‘s Gravesande’s Appropriation of Newton’s Natural Philosophy, Part I: Epistemological and Theological Issues

Steffen Ducheyne

This is a preprint of a paper forthcoming in Centaurus. This pre-print should not be quoted or posted on other websites without prior permission from the author. ‘s Gravesande’s Appropriation of Newton’s Natural Philosophy, Part I: Epistemological and Theological Issues Steffen Ducheyne* Abstract. In this essay I reassess Willem Jacob ‘s Gravesande’s Newtonianism. I draw attention to ‘s Gravesande’s a-causal rendering of physics that went against Newton’s causal understanding of natural philosophy and to his attempt to establish a solid foundation for the certainty of Newton’s natural philosophy, which he considered as a powerful antidote against the theological aberrations of Descartes and especially Spinoza. I argue that, although ‘s Gravesande clearly took inspiration from Newton’s natural philosophy, he was running his own scientific and intellectual agenda and that he was combining Newtonian and non-Newtonian elements. Keywords. W. J. Gravesande, I. Newton, Eighteenth-century Newtonianism, Spinozism 1. Introduction In the historiography on Newtonianism we have moved away from the view defended in the earlier literature, according to which physics during the Enlightenment period should primarily be considered as a period of consolidation of Newton’s natural philosophy and according to which ‘Newtonianism’ served as the unifying element in scientific thought and practice throughout the eighteenth century (Porter, 2003; Home, 1979). 1 Correspondingly, eighteenth-century scholars are now coming to terms with the full complexity of eighteenthcentury physics and they are gradually freeing Enlightenment science from its ‘Newtonian straight jacket’. 2 Recent studies on Newtonianism have shown that, although Newton provided a critical impulse, eighteenth-century scientists or natural philosophers had to develop their own solutions to new pressing challenges.3 In the essay at hand, I provide a modest contribution to the study of eighteenth-century Newtonianism by focussing on Willem * Centre for Logic and Philosophy of Science, Vrije Universiteit Brussel, Pleinlaan 2, room 5B425, B-1050 Brussels, Belgium. E-mail: steffen.ducheyne@vub.ac.be. 1 Examples of this past tradition are, of course, legion. A selection of relevant examples should contain at least the following – in chronological order: Burtt, 1924; Metzger, 1930; Brunet, 1931; Hall, 1954; Cohen, 1956; Schofield, 1970; and, Thackray, 1970. 2 For recent studies on eighteenth-century Newtonianism, see – in chronological order: Stewart, 1992; Dobbs and Jacob, 1995; Force and Hutton (eds.), 2004; Feingold, 2004; Mandelbrote, 2004; Shank, 2008; and, Jorink and Maas (eds.), 2012. Scott Mandelbrote and Helmut Pulte are currently editing The Reception of Isaac Newton in Europe, which will no doubt be a major contribution (Mandelbrote and Pulte (eds.), forthcoming). 3 From a technical perspective this has been documented in: Bos, 1980; Greenberg, 1995, esp. Chapter 10; and, Wilson, 2003. Jacob ‘s Gravesande (1688-1742). 4 In order to understand ‘s Gravesande’s work, which I approach from a methodological, epistemological and theological perspective, we should pay equal attention to its Newtonian and non-Newtonian features, or so I argue. I do so thematically rather than strictly chronologically. Willem Jacob ‘s Gravesande has traditionally been portrayed as a ‘Newtonian’ (Cohen, 1956, pp. 234-243; de Pater, 1994, p. 261; Schofield, 1970, Chapter 7) and even as a ‘Baconian Newtonian’5 (Schofield, 1978, pp. 179-180). He was, we are told, ‘one of the most influential advocates of Newtonianism on the Continent’ (de Pater, 1994, p. 257),6 who stood in direct contact with his British peers. In 1715 ‘s Gravesande was secretary of a Dutch embassy which was sent to England to honour the coronation of George I and to negotiate about the barrier towns (Allamand, 1774, I, xxi-xxii). During his stay, he was introduced to England’s leading natural philosophers: Isaac Newton (1642-1727), who was president of the Royal Society at the time, the Royal Society’s curator of experiments, J. T. Desaguliers (1683-1744), who would later publish his famous A course of experimental philosophy (17341744), and the Savillian Professor of Astronomy at Oxford, John Keill (1671-1721), who had began teaching Newton’s natural philosophy ‘by Experiments in a mathematical Manner’ around 1704 or 1705 (Desaguliers, 1763, viii). 7 In June 1715, ‘s Gravesande was elected Fellow of the Royal Society and during his stay in England he was won over by the Newtonian cause, the story goes.8 Shortly after his return, in 1717, he became professor of mathematics and astronomy at the University of Leiden, where he taught Newton’s natural philosophy (see Fig. 1) (Molhuysen (1910-1924), IV, p. 295).9 In 1720/1 the first edition of ‘s Gravesande’s magnum opus appeared – a work which carried the telling title Physices elementa mathematica experimentis confirmata, sive introductio ad philosophiam Newtoniam.10 Physices elementa has been called ‘the most important and stimulating physics textbook in the West until well after 1750’ (Jacob and Stewart, 2006, p. 85). It went through three editions during ‘s Gravesande’s lifetime. Due to its publication ‘s Gravesande soon acquired an international reputation as a premier Newtonian, which can be gleaned from the fact that Voltaire came to consult ‘s Gravesande in Leiden on matters Newtonian in 17361737, i.e. at the time when he was finishing his Eléments de la philosophie de Newton, which On the life and work of ‘s Gravesande, Allamand, 1774, I, ix-lix; Hall, 1972; Gori, 1972, Chapter 2; and, de Pater, 1988, pp. 13-58. The editor of ‘s Gravesande’s collected work, Jean Nicolas Sébastien Allamand (1716-1787), was a student of his who later succeeded him as director of the Theatrum physicum. 5 ‘s Gravesande owned a 1665 edition of Bacon’s Opera omnia ([anon.], 1742, p. 1 [item n° 6]). Yet, it does not appear that the details of Bacon’s work played a crucial role in ‘s Gravesande’s thinking. Accordingly, the label ‘Baconian Newtonian’ does little explanatory work in ‘s Gravesande’s case. 6 Cf. Allamand (1774[1744]), I, xxxiii: ‘Les idées Newtoniennes n’étoient guéres connues en deça de la mer: personne n’avoit encore travaillé à en former un système. Mr. ‘sGravesande fut le premier qui entreprit la chose & qui l’exécuta avec succès.’ 7 ‘s Gravesande owned both Keill, 1702 and 1718 ([anon.], 1742, p. 56 [item n° 225], p. 17 [item n° 21], respectively). 8 During his years as a student, ’s Gravesande was drawn towards scientific subjects and optics, more specifically. His early scientific interest culminated in the publication of ‘s Gravesande, 1711. See, furthermore, Cantor (1880-1908), IV, pp. 594-597. 9 ‘s Gravesande was of course not Leiden’s first experimental philosopher. Prior to him Burchard de Volder (1643-1709), Wolfert Senguerd (1646-1724), and Herman Boerhaave (1668-1738) were actively involved in experimental research. On the experimental and mathematical tradition at Leiden prior to ‘s Gravesande, see de Pater, 1975; Ruestow, 1973, Chapters 2-6; de Hoog, 1974; van Berkel, 1999; and, especially Wiesenfeldt, 2002. Many of ‘s Gravesande’s predecessors were developing the experimental strands within Descartes’ natural philosophy (van Bunge, unpublished manuscript; cf. Cook, 2007, p. 259). 10 The second edition of Physices elementa was published in 1725 and the third in 1742. Throughout this essay I will rely on ’s Gravesande, 1742 and 1747. On Desaguliers’ translation of Physices elementa, see Wigelsworth, 2003. 4 would be published in 1738 in Amsterdam (Brunet, 1926, pp. 117-119).11 Upon receiving the news that he was visiting ‘s Gravesande in Leiden, the Prussian Crown Prince Frederick (1712-1786) wrote to Voltaire in January 1737 that ‘s Gravesande ‘doit posséder la philosophie de Newton dans la dernière perfection’ (Koser and Droysen (1908-1909), I, p. 30). The above details have been frequently repeated in the literature and, for the most part, they have been used to highlight the close connexion between ‘s Gravesande and Newton. Prima facie there are good reasons for portaying ‘s Gravesande as a full-blown ‘Newtonian’, for Physices elementa contained the basic doctrines of Newton’s natural philosophy: in its preface a short exposition of Newton’s method of first and ultimate ratios was included, in Book I, Part I, Chapter VI ‘s Gravesande distinguished between relative and absolute time and space, in the same book, Part III, Chapter XVII he accepted Newton’s three laws of motion as being deduced from phenomena, in Book V, Part IV, Chapters XXIII, XXIV and XXVI, he endorsed Newton’s theory of the heterogeneity of white light, his account of the rainbow and his explanation of the colours of natural bodies, respectively, and in Book VI, Part II, Chapters XI-XX he explained the planetary system with the theory of universal gravitation (’s Gravesande, 1747, I, liv-lvi, p. 26, pp. 78-81, II, p. 256, pp. 259-266, pp. 273-276, pp. 319-389). However, as is well known ‘s Gravesande occasionally treated Newton’s doctrines in a selective manner: for instance, Physices elementa did not contain a detailed discussion of Newton’s fits of easy transmission and reflection and the ether which Newton introduced to explain optical phenomena was hardly mentioned (Hakfoort, 1995, pp. 42-45). Moreover, ‘s Gravesande did not accept all of Newton’s doctrines without reservation, which is clear from the position he took in the vis viva dispute. 