted, Encyclopaedia septem tomis distincta, 2 vols. (Herborn, 1630), vol. 1, p. 613a (again using the standard fire–heat example). For Zabarella see W.A. Wallace, Prelude to Galileo: Essays on Medieval and Sixteenth-Century Sources of Galileo's Thought, Dordrecht: Reidel, 1981, p. 113.

84 CUL MS Add. 3996, fol. 46v: (‘Omnis causa agit. [hoc ffalsum est in Materiali, fformali, et causa finali. Si etenim hae causae agunt sunt omnes efficientes, nam omnis causa agens est efficiens. Omnis vero & sola causa efficiens agit hoc est causa physica (nam Gubernatoris somnum, vel negligentiam, esse causam [one illegible deleted word] naufragii fit naturaliter.) (Object. fforma & essentia rei est causa efficiens propriorum accidentium: non vero per veram actionem sed per emanationem tantum et resultantiam …’).

85 E.g. Gideon Harvey, Archeologia philosophica nova, London, 1663, pp. 75–76; Joseph Glanvill, The vanity of dogmatizing, London, 1661, p. 37.

86 See Des Chene, op. cit. (70), pp. 90–91.

87 More, Enchiridion metaphysicum, in Opera omnia, vol. 1, London, 1679, p. 148.

88 Mordechai Feingold, The Newtonian Moment: Isaac Newton and the Making of Modern Culture, New York, 2004, pp. 26–27. The key evidence is a letter from the important Trinity College Greek scholar Thomas Gale to Edward Bernard, Bod. MS Smith 8, fol. 147r. Feingold suggests that the final version of ‘De gravitatione’ is a later one, because of ‘its invocation of the concept of inertia, a term not used by Newton before the mid-1680s’ (p. 194 n. 38). This reasoning (albeit not with Feingold in mind) is convincingly challenged in Ruffner, J.A., ‘Newton's De gravitatione: a review and reassessment’, Archives of the History of the Exact Sciences, 66 (2012), pp. 241264, 256. I thus accept Feingold's argument about the early 1670s pedagogical origins of the work, but, on the basis of the evidence gathered by Ruffner, reject the claim that the final version stems from the 1680s: the whole document should be seen as a product of lectures delivered in the early 1670s.

89 For disparaging comments on metaphysics see John Locke, An essay concerning human understanding, London, 1690, pp. 240, 310; for the recommendation to study it, see [Locke], Some thoughts concerning education, London, 1693, p. 225 (albeit taking into account the strong qualification at 197).

90 See e.g. Buchwald and Feingold, op. cit. (7), pp. 9–10. Shapiro, op. cit. (12), is also of great importance on this score.

91 The key work being Schmitt, op. cit. (2).

92 For the fullest overview of anti-Aristotelianism see now Craig Martin, Subverting Aristotle: Religion, History & Philosophy in Early Modern Science, Baltimore: Johns Hopkins University Press, 2014; also Levitin, op. cit. (31), Chapters 4 and 5.

93 Isaac Newton, Lectiones opticae, in The Optical Papers of Isaac Newton, ed. A.E. Shapiro, vol. 1, Cambridge: Cambridge University Press, 1984, pp. 81–83.

94 The key overall study of the reception of Cartesianism in England remains Arrigo Pacchi, Cartesio in Inghilterra: Da More a Boyle, Rome and Bari: Editori Laterza, 1973. For some recent findings on early English anti-Cartesianism see Levitin, Dmitri, ‘Rethinking English physico-theology: Samuel Parker's Tentamina de Deo’, Early Science and Medicine (2014) 19, pp. 2875.

95 For the importance of 1650s Oxford see esp. Mordechai Feingold, ‘The origins of the Royal Society revisited’, in M. Pelling and S. Mandelbrote (eds.), The Practice of Reform in Health, Medicine and Science, 1500–2000, Aldershot: Ashgate, 2005, pp. 167–183. For Bathurst, Highmore, their scientific practice and their intellectual debts, the key study remains Robert G. Frank, Harvey and the Oxford Physiologists: A Study of Scientific Ideas (Berkeley, CA: Berkeley University Press 1980), supplemented on Highmore in Levitin, op. cit. (31), Chapter 4.

An early version of this paper was delivered at the Newton's Principia in the Age of Enlightenment conference held at the Royal Society, 11–13 December 2013, co-organized by Mordechai Feingold and Rob Iliffe. I am very grateful to them, and to the many other delegates who asked perceptive questions. In particular, I would like to thank Steffen Ducheyne, and also Stephen Clucas, who encouraged me to re-examine the relationship between Newton and Hobbes on the issue of analysis and synthesis. The research for this article was conducted while I was a fellow of Trinity College, Cambridge, where I was fortunate enough to have daily access to Newton's books: I am very grateful to all the staff at the Wren Library. The comments of the two anonymous BJHS referees have also led to some important modifications. Unless stated otherwise, MS transcriptions are those published in the Newton Project: www.newtonproject.sussex.ac.uk. References to the Principia are to Isaac Newton, The Principia: Mathematical Principles of Natural Philosophy, trans. I.B. Cohen and Anne Whiteman, Berkeley, University of California Press, 1999. Other abbreviations are: Correspondence = H.W. Turnbull (ed.), The Correspondence of Isaac Newton, 7 vols., Cambridge: Cambridge University Press, 1959–1977; CUL = Cambridge University Library; Math. papers = D.T. Whiteside, The Mathematical Papers of Isaac Newton, 8 vols., Cambridge: Cambridge University Press, 1967–1981; ODNB = Oxford Dictionary of National Biography, at www.oxforddnb.com.

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