12 In view of this, ‘s Gravesande’s oftentimes critical attitude towards Newton’s doctrines has been rightly highlighted. In the wake of the quibble over vis viva, which was fiercely opposed by Newton’s epigones such as Samuel Clarke, who noted that the principle of vis viva “subverts all Science” (Clarke, 1727, p. 382), ‘s Gravesande signalled that being a Newtonian philosopher is not contingent upon whether one accepts Newton’s doctrines ad literam; rather, a Newtonian philosopher is he who follows Newton’s method (’s Gravesande, 1747, I, xi). My aim is to provide a detailed reconstruction of how ‘s Gravesande combined Newtonian and non-Newtonian elements. What is especially striking about ‘s Gravesande’s thought is, as we will see in what follows, that it was based on a variety of sources of which Newton was only one. Accordingly, one has good reasons to remain sceptical of attempts to characterize ‘s Gravesande’s thought by aligning it to a single school or tradition. Let me provide an overview of this essay, in which I focus on ‘s Gravesande’s epistemological and theological appropriation of Newton’s natural philosophy. In section 2, I argue that, although ‘s Gravesande took over certain elements of Newton’s empiricist epistemology, his a-causal rendering of physics went against Newton’s causal understanding of natural philosophy. In section 3, I show that, in response to the atheistic dangers of Spinoza’s and Descartes’ a priori manner of philosophizing, ‘s Gravesande attempted to provide a solid epistemological and theological foundation for the certainty of Newton’s natural philosophy. In section 4, I provide further discussion ‘s of Gravesande’s alleged crypto-Spinozism. 2. ‘s Gravesande on ‘Learned Ignorance’ and the Scope of Physics 11 1989. The influence of ‘s Gravesande’s magnum opus has not been studied in detail. See, however, de Pater, For ‘s Gravesande’s endorsement of vis viva, see Costabel, 1964; Iltis, 1967, Chapters V and VI; Gori, 1972, pp. 296-308; Hankins, 1965, pp. 286-291; Schaffer, 1995, pp. 176-181; and, Boudri, 2002, pp. 107-109. I shall return to ‘s Gravesande’s and vis viva in Part II of this essay. 12 Given the human inability to achieve a complete understanding of the workings of nature, a ban should be put on speculative theorizing, ‘s Gravesande urged (Ruestow, 1973, pp; 122127). Because of an ‘immoderate Desire of Knowledge’ natural philosophers have been tempted to do otherwise and, accordingly, they have based their explanations of natural phenomena on idle fancies. Since physics considers ‘the Works of supreme Wisdom,’ one should instead proceed cautiously, refrain from hypotheses altogether, and embrace, ‘a learned Ignorance,’ ‘s Gravesande wrote in the preface to the first edition of Physices elementa:13 We must take care not to admit Fiction for Truth, for by that means we shut out all further Examination. No true Explanation of Phænomena can spring out of a false Principle: And what a vast difference there is betwixt learning the Fictions of whimsical Men, and examining the Works of the most wise God! Since an Enquiry into Divine Wisdom, and the Veneration inseparable from it, is to be the Scope of a Philosopher; we need not enlarge upon the Vanity of reasoning upon fictitious Hypotheses. Nature herself is therefore attentively and incessantly to be examined with indefatigable Pains. That way indeed our Progress will be but slow, but then our Discoveries will be certain; and oftentimes we shall even be able to determine the Limits of human Understanding. What has led most People into Errors, is an immoderate Desire of Knowledge, and the Shame of confessing our Ignorance; but Reason shou’d get the better of that ill-grounded Shame, since there is a learned Ignorance that is the Fruit of Knowledge, and which is much preferable to an 14 ignorant Learning. (’s Gravesande, 1747, I, i-ii [italics added]; ‘s Gravesande, 1742, I, i-ii) In line with his ‘learned Ignorance,’ ‘s Gravesande underscored the incompleteness of human knowledge and, hence, the limitations of physica. He observed that, although we can acquire knowledge of some of the properties of things, we cannot know their substances or essences: ‘What Substances are, is one of the Things hidden from us. We know, for instance, some of the Properties of Matter, but we are absolutely ignorant in what Subject they are inherent.’ (’s Gravesande, 1747, I, iii; ‘s Gravesande, 1742, I, iv; cf. ‘s Gravesande, 1736, §18, p. 8). We only know substances by their attributes (‘s Gravesande, 1736, § 18, p. 8). ‘s Gravesande’s denial that we have epistemic access to the substances of things is perfectly compatible with Newton’s ideas on the matter. In the General Scholium (1713) Newton recorded that: ‘We see only the shapes and colors of bodies, we hear only their sounds, we touch only their external surfaces, we smell only their odors, and we taste only their flavors. But there is no direct sense and there are no indirect reflected actions by which we know innermost substances […]’ (Newton, 1999, p. 942 [italics added]).15 In the preface to the first edition of Physices elementa, ‘s Gravesande argued that it is illusory to think that we can obtain a complete knowledge of things: Who dares affirm that there are not in Body many other Properties, which we have no Notions of? And whoever could certainly know, that besides the Properties of Body which flow from the Essence of Matter, there are not others depending upon the free Power of GOD, and that extended and solid Substance (for thus we define Body) is endowed with some Properties without which it could exist? We are not, I own, to affirm or deny any thing concerning what we do not know. But this Rule is not followed by those, who reason in physical Matters, as if they had a complete Knowledge of whatever belongs to Body, and who do not scruple to affirm, that the few Properties 13 Bernard Nieuwentijt had explicitly aligned his Het regt gebruik der wereltbeschouwingen (1715) and Gronden van Zekerheid (1720), both of which ’s Gravesande owned ([anon.], 1742, p. 29 [item n° 286] and p. 25 [n° 194], respectively), with the tradition of ‘learned ignorance’ (Ducheyne, 2007). Docta ignorantia also featured in the work of John Locke and Gisbertus Voetius (Schuurman, 2010). 14 For ’s Gravesande’s anti-hypothetical stance, see, furthermore, ’s Gravesande, 1747, I, viii, ix, xi. 15 Locke had also forcefully denied that we have knowledge of the internal constitutions of things or ‘real essences’ (Locke, 1975, III.iv, §§1-13, pp. 438-448). ‘s Gravesande owned Locke, 1700 and 1714 ([anon.], 1742, p. 4 [item n° 62] and p. 24 [n° 162], respectively). of Body which they are acquainted with, constitute the very Essence of Body. […] We must give up as uncertain what we find to be so, and not be ashamed to confess our Ignorance. (’s Gravesande, 1747, iii-iv [italics added]; ’s Gravesande, 1742, I, iv) It seems that in the above quotation ‘s Gravesande was, amongst other things, targeting Descartes’ famous equivocating of body and res extensa. With respect to the laws of nature (such as Newton’s law of universal gravitation), ‘s Gravesande emphasized in the same preface that we are at loss ‘whether they [i.e. the laws of nature] flow from the Essence of Matter, or whether they are deducible from Properties, given by GOD to the Bodies which the World consists of, but no way essential to Body; or whether finally those Effects, which pass for Laws of Nature, do not depend upon external Causes, which even our Ideas cannot attain to.’ (’s Gravesande, 1747, I, iv; ’s Gravesande, 1742, I, v). For Newton, on the other hand, some of these issues were quite important. For instance, it was of vital theological importance to him to show that gravity is not an essential quality of matter. 16 While Newton was prepared to state in the commentary to the third rule of philosophizing that he was ‘by no means affirming that gravity is essential to matter’ (Newton, 1999, p. 796). ‘s Gravesande pleaded ignorance on this matter and sought to eliminate such issues from Physices elementa. In denying the meaningfulness of such questions outright, ‘s Gravesande was consciously restricting the scope of natural philosophy and gradually turning it into physics (Heilbron, 1980, p. 362ff.; Heilbron, 1982, pp. 1-11; Home, 2003, p. 358). 17 As we will see, ‘s Gravesande’s disciplinary reorganization was accompanied by an expurgation of the potentially controversial issues associated with Newton’s natural philosophy (such as the status of causation, the cause of gravity, the socalled ‘active principles’ that are the sources of motion and activity in the world, God’s relation to the physical world, and so forth).18 In section 4, I shall indicate that this does not at all imply that ‘s Gravesande’s was running an anti-theological agenda, for he ultimately thought that theological considerations serve as the safeguard of the certainty of physics. In the very first chapter of Physices elementa entitled ‘De Scopo Physices et Regulis philosophandi’, ‘s Gravesande recorded that physics (physica 19) is ‘conversant about natural Things [i.e. bodies, according to Definition 1] and their Phænomena [circa res naturales & harum Phænomena versatur].’ Phenomena are defined as ‘all Situations, and Motions, of natural Bodies, not immediately depending upon the Action of an intelligent Being, and which may be observed by our Senses [omnes situs, & omnes motus, Corporum naturalium, ab actione Entis intelligentis immediate non pendentes, & qui à nobis sensibus observari possunt]’ (Definition 3) (’s Gravesande, 1747, I, p. 1; ‘s Gravesande, 1742, I, p. 1). Accordingly, the above definition entails the exclusion of acts of volition from physics. More precisely, Definition 3 implies that, while the study of the muscular motion ‘proceeding from the Action of the Muscles’ pertains to physics, the study of the ‘Action of the Mind,’ which ultimately produces these motions, does not, because it relates to causes which are ‘entirely unknown,’ i.e. unobservable. Whatever is entirely unknown (‘omninò ignotus’) is not a natural phenomenon, ‘s Gravesande stressed. Physics restricts itself to the observable motion of bodies and, correspondingly, it does not address the mind-body problem (’s Gravesande, 1747, II, p. 48). 20 Physics also ‘explains natural Phænomena, i.e. treats of their Causes 16 For further discussion and references, see Ducheyne, 2012, pp. 37-45 and Ducheyne (in press). On Dutch science during the Enlightenment, see Roberts, 1999. On the Dutch Enlightenment, more generally, see: Jacob and Mijnhardt, 1992 and, of course, Israel, 1995, esp. Chapter 39. 18 Cf. Maas, 2012, p. 130. 19 In his translation of ‘s Gravesande’s Physices elementa, Desaguliers consistently translated ‘physica’ as ‘natural philosophy’. In his own vernacular, ‘s Gravesande used the term ‘natuurkunde’. 20 In his Essais de métaphysique, ‘s Gravesande pointed out that the mind-body problem pertains to metaphysics (Allamand (1774), II, p. 181). 17 [Phænomena naturalia explicat, id est, horum causas tradit]’ and it is here that, according to ‘s Gravesande, the laws of nature come into play: ‘When we enquire into these Causes, we must consider Body it self in general; then we must discover by what Rules the Creator [Conditor] of all things pleas’d that all their Motions should be perform’d [peragi voluerit].’ (’s Gravesande, 1747, I, p. 2; ‘s Gravesande, 1742, I, p. 2). Once we have established the laws of nature, ‘we cannot penetrate farther into the Knowledge of Causes [non ulterius in causarum cognitionem penetrare possimus]’ (’s Gravesande, 1747, I, v; ‘s Gravesande, 1742, I, vi ). ‘s Gravesande defined a law of nature as ‘the Rule and Law according to which God thought fit that certain Motions should always, i.e. in all Cases, be perform’d [Regula & Norma, secundum quam Deus voluit certos motus semper, id est, in omnibus occasionibus, peragi]’ (’s Gravesande, 1747, I, p. 2; ‘s Gravesande, 1742, I, p. 2). In line with the empiricist strands in his thinking, ‘s Gravesande denied that we have epistemic access to the realm of causation, which remains observably hidden from us. 21 Consequently, with respect to us (‘nostro respectu’), a law of nature is ‘every simple Effect, which continues the same upon all Occasions, whose Cause is unknown to us,22 and which we find cannot flow from any Law known to us, tho’ perhaps it may from a more simple Law, unknown to us [omnis effectus simplex, qui in omnibus occasionibus idem est, cujus causa nobis est ignota, & quem videmus ex nullâ Lege, nobis notâ, fluere posse, quamvis fortè ex simpliciori Lege, nobis ignotâ, fluat]’ (’s Gravesande, 1747, I, p. 2; ‘s Gravesande, 1742, I, pp. 2-3). ‘s Gravesande’s statement that physics ‘explains’ phenomena is therefore highly puzzling at first sight. Prima facie he seems to be taking over Newton’s causal talk. However, it is vital to realize that, immediately after introducing causal talk in his Physices elementa, he provided a highly revisionist reinterpretation of our causal talk in physics and he stressed, in contrast to Newton, that physics is the study, not of causes, but of universal effects.23 Newton, by contrast, urged that ‘the main Business of natural Philosophy is to argue from Phaenomena without feigning Hypotheses, and to deduce Causes from Effects’ (Newton, 1952, p. 369).24 In his first optical paper, Newton claimed that he had established the ‘true cause’ of refraction: the heterogeneity of white light (Cohen (ed.), 1978, p. 51). Similarly, in Propositions I-III of Book I of the Principia Newton established the necessary and sufficient cause, given the laws of motion, for the area law to hold exactly or as most closely as possible (quam proxime) (Newton, 1999, pp. 444-448). In emphasizing that physics is the study of the universal effects, ‘s Gravesande was once again restricting the scope of natural philosophy as it was originally envisioned by Newton. ‘s Gravesande’s causal revisionism in physics does not mean, however, that he endorsed the view that all causal talk is entirely meaningless. In his metaphysical work, he discussed the nature of causation, which he characterized in necessitarian terms (‘s Gravesande, 1736, § 88, p. 32). 25 Seen from this perspective, ‘s It is quite unsatisfactory to consider ‘s Gravesande’s as a full-blown empiricist: he pleaded ignorance on the origin of ideas and on whether ideas are innate: ‘Inter incerta, ideò, reliquimus, utrum Ideæ innatæ sint, an non; & ex obscuritate, in quâ circa Originem Idearum hæremus, hac viâ exire non conceditur.’ (‘s Gravesande, 1736, § 288, p. 95, cf. § 307, p. 100). 22 Similarly, in his De comparando certo in physicis, Herman Boerhaave, who had, as the story goes, paved the way for the emergence of the university of Leiden as a leading centre for the dissemination of Newton’s natural philosophy and who called Newton the ‘Principe omnium Philosophorum,’ pointed out that: ‘Namque attractio aliud nihil denotat, quam causam ignotam, quae creat motum quasi sponte natum, quo corpora quaedam agantur in contactus mutuos, non verô explanat quaenam haec causa sit, nec exponit quo intelligibili modo mutum huncce excitet.’ (Boerhaave, 1715, p. 18 [italics added]). On Boerhaave, see Metzger, 1930; Lindeboom, 2007; and, Knoeff, 2002. 23 For causal-realist accounts of Newton’s stance on forces, see Janiak, 2007; Janiak, 2008, Chapter 3; and, Ducheyne, 2021, Chapter 2, esp. pp. 25-36. 24 See, furthermore, Newton, 1999, p. 415 and Ducheyne, 2012, pp. 18-25. 25 See, furthermore, ‘s Gravesande’s Essais de métaphysique in: Allamand (ed.) (1774), II, pp. 176-180. 21 Gravesande causal revisionism within the realm of physics can, and in my opinion should, be seen as the result of his attempt to separate metaphysical issues such as causation from physics.26 Since the realm of causation is hidden from us, ‘s Gravesande pointed out that ‘it matters not, whether any thing depends immediately upon the Will of God, or is produc’d by an intermediate Cause, of which we have no Idea [non interest, utrùm quid immediatè à Dei voluntate pendeat, an verò mediante causâ, cujus nullam ideam habemus, producatur]’ (’s Gravesande, 1747, I, p. 2; ‘s Gravesande, 1742, I, pp. 2-3). In view of this, the search for the cause of gravity is a futile endeavour. How gravitational forces operate is simply beyond human comprehension (‘s Gravesande (1717), pp. 20-21; ‘s Gravesande, 1747, II, pp. 326327; ‘s Gravesande, 1742, II, pp. 996-997).27 Because gravitational interaction does not allow for a mechanical explanation, it simply defies our understanding. In denying the fundamental impossibility of unravelling the cause of gravity, ‘s Gravesande defended a stance more radical than the one originally endorsed by Newton. In the speculative parts of his natural philosophy, i.e. in the Queries of the Opticks, Newton proposed a hypothesis on the cause of gravity. More precisely, in Query 21 he introduced an extremely subtle ‘elastick’ ether endowed with strong inter-particular repulsive forces as a possible explanation or cause of gravity (Newton, 1952, pp. 350-352). Newton was clearly aware that such ether was entirely conjectural, for in the Advertisement added to the 1717 edition of the Opticks he observed that he was ‘not yet satisfied about it [i.e. about his explanation of gravity] for want of Experiments’ (Newton, 1952, cxxiii). Although Newton never succeeded in establishing the cause of gravity in a way that could meet his own sophisticated methodological desiderata, he was not unsympathetic to the idea that the cause of gravity could in principle be discovered through extensive empirical research. For ‘s Gravesande, however, this was simply a futile exercise, given our inability to unravel nature’s causes. 3. ‘s Gravesande’s Theological Foundation of Newtonian Science ‘s Gravesande was dismissive of attempts to understand the physical world on the basis of a priori reasoning, which according to him not only lead to mistakes in physics, but also to certain misguided theological and moral views. Not surprisingly, he forcefully reacted against what he perceived as the theologically unacceptable implications of Descartes’ views, 28 according to which the laws of motion are sufficient to account for the formation of the universe. In Physices elementa, he wrote: It is confounding and oversetting all our clearest Notions, to assert that the World may have taken its Rise from some general Laws of Motion, and that it imports not what is imagined concerning the first Division of Matter. And that there can hardly be anything supposed, from which the same Effect may not be deduced by the same Laws of Nature: and that for this Reason; That since Matter successively assumes all the Forms it is capable of by means of those Laws, if we consider all those Forms in order, we must at last come to that Form wherein this present World was framed; so that we have no Reason in this Case to fear any Error from a wrong Supposition. This Assertion, I say, overthrows all our clearest Notions, as had been fully proved by many learned Men; and is indeed so unreasonable, and so injurious to the Deity, that it will seem unworthy of an Answer to any one that does not know that it has been maintain’d by any antient and modern This results in a more complex view of the role of causation in ‘s Gravesande’s physics than the one sketched by Ruestow (Ruestow, 1973, pp. 125-131). 27 Cf. Boerhaave, 1715, pp. 13-16. See, furthermore, Ruestow, 1973, pp. 123-125. 28 In the following quotation in the main text, ‘s Gravesande took issue with a statement in Descartes’ Principia philosophiae, which ‘s Gravesande owned (Adam and Tannery (eds.) (1897-1913), VIII, pp. 101-103; [anon.], 1742, p. 17 [item n° 1] and p. 25 [item n° 196]). 26 Philosophers, and some of them of the first Rank, and far removed from any Suspicion of Atheism. (’s Gravesande, 1747, I, ii-iii ; ‘s Gravesande, 1742, I, ii-iii) In his Discours sur la vraie philosophie (1734), ‘s Gravesande noted that Descartes, who although he has ‘recommandé l’observation, comme le seul moyen de parvernir à la découverte de la verité; souvent il a été obligé d’employer dès méthodes opposées,’ ‘‘s accorde avec ces anciens Philosophes [i.e. Democritus and Epicurus] en ceci, c’est que suivant lui le Monde auroit pu être formé sans le concours particulier d’un Etre intelligent, & que la matière, une fois créée & mue suivant des loix quelconques, suffisoit pour le produire.’ (Allamand (ed.), 1774, II, p. 352, p. 353). In his Oratio inauguralis, de matheseos, in omnibus scientiis (1717), which was delivered when ‘s Gravesande became professor of mathematics and astronomy at the university of Leiden and which contained a vigorous defence of Newton’s systema mundi, he argued against the alleged conduciveness of the empirico-mathematical study of nature towards atheism (‘s Gravesande, 1717, p. 3, pp. 10-11). When observation is properly combined with mathematics, God’s wisdom is put before our eyes. However, when observation is negelected by focussing too narrowly on mathematics and a priori reasoning, theological aberrations will arise. Characteristically, mathematicians only admit what can be proven by rigid demonstration and, because of this, some of them have been tempted to cast doubt on the truths of Scripture. Such aberrations are a consequence of a misguided use of mathematics, not of the use of mathematics per se, ‘s Gravesande underscored, for not everything can be subjected to reason. In his Oratio de evidentia (1724), he pointed out: ‘While they [i.e. misguided mathematicians] contend that nothing is to be taken for Truth but what is prov’d by mathematical Demonstration, in many things they take away all Criterium of Truth, while they boast that they defend the only Criterium of Truth.’ (’s Gravesande, 1747, I, xxxvi; ‘s Gravesande, 1742, I, xxxix-xl; cf. ‘s Gravesande, 1717, p. 11). According to ‘s Gravesande, Spinoza’s work provides a key example of how the mathematical method has been greatly abused. In his Discours sur la vraie philosophie (1734) ‘s Gravesande criticized Spinoza’s geometrical approach, as follows: Cet Auteur [i.e. Spinoza] a écrit avec tout l’appareil mathématique: en parcourant sa morale, on croit voir un Traité de Géometrie, mais bientôt on découvre l’abus qu’il a fait de cette méthode. Après plusieurs propositions qu’il a fait précéder, & par plusieurs détours, il parvient enfin à une conclusion qu’il auroit pu tirer de ses seules définitions, s’il les avoit proposées clairement. Mais il a eu ses raisons en agir ainsi. Ses définitions sont captieuses, & si artistement conçues qu’on ne s’aperçoit par d’abord qu’il donne aux mots, qu’il y employe, un sens différent de celui qu’on leur attache ordinairement. S’il en avoit déduit immédiatement ses conclusions, pour les appliquer aux choses mêmes, exprimées par les mêmes mots, mais pris dans le sens qu’on leur donne dans le languagee ordinaire, l’artifice auroit bientôt été découvert. A l’aide de l’ambiguité de ses définitions, & des longs circuits qu’il fait fair à ses Lecteurs, il empêche qu’on ne démèle aisément ses sophismes, & par là it fait tomber ceux qui ne sont pas sur leurs gardes dans plusieurs erreurs absurdes, & même très dangereuses. (Allamand (ed.), 1774, II, p. 355 [italics added]) ‘s Gravesande was hereby echoing Nieuwentijt’s criticism on Spinoza. The latter had criticized Spinoza for having made conclusions about things outside the mind by relying exclusively on a priori reasoning (e.g., Nieuwentijt, 1720a, p. 10). Instead of reaching conclusions about things outside our minds on the basis of mixed mathematics, Spinoza had reached them by a train of pure mathematical reasoning. As a way of immunizing the atheistic implications of a priori reasoning, Nieuwentijt had forcefully argued that proper knowledge of the empirical world is to be obtained by mixed mathematics. While pure mathematics (‘suyvere Wiskunde’) deals with ‘naked ideas’ (‘blote Denkbeelden’) only, mixed mathematics (‘gemengde Wiskunde’) is concerned with those things which exist outside our mind (‘Wesentlyke saken’) (Nieuwentijt, 1720b, pp. 2-3, p. 9, p. 11). Pure mathematics proceeds conditionally, for it establishes the deductive consequences of those mathematical ideas, which serve as the hypotheses of our reasoning (Nieuwentijt, 1720b, p. 9). Mixed mathematics (also called ‘sakelyke Wiskunde’), by contrast, proceeds from phenomena: it does not posit hypotheses as its principles, but instead proceeds from ‘indubitable appearances, experiments and observations’ (‘onbetwistelyke Verschynselen, en derselver Ondervindingen of Waarnemingen’), which serve as the starting point of mathematical reasonings and deductions (Nieuwentijt, 1720b, pp. 30-31). Emphasis on the harmonious relation between mathematics and religion was a common theme in the Dutch Republic, where Spinoza’s deductive approach was perceived as a great danger (Vermij, 2003, pp. 189-192; Jorink, 2009). According to ‘s Gravesande, the empiricomathematical manner of philosophizing cultivated by Newton, the ‘prince of the mathematicians and renewer of the true philosophy [Mathematicorum Princeps & veræ Philosophiæ Instaurator]’ (‘s Gravesande, 1717, p. 17), provides a powerful antidote against the atheistic implications of Descartes’ and Spinoza’s systems. Since the laws of nature that ‘depend only on the will of the Creator [a sola Creatoris voluntate pendentes]’ are ‘not disclosed to us by divine revelation [nulla divina revelatione nobis detegantur],’ their discovery ought to be established on the basis of observation and experimentation, i.e. a posteriori (‘s Gravesande, 1717, p. 16). ‘s Gravesande was convinced that Newton’s empirico-mathematical approach is conducive to the belief in and the veneration of an allpowerful deity. Despite his expurgation of metaphysical and potentially theologically-laden topics from Newton’s natural philosophy, for ‘s Gravesande physica was an enterprise with an undeniable theological dimension. In the preface to the first edition of Physices elementa, ‘s Gravesande wrote, as follows: The Study of Natural Philosophy is not however to be contemned, as built upon an unknown Foundation. The Sphere of human Knowledge is bounded within a narrow Compass; […]. […] Though many Things in nature are hidden from us, yet what is set down in Physics, as a Science, is certain. From a few general Principles numberless particular Phænomena or Effects are explain’d and deduced by mathematical Demonstration. […] How much soever may be unknown in Natural Philosophy, it still remains a vast, certain, and very useful Science: It corrects an infinite Number of Prejudices concerning natural Things, and divine Wisdom; and as we examine the Works of God continually, sets that Wisdom before our Eyes; and there is a wide Difference betwixt knowing the divine Power and Wisdom by a metaphysical Argument, and beholding them with our Eyes every Minute in their Effects. (’s Gravesande, 1747, I, v [italics added]; s Gravesande, 1742, I, v-vi) Note that here, as in the rest of his work, ‘s Gravesande did not mention final causes. As is well known, in the General Scholium (1713) Newton declared that ‘[w]e know him [i.e., God] only by his properties and attributes and by the wisest and best construction of things and their final causes’ (Newton, 1999, p. 942 [italics added]). Although ‘s Gravesande agreed in his Discours sur la vraie philosophie (1734) that ‘[l]a contemplation de cet Univers nous offre les preuves les plus convaincantes de sa Toute-Puissance [i.e. God’s omnipotence]: à chaque moment nous y découvrons des traces de sa Sagesse & de sa Bonté,’ (Allamand (ed.), 1774, II, p. 362)29 he did not, in line with his views on man’s limited understanding of the workings 29 On Dutch physico-theology, see Bots, 1972; Vermij, 1991 and 2003; van der Wall, 2004; and, Jorink 2010. On the absence of final causes in ‘s Gravesande’s Physices elementa, see Israel, 2006, pp. 216-217 and Schliesser, 2011, p. 106. In his essay Démonstration mathématique du soin que Dieu prend diriger ce qui passé dans ce Monde, tirée du nombre des garçons & des filles qui naissant journellement (1712), ‘s Gravesande concluded: ‘Il n’a qu’un Etre intelligent qui puisse faire naitre des garçons & des filles précisément autant qu’il en faut des uns & des autres, pour que tout reste dans l’ordre, malgré la prodigieuse probabilité qui s’y oppose, si on ne sait fait attention qu’à ce qui peut découler des loix générales & physique.’ (Allamand (ed.), 1774, II, p. 236). of God and nature, endorse the idea that humans are able to penetrate the ends for the sake of which God has created all things. According to him, physics does not meddle with ‘the first Foundation of Things,’ and restricts itself to uncovering ‘[h]ow the whole Universe is governed by those Laws, and how the same Laws run thro’ all the Works of Nature, and are constantly observed with a wonderful Regularity’ (’s Gravesande, 1747, I, ii-iii).30 That ‘s Gravesande was not just paying lip service to theology to soothe the opponents of an empirico-mathematical study of nature can furthermore be gathered from the fact that according to him God’s infinite benevolence was ultimately the foundation of certainty in physics. Given his preoccupation with certainty, it was crucial for ‘s Gravesande to elaborate on the kind of certainty that is established in physics. In order to understand his take on the matter, we should turn to his distinction between mathematical and moral certainty.31 Their immediate perception is called mathematical or moral ‘evidentia’ (’s Gravesande, 1736, § 456, p. 137). A peculiar feature of his thought on certainty is that he maintained that, despite the fundamental difference between mathematical and moral certainty, the persuasion arising from both is equally certain (‘s Gravesande, 1736, § 481, p. 145), i.e. both kinds of certainty do not leave room for doubt: But although these Foundations differ, tho’ mathematical Evidence does not agree with moral, yet a different persuasion does not proceed from thence. I can no more deny my Assent to such Things, as are drawn from the Foundations of moral Evidence which I have explain’d, when due Care is taken [legitimis observatis cautelis], than to those which are prov’d by a mathematical Demonstration. (’s Gravesande, 1747, I, xlviii; ‘s Gravesande, 1742, I, lv-lvi; cf. ‘s Gravesande, 1717, pp. 11-12 and ‘s Gravesande, 1736, § 481, pp. 144-145) The addition ‘legitimis observatis cautelis’ – ‘with appropriately guarded precautions’ – may be considered as shorthand for the range of criteria for attaining moral evidence which ‘s Gravesande subsequently explicated in Book II, Parts I and III of his Introductio ad philosophiam (‘s Gravesande, 1736, pp. 149-175, pp. 258-333). 32 ‘s Gravesande made a categorical distinction between morally certain knowledge or certainty and probable knowledge, which is ‘vulgarly called moral certainty’ [vulgò Moralis dicitur] (‘s Gravesande, 1736, § 583, p. 176). Paul Schuurman has correctly stressed that ‘s Gravesande tried ‘to secure the epistemological status of his Newtonian physics by giving a new and stronger definition of ‘moral evidentia’’ (Schuurman, 2004, p. 143, cf. p. 132). He, one might say, sought to challenge the ‘vulgarly’ accepted notion of moral certainty (de Pater, 1995). ‘s Gravesande differed from other natural philosophers, whom like him took empirical investigation as the starting point for attaining knowledge about the physical world, in that he was convinced that, if we carefully follow the methodological precepts spelled out in his Introductio ad philosophiam, certain – and not merely probable – knowledge can be established. Giambattista Gori has pointed out that ‘s Gravesande’s views on moral certainty were likely indebted to Humphry Ditton’s (1675-1715) A Discourse concerning the Resurrection of Jesus Christ (1712) (Gori, 1972, p. 218, p. 232, footnote 11, p. 247, footnote 45, p. 249, footnote 49),33 in which the author wrote: In Essais de métaphysique, ‘s Gravesande wrote: ‘Tout ce qui arrive en conséquence de la volonté de Dieu […], ou immédiatement, ou par une suite de causes & d’effets, que Dieu, par son intelligence infinie, a tous prévus, puisque l’enchainure en est nécessesaire […].’ (Allamand (ed.), 1774, II, p. 201). 31 ‘s Gravesande elaborated on mathematical versus moral certainty in the aforementioned Oratio inauguralis, de matheseos, in omnibus scientiis (1717) and Oratio de evidentia (1724). The latter was added to the third edition of Physices elementa (’s Gravesande, 1747, I, xxxvi-liii; ‘s Gravesande, 1742, I, xxxix-lxi). 32 See Part II of this article for further discussion of ‘s Gravesande’s Introductio ad philosophiam. 33 Prior to A Discourse, Humphry Ditton had already published a treatise on the laws of nature and a treatise on fluxions (Ditton, 1705 and 1706). In the preface of the former, Ditton fiercely opposed John Toland’s views on the essentiality of motion to matter. 30 Coroll. Therefore it may be as absurd, to deny some Propositions, which admit only of Moral Proof, as to deny others capable of strict Geometrical Demonstrations. For the Absurdity is heightned in proportion to the Evidence of the Proposition denied. So that if two Propositions of an equal Evidence, tho of different Nature, are propos’d; the Absurdities of denying them will be equal. And since some Moral Propositions may be equally evident with some Geometrical ones, ‘twill be as absurd to deny the former as the latter. Because I say, ‘tis the Evidence or Plainness of Propositions, and not the Subject Matter, which makes it absurd to deny them. (Ditton, 1712, pp. 153-154) ‘s Gravesande was probably the author of the review of A Discourse concerning the Resurrection of Jesus Christ which appeared in the journal which he co-founded, the Journal litéraire de la Haye (Allamand (ed.), 1774, I, pp. lvii-lviii; Gori, 1972, p. 218, footnote 35).34 Let us now focus on the difference between mathematical and moral certainty. A mathematician is not at all examining ‘whether or no the Ideas, about he reasons, agree with any thing being,’ rather he is concerned with the relations between ideas themselves (’s Gravesande, 1747, I, xxxix). The foundation of mathematical certainty is the perception of Ideas, which ‘brings its own Conviction with it [suâ naturâ assensum secum trahit]’ (‘s Gravesande, 1747, I, lxvi). Mathematical demonstrations depend on ‘the comparison of Ideas, and their Truth is evinced by implying a Contradiction in a contrary Proposition,’ ‘s Gravesande observed (‘s Gravesande, 1747, I, vi). True mathematical propositions are, in other words, true by necessity, for their negation leads to a contradiction. The necessity of mathematical truths corresponds to what ‘s Gravesande calls absolute necessity (necessitas absoluta) in his Introductio ad philosophiam, metaphysicam et logicam continens (1736), namely a truth of which the contrary is absolutely impossible (‘s Gravesande, 1736, § 48, p. 18). Mathematical truths do not depend on the constitution of the universe nor on the will of God (‘s Gravesande, 1717, p. 11). Mathematical certainty, is, however, not the privilege of mathematics alone (Brunet, 1926, p. 63). According to ‘s Gravesande, ‘the Part of Pneumatology [i.e. the study of intelligences] which treats of GOD,’ for instance, is ‘wholly conversant about Ideas, and deduc’d from such Notions, of which the Mind can in no wise doubt’ (‘s Gravesande, 1747, I, vi, xli). Metaphysics, logic and the foundational parts of ethics are further examples of disciplines which contain necessary truths. Physical truths, by contrast, do not partake in mathematical certainty, for ‘when the Question is about natural Things, the first Requisite is, that our Ideas agree with those Things, which cannot be proved by any mathematical Demonstration [ut cum rebus ideæ conveniant, quod nullâ mathematicâ demonstratio probari potest].’ When dealing with empirical matters, ‘a contrary Proposition is not always impossible [contraria propositio impossibilis non semper datur]’ (’s Gravesande, 1747, I, vi [italics added]; ‘s Gravesande, 1742, I, vii). Physical truths are thus contingently true.35 According to ‘s Gravesande, there is a clear-cut difference between mathematical and moral certainty: You see that moral Evidence, and the Persuasion thence arising, relates to the Agreement between the Ideas in our Mind, and the Things themselves external to us; whist mathematical Evidence is conversant about the Agreement which is between the Comparison of Ideas and the Idea of this Comparison. […] When we are conversant about Things external to us, we do not acquire an Idea of a thing by the Perception of it; Things themselves don’t act upon our Minds, we can’t conceive how they shou’d. Therefore we can’t deduce the Foundations of moral Evidence from a simple 34 The review, in which Ditton’s views on moral certainty are discussed on pp. 406-417, appeared in 1713 in the first volume (May-June) of the Journal litéraire (pp. 391-435). In A Discourse Ditton paid considerable attention to testimony, but none to analogy. On the Journal litéraire see Hemprich, 1915 and Bots and de Vet (eds.), 1986. 35 ‘s Gravesande defined contingent as that which can or cannot be: ‘Contingens dicitur, quod potest esse, aut non esse; id est, quod ex propriâ naturâ non determinatur.’ (‘s Gravesande, 1736, § 51, p. 18). Examination of the Mind, and of Things consider’d by themselves. We have Assistances external to the Things themselves, by which we acquire Ideas of Things themselves, by which we acquire Ideas of Things external to us. (’s Gravesande, 1747, I, xlvi; ‘s Gravesande, 1742, I, lii) While mathematical certainty depends, as we have seen, ‘on such an Evidence as brings along its own Conviction along with it,’ moral certainty depends on the external aids which God has given us: to wit, the senses, testimony, and analogy, which are the ‘fundaments’ of moral evidence. Reasoning by analogy refers to making inductive generalizations. Analogical arguments ‘are daily taken for granted as undoubtedly true, without any previous Examination; because every body sees that they cannot be called into question without destroying the present Oeconomy of Nature [sine præsentis rerum constitionis destructione]’ (’s Gravesande, 1747, I, vii; ‘s Gravesande, 1742, I, viii). Without the use of analogy human life would result in chaos. Imagine how society would look if we cannot be certain that the sun will rise tomorrow or that a ‘Building, this Day firm in all its Parts, will not of itself run to Ruin To-morrow’ (’s Gravesande, 1747, I, vii). However, ‘s Gravesande was not justifying analogy from its success in everyday contexts, for in his opinion the reliability of analogy results from God’s infinite goodness (s Gravesande, 1736, § 492, p. 148, cf. Ditton, 1712, p. 209). In this context he observes that it would be a contradiction to suppose ‘that God intended these [i.e. the senses, testimony and analogy] to be the Foundations of Persuasion, and that they shou’d not lead us to Truth, when we make use of them with due Care’ (’s Gravesande, 1747, I, lxvi-xlvii). The reliability of the senses, testimony and analogy follows with mathematical certainty from the infinite goodness of God: ‘If moral Evidence, which we have from God, was not firm, and sufficient to make us give our Assent to it, we cou’d, by a mathematical Demonstration, prove God not to be good.’ (‘s Gravesande, 1747, I, xlix; ‘s Gravesande, 1742, I, lvi). Furthermore, analogy is guaranteed by the fact that God governs the universe by invariable laws: Now there being numerous Cases of that kind, where one may affirm or deny with equal certainty; it follows that there are many Reasonings very certain, tho’ altogether different from the mathematical ones. And they evidently follow from the Establishment of Things, and therefore from the pre-determined Will of GOD. […] All these Reasonings are grounded upon Analogy; and there is no doubt that our Creator has, in many Cases, left us no other way of Reasoning, and therefore it is a right Way. But the Foundation of Analogy is this, That the Universe is govern’d by unchangeable Laws. (’s Gravesande, 1747, I, vi-vii; ‘s Gravesande, 1742, I, vii-viii, ix) Given these unchangeable laws, ‘Analogy stands upon a good Foundation, and being taken away, all Things in Physicks are uncertain, and the whole human Race wou’d soon be extinct.’ (’s Gravesande, 1747, I, xlviii). In other words, for ‘s Gravesande the methodological legitimacy of analogy was ultimately grounded in theological considerations: the reliability of analogy follows from God’s infinite goodness and from the unchangeable laws he has installed (Brunet, 1926, pp. 58-59; Sassen, 1959, pp. 225-226; Cassirer, 1965, p. 62; de Pater, 1994, p. 257; and, Gori, 1972, pp. 257-260, pp. 281-282). ‘s Gravesande warned that he did not claim ‘that the Senses never lead us into Error, that we are to give Credit to every Testimony, and that all kinds of Observations whatever give us room to reason analogically’ (’s Gravesande, 1747, I, li). He maintained, however, that errors could be avoided quite straightforwardly as they arise from ‘a defect of attention or from ignorance’ (‘s Gravesande, 1736, § 538, p. 163). 4. ‘s Gravesande’s Alleged Crypto-Spinozism In the previous section we have seen ‘s Gravesande saw empirico-mathematics as a powerful tool in the battle against Spinoza. In recent literature it has been claimed, however, that ‘s Gravesande was a crypto-Spinozist (Israel, 2006). In this section, I argue that such reading is questionable. In an anonymously published booklet, in which the author concluded that ‘il n’y a nulle différence entra la Fatalité Spinoziste ou Mahometane & la votre’ ([anon.], 1736, p. 20), ‘s Gravesande was accused of endorsing Spinoza’s (and Hobbes’) ideas on human liberty in his Introductio ad philosophiam (1736), which was published two years after ‘s Gravesande had become professor totius philosophiae at Leiden in 1734 (see Fig. 2) (Molhuysen, 1910-1924, V, p. 137).36 On the basis of this episode, Jonathan I. Israel has drawn attention to what he considers to be certain crypto-Spinozist strands in ‘s Gravesande’s thought (Israel, 2006, pp. 216-220). The anonymous author of Lettre à Monsieur G. J. S’Gravesande, whom possibly was Jean Fréderic Bernard (1683-1744),37 warned that ‘[l]a Doctrine de la Necessité daus [sic] le sens que Spinoza & Hobbes l’entendent, ou quelque autre necessité Physique que ce soit nommée proprement ainsi, ne peut que conduire les hommes au vice’ ([anon.], 1736, p. 7). Moreover, the author lamented: ‘c’est dommage qu’une Introduction à la Philosophie & des Institutions pour la jeunesse donnent occasion à la propagation des certaines Idées dangereuses dans le monde, sur tout d’une morale relâchée, qui n’est chez nous que trop dangereuse; & je crains bien que de tels principes n’y conduisent’ ([anon.], 1736, p. 69). Before attacking ‘s Gravesande’s views, the author cast doubt on ‘s Gravesande authority on metaphysical issues: ‘Il ne s’ensuit pas qu’un homme soit Maître parfait en Metaphysique, parce qu’il entend parfaitement la Philosophie Newtoniene; de même qu’on ne peut pas conclure que Ciceron étoit un grand Poëte parce qu’il a été le plus grand des Orateurs, ou que nôtre Stillingfleet à terrassé Locke pour l’avoir attaqué avec les mêmes armes par lesquelles il a vaincu les Catholiques Romains.’ ([anon.], 1736, pp. 5-6). In Lettre à Monsieur G. J. S’Gravesande, two main criticisms were raised against ‘s Gravesande’s treatment of human liberty. First of all, it was claimed that in ‘s Gravesande’s account physical and moral necessity boil down to one and the same thing.38 Secondly, it was argued that ‘s Gravesande’s account is incompatible with acts of volition properly conceived of: ‘Tout être intelligent est, comme vous l’avouez, déterminé à agir par la Volonté […]. La volonté est entierement reglée par une Nécessité aussi inévitable qu’une Balance est determinée à détruire son équilibre par les poids. Or les poids sont quelque chose d’exterieur qui est appliqué à la balance; & ce qui est determiné de dehors est necessaire […].’ ([anon.], 1736, p. 11, cf. p. 23, pp. 58-60).39 However, on a proper reading ‘s Gravesande explicitly distanced himself from Spinoza’s (and Hobbes’) ideas on liberty and ‘s Gravesande’s distinction between physical and moral necessity did not collapse. In order to illustrate this distinction he introduced the following example (‘s Gravesande, 1736, § 134, pp. 47-48). Suppose that a man is locked in a room without exit and that he wants to leave the room. In this case, that what hinders the man from leaving the room is a physical constraint: it is physically necessary for the man to stay in the room. Now suppose that the same man is in a 36 See Israel, 2006, pp. 219-220 for an earlier treatment, which does not quote from this source. On Bernard, see Hunt, Jacob and Mijnhardt, 2010, Chapter 4. 38 Cf.: ‘Il me semble, Monsieur, que vôtre distinction entre Necessité Physique & Necessité Morale […] n’est qu’une distinction faite à plaisir qui consiste seulement en paroles, n’y ayant au fond aucune difference réelle […].’ ([anon.], 1736, pp. 7-8). 39 In footnote † on [anon.], 1736, pp. 41-42, the author underscored: ‘Une balance n’est pas un agent: elle est tout-à-fait passive, & les poids sont égaux, il n’y a rien qui la puisse mouvoir: mais les êtres intelligens sont des agents; […].’ The author was referring to ‘s Gravesande, 1736, § 139, p. 50. Properly contextualized, ‘s Gravesande introduced the balance analogy to make the point that real human decisions are not mechanically or physically determined (‘s Gravesande, 1736, § 141, p. 50). 37 room with a window, but that the height from the bottom of the room to the ground floor is such that, when jumping through the window, a certain death would follow. In this case, that what hinders the man from leaving the room is a moral constraint: it is morally necessary for this man, who is of good sense (‘sanâ Mente præditus’), not to jump out the window.40 In the first case, the necessity which makes the man stay in the room is absolute: it is absolutely impossible for the man to leave the room. In the second case, the necessity which makes the man stay in the room is not absolute: although the man is bound by his good sense not to jump out of the window, it is not physically impossible for him to decide otherwise. ‘s Gravesande, in other words, had the conceptual resources to show that physical and moral necessity are distinct: moral necessity is not ‘absolute or fatal’ and as such is distinct from physical necessity (‘s Gravesande, 1736, § 167, p. 59). In the chapter ‘De fato’ in Introductio ad philosophiam, ‘s Gravesande argued that humans are free because they have the capacity to act on reasons and rational deliberation. 41 That ‘s Gravesande maintained that ‘every human volition is mechanically determined,’ as Jonathan I. Israel states (Israel, 2006, p. 218 [italics added]), is quite incorrect. Although ‘s Gravesande claimed that, when our physical constitution is out of order, mechanical causes determine our decisions, he stated that, when our physical constitution is fine, we act upon reasons (‘s Gravesande, 1736, § 155, p. 55). Those who admit of fatality are simply blind to the fact that we act on our ideas, he urged. 42 At this point, ‘s Gravesande pointed out that Spinoza admitted of fatality and as an illustration he quoted from what is now known as Spinoza’s famous Letter 58, in which Spinoza argued that freedom is illusory (‘s Gravesande, 1736, § 145, pp. 51-52). After quoting from the letter, ‘s Gravesande reiterated his conclusion: our actions are determined by reasons and not by mechanical causes (s Gravesande, 1736, § 147, p. 53). In Spinoza’s work, fatality not only applies to the way in which nature works, but also to how it was created. In Proposition 33 of his Ethica, Spinoza indeed stated that ‘[t]hings could have been produced by God in no other way, and in no other order than they have been produced’ (Curley, 1985, p. 436). 43 In explicit opposition to this opinion, Samuel Clarke (1675-1729) argued in his A Demonstration of the Being and Attributes of God, a work which ‘s Gravesande owned ([anon.], 1736, p. 52 [item n° 117]), that God ‘is not a necessary Agent, but a Being indued with Liberty and Choice’ (Clarke, 1705, p. 131). Moreover, according to Clarke, ‘’Tis evident He must of Necessity (meaning, not a Necessity of Fate, but such a Moral Necessity as I before said was consistent with the most perfect Liberty,) Do always what he Knows to be Fittest to be Done: that is, He must Act always according to the strictest Rules of Infinite Goodness, Justice and Truth, and all other Moral Perfections.’ (Clarke, 1705, pp. 236-237). The position which ‘s Gravesande developed in his (unpublished) Essais de métaphysique, which was intended for ‘un petit nombre de personnes,’ is similar to Clarke’s. ‘s Gravesande emphasized that: ‘Rien ne sauroit règler la puissance de Dieu que sa volonté; il peut donc tout ce qu’il veut, & par là même qu’il le veut, il le fait; rien ne pouvant In 1707 ‘s Gravesande obtained his doctoral degree in law with a twelve pages long dissertation on, or better against, suicide: Dissertatio juridica inauguralis de Autocheira (Lugduni Batavorum, Apud Abrahamum Elzevier). 41 Cf.: ‘Quamdiu, quæ nos ad agendum movent, in ipsam Intelligentiam, quà Intelligentiam, agunt; ita ut tantum agamus, quia volumus, & determinatio voluntatis persuasionem, ex judico, aut ratiocinio, deductam, pro fundamento habeat, nulla Mechanica, aut Physica, Necessitas concipi potest, & non Fato regimur .’ (‘s Gravesande, 1736, § 141, p. 50 [italics added]). 42 Cf. ‘Qui Fatum admittunt, non ideis nostris, in quibus solis persuasio quærenda est, actiones nostras tribuunt, sed Causæ Mechanicæ, quæ eadem Causa etiam nostræ voluntatis determinationem secum trahit; ita ut non agamus, quia volumus; sed velimus, quia agimus: hæcque est distinctio inter Libertatem & Fatum.’ (‘s Gravesande, 1736, § 142, pp. 50-51). 43 Spinoza’s Ethica was published in Opera posthuma (1677), which ‘s Gravesande owned ([anon.], 1742, p. 101 [item n° 2 in the list ‘libri prohibiti in quarto’]). 40 l’empêcher, puisque c’est une suite de son existence par lui meme.’ (Allamand (ed.), 1774, II, p. 197). He stated, furthermore, that it is by no means physically necessary that God created the world in the way it is, but that God is nevertheless bound by moral necessity to create the world in a way that is consistent with his attributes: ‘Pour ce qui regarde le Pouvoir physique, Dieu peut tout ce qui n’est pas contradictoire en soi […]. Mais si nous faisons attention ou Pouvoir moral, il est clair qu’il est contradictoire que Dieu fasse autre chose que ce qu’il veut; il ne peut donc que ce qu’il veut. Mais il est contradictoire qu’il ne veuille pas ce qui est conforme à ses attributs, ou qu’il veuille autre chose; il est donc contradictoire que Dieu eusse une autre volonté que celle qu’il a, & par conséquent il est de même contradictoire qu’il fasse autre chose que ce qui’l fait, & dans le sens moral Dieu ne peut que ce qu’il fait.’ (Allamand (ed.), 1774, II, p. 208). 44 Spinoza’s views on human and divine liberty were incompatible with ‘s Gravesande’s. 5. Conclusion In this essay we have seen ‘s Gravesande was selective in his endorsement of Newton’s epistemology. Although he accepted certain aspects of it, his a-causal rendering of physics went against Newton’s views of the matter. Moreover, ‘s Gravesande’s expurgation of potentially controversial issues associated with Newton’s natural philosophy lead to the dismissal of certain topics (e.g. the status of causation, the cause of gravity, the so-called ‘active principles’, God’s relation to the physical world, etc.) which Newton himself considered as meaningful. We have also seen that ‘s Gravesande considered Newton’s empirico-mathematical approach towards nature as a powerful tool in the battle against Spinoza’s a priori manner of philosophizing which in his view lead to theological aberrations. His attempt to provide a solid foundation for the new Newtonian science, which was to a certain degree inspired by Nieuwentijt and Ditton, also resonates well with the anti-Spinozist strands in his thinking. As we have seen above, ‘s Gravesande criticized those who accept that ‘nothing is to be taken for Truth but what is prov’d by mathematical Demonstration.’ In arguing that empirically based conclusions can have a solid foundation, he attempted to show that certainty is not a prerogative of mathematics alone and that, ‘when due Care is taken,’ physics leads to certain knowledge. Acknowledgement I am indebted to Eric Schliesser, Paul Schuurman, Charles T. Wolfe, Gerhard Wiesenfeldt, and the two anonymous referees for useful comments on earlier draft versions of this paper, which resulted in several improvements. Parts of the present paper were presented at the international conference ‘The Reception of Newton’ (The Edward Worth Library, Dublin, 1213 July 2012) and at the 24th International Congress of History of Science, Technology and Medicine (The University of Manchester, 21-28 July 2013). I also wish to thank Wiep van Bunge for sharing his paper ‘Dutch Cartesian Empiricism and the Advent of Newtonianism’ before publication and the staff of the Special Collections at the Leiden University Library for their kind assistance during his consultation of the material in their care. My research is funded by the Free University of Brussels (Vrije Universiteit Brussel) in the form of a Research Professorship. In her recent mitigation of Boerhaave’s alleged Spinozism, Knoeff underscored a similar point: ‘according to Boerhaave the inherent necessity of nature would not restrict the omnipotence of God’ (Knoeff, 2002, p. 48). For a crypto-Spinozistic reading of Boerhaave, see Klever, 1988. 44 REFERENCES [anon.] (1736) Lettre à monsieur G. J. S’Gravesande, Professeur en Philosophie à Leide, Sur son Introduction à la Philosophie, & particulierement sur la nature de la liberté (Amsterdam: Chez J. F. Bernard). [anon.] (1742) Bibliotheca ‘sGravesandiana, sive catalogus librorum bibliothecæ selectissimæ viri clarissimi D. Gul. Jac. ‘s Gravesande (Lugduni Batavorum: Apud Joh. & Herm. Verbeek). Adam, C. and Tannery, P. (eds.) (1897-1913) Œuvres de Descartes (11 vols.) (Paris: Léopold Cerf). Allamand, J. N. S. (ed.) (1774[1744]) Oeuvres philosophiques et mathématiques de Mr . G. J. ‘s Gravesande (2 vols.) (Amsterdam: Marc Michel Rey). Bierens, D. de Haan, Bosscha, J., Korteweg, D. J., and Vollgraff, J. A. (eds.) (1888–1950) Oeuvres complètes de Christiaan Huygens (23 vols.) (The Hague: Martinus Nijhoff). Boerhaave, H. (1715) Sermo academicus, de comparando certo in physicis (Lugduni Batavorum: Apud Petrum vander Aa). Bos, H. (1980) Mathematics and rational mechanics, in: G. S. Rousseau and R. Porter (eds.), The ferment of knowledge: Studies in the historiography of eighteenth-century science (Cambridge: Cambridge University Press), pp. 327-355. Bots, J. (1972) Tussen Descartes en Darwin: Geloof en natuurwetenschap in de zeventiende en achttiende eeuw (Assen, Van Gorcum). Bots, J. A. H. and de Vet, J. J. V. M. (1986), Special issue on the Journal litéraire, Documentatieblad werkgroep achttiende eeuw, 18(2). Boudri, J. C. (2002) What was mechanical about mechanics? The concept of force between metaphysics and mechanics from Newton to Lagrange, Series: Boston Studies in the Philosophy of Science vol. 224 (Dordrecht: Kluwer). Brunet, P. (1926) Les physiciens Hollandais et la méthode expérimentale en France au XVIII e siècle (Paris: Albert Blanchard). Brunet, P. (1931) L’introduction des théories de Newton en France au XIIIe siècle (Paris: Albert Blanchard). Burtt, E. A. (1924) Metaphysical foundations of modern physical science: A historical and critical essay (London: Kegan Paul, Trench, Trübner & Co., Ltd.). Cantor, M. (1880-1908) Vorlesungen über Geschichte der Mathematik (4 vols.) (Leipzig: B. G. Teubner). Cassirer, E. (1965) The philosophy of the Enlightenment, transl. by Fritz C. A. Koelln and James P. Pettegrove (Boston: Beacon Press). Clarke, S. (1705) A demonstration of the being and attributes of God: More particularly in answer to Mr. Hobbs, Spinoza, and their followers. Wherein the notion of liberty is stated, and the possibility and certainty of it proved, in opposition to necessity and fate (London: W. Botham, for J. Knapton). Clarke, S. (1727) A Letter from the Rev. Dr. Samuel Clarke to Mr. Benjamin Hoadly, F. R. S. Occasion’d by the Present Controversy among Mathematicians, concerning the Proportion of Velocity and Force in Bodies in Motion, Philosophical Transactions of the Royal Society of London, 35, pp. 381-388. Cohen, I. B. (1956) Franklin and Newton: An inquiry into speculative Newtonian experimental science and Franklin’s work in electricity as an example thereof (Philadelphia: American Philosophical Society). Cohen, I. B. (ed.) (1978 [1958]) Isaac Newton’s papers and letters on natural philosophy and related documents (Cambridge (Mass.): Harvard University Press). Cook, H. J. (2007) Matters of Exchange: Commerce, Medicine, and Science in the Dutch Golden Age (New Haven and London: Yale University Press). Costabel, P. (1964) ‘s Gravesande et les forces vives ou des vicissitudes d’une expérience soi-disant cruciale, in: I. B. Cohen and R. Taton (eds.), Mélanges Alexandre Koyré, Volume I: L’aventure de la science (Paris: Hermann), pp. 117-134. Curley, E. M. (1985) The collected writings of Spinoza, Volume I (Princeton: Princeton University Press). de Hoog, A. C. (1974) Some Currents of Thought in Dutch Natural Philosophy, 1675-1720 (Ph.D. dissertation, University of Oxford). de Pater, C. (1975) Experimental Physics, in: Th. H. Lunsingh Scheurleer and G. H. M. Postumus Meyjes (eds.), Leiden University in the Seventeenth Century, An Exchange of Learning (Leiden, Universitaire Pers Leiden/E. J. Brill), pp. 308-327. de Pater, C. (1988) Willem Jacob ‘s Gravesande, Welzijn, wijsbegeerte en wetenschap (Baarn, Ambo). de Pater, C. (1989) The textbooks of ‘s Gravesande and Van Musschenbroek in Italy, in: C. S. Maffioli and L. C. Palm (eds.), Italian Scientists in the Low Countries in the 17 th and 18th Centuries (Amsterdam: Rodopi), pp. 231-241. de Pater, C. (1994) Willem Jacob ’s Gravesande (1688-1742) and Newton’s regulae philosophandi, 1742, Lias, 21(2), pp. 257-294. C. de Pater (1995) ’s Gravsande on Moral Evidence, in: M. F. Fresco, L. Geeraedts, and K. Hammacher (eds.), Frans Hemsterhuis (1721-1790), Quellen, Philosophie und Rezeption (Münster/Hamburg: Lit), pp. 221242. Desaguliers, J. T. (1763 [1734-1744]) A course of experimental philosophy (3rd edition) (London: A. Millar e.a.). Ditton, H. (1705) The general laws of nature and motion; with their application to mechanics (London: Printed by T. Mead for Fer. Seller and Cha. Price and John Senex). Ditton, H. (1706) An institution of fluxions: Containing the first principles, the operations, with some of the uses and applications of that admirable method (London: Printed by W. Botham for James Knapton). Ditton, H. (1712) A discourse concerning the resurrection of Jesus Christ (London: Printed by J. Darby). Dobbs, B. J. T. and Jacob, M. C. (1995) Newton and the culture of Newtonianism (Atlantic Highlands (N.J.): Humanities Press). Ducheyne, S. (2007) ‘Ignorance is Bliss’: On Bernard Nieuwentijt’s doctrina ignorantia and his contribution to our understanding of scientific idealisation’, Rivista di storia della filosofia, 62(4), pp. 699-710. Ducheyne, S. (2012) ‘The main Business of Natural Philosophy:’ Isaac Newton’s natural-philosophical methodology, Series: Archimedes, New studies in the history and philosophy of science and technology, vol. 29 (Dordrecht: Springer). Ducheyne, S. (in press) Newton on Action at a Distance, Journal of the history of philosophy. Feingold, M. (2004) The Newtonian moment: Isaac Newton and the making of modern culture (New York/Oxford: The New York Public Library/Oxford University Press). Force, J. E. and Hutton, S. (eds.) (2004) Newton and Newtonianism: New Studies, Series: International Archives of the History of Ideas, vol. 188 (Dordrecht: Springer). Gori, G. (1972) La fondazione dell’esperienza in ‘sGravesande (Firenze: La Nuova Italia). ‘s Gravesande, W. J. (1711) Essai de perspective (The Hague: Chez la Veuve d’Abraham Troyel). ‘s Gravesande, W. J. (1717) Oratio inauguralis, de matheseos, in omnibus scientiis, præcipue in physicis, usu, nec non de astronomiæ perfectione ex physica haurienda (Lugduni Batavorum, Apud Samuelem Luchtmans). ‘s Gravesande, W. J. (1736) Introductio ad philosophiam: metaphysicam et logicam continens (Leidiae: Apud Joh. et Herm. Verbeek). ’s Gravesande, W. J. (1742 [1720-1721]) Physices elementa mathematica experimentis confirmata, sive introductio ad philosophiam Newtoniam (2 vol.; 3rd edition) (Leidae: Apud Johannem Arnoldum Langerak, Johannem et Hermannum Verbeek). ’s Gravesande, W. J. (1747 [1720-1721]) Mathematical elements of natural philosophy, Confirm’d by experiments: or, an introduction to Sir Isaac Newton’s philosophy, transl. by J. T. Desaguliers (2 vol.; 6 th edition) (London: Printed for T. Longman e.a.). Greenberg, J. L. (1995) The problem of the shape of the earth from Newton to Clairaut: The rise of mathematical science in eighteenth-century Paris and the fall of ‘normal’ science (Cambridge: Cambridge University Press). Hakfoort, C. (1995) Optics in the age of Euler: Conceptions of the nature of light, 1700-1795 (Cambridge: Cambridge University Press). Hall, A. R. (1972) ‘s Gravesande, Willem Jacob, in: Charles C. Gillispie (ed.) (1970-1980), Dictionary of scientific biography (16 vol.) (New York: Charles Scribner’s Sons), V, pp. 509-511. Hall, A.R. (1954) The Scientific Revolution, 1500-1800 (London: Longman). Hankins, T. L. (1965) Eighteenth-century attempts to revolve the vis viva controversy, Isis, 56(3), pp. 281-297. Heilbron, J. L. (1980) Experimental natural philosophy, in: G. S. Rousseau and R. Porter (eds.), The ferment of knowledge: Studies in the historiography of eighteenth-century science (Cambridge: Cambridge University Press), pp. 357-387. Heilbron, J. L. (1982) Elements of early modern physics (Berkeley: University of California Press). Hemprich, P. (1915) Le Journal litéraire de la Haye 1713-1737 (Berlin: Herrmann). Home, R. W. (1979) Out of the Newtonian straightjacket: Alternative approaches to eighteenth-century physical science, in: R. F. Brissenden and J. C. Eade (eds.), Studies in the Eighteenth Century, Vol. 4: Papers presented at the Fourth David Nichol Smith Memorial Seminar, Canberra, 1976 (Canberra: Australian National University Press), pp. 235-249. Home, R. W. (2003) Mechanics and experimental physics, in: R. Porter (ed.), The Cambridge History of Science, Volume 4: Eighteenth-century science (Cambridge: Cambridge University Press), pp. 354-374. Hunt, L. Jacob, M. C. and Mijnhardt, W. W. (2010) The book that changed Europe: Picart & Bernard’s religious ceremonies of the world (Cambridge (Mass.): Belknap Press of Harvard University Press). Hunter, M. and Davies, E. B. (eds.) (1999-2000) The works of Robert Boyle (14 vols.) (London: Pickering and Chatto). Iltis, C. (1967) The controversy over living forces: Leibniz to D’Alembert. Unpublished PhD dissertation, University of Wisconsin. Israel, J. I. (1995) The Dutch Republic: Its rise, greatness, and fall (Oxford: Clarendon Press). Israel, J. I. (2006) Enlightenment contested: Philosophy, modernity, and the emancipation of man 1670-1752 (Oxford: Oxford University Press), pp. 216-217. Jacob, M. C. and Mijnhardt, W. W. (eds.) (1992) The Dutch Republic in the eighteenth century: Decline, Enlightenment and revolution (Ithaca: Cornell University Press). Jacob, M. C. and Stewart, L. (2006) Practical matter: Newton’s science in the service of industry and empire, 1687-1851 (Cambridge (Mass.): Harvard University Press). Jorink, E. (2009) Honouring Sir Isaac, or, exorcizing the ghost of Spinoza: Some remarks on the success of Newton in the Dutch Republic, in: S. Ducheyne (ed.), Future perspectives on Newton scholarship and the Newtonian legacy in eighteenth-century science and philosophy (Brussel: Koninklijke Vlaamse Academie van België voor Wetenschappen en Kunsten), pp. 23-43. Jorink, E. (2010) Reading the book of nature in the Dutch Golden Age, 1575-1715, transl. by P. Mason, Series: Brill’s Studies in Intellectual History, vol. 191 (Leiden: Brill). Jorink, E., and A. Maas (eds.) (2012), Newton and the Netherland, How Isaac Newton was Fashioned in the Dutch Republic (Leiden: Leiden University Press). Keill, J. (1702) Introductio ad veram physicam (Oxoniæ: E Theatro Sheldoniano, Impensis Thomæ Bennet). Keill, J. (1718) Introductio ad veram astronomiam, seu lectiones astronomicæ (Oxoniæ: E Theatro Sheldoniano, Impensis Hen. Clements). Klever, W. N. A. (1988) Burchard de Volder (1643-1709), A crypto-Spinozist on a Leiden cathedra, Lias, 15(2), pp. 191-241. Knoeff, R. (2002) Herman Boerhaave (1668–1738): Calvinist chemist and physician, Series: History of Science and Scholarship in the Netherlands, vol. 3 (Amsterdam, Koninklijke Nederlandse Akademie van Wetenschappen). Koser, R. and Droysen, H. (eds.) (1908-1909) Briefwechsel Friederichs des Grossen mit Voltaire (2 vols.) (Leipzig: S. Hirzel). Lindeboom, G. A. (2007) Herman Boerhaave. The man and his work (Rotterdam: Erasmus Publishing). Locke, J. (1700) Essai philosophique concernant l’entendement humain, transl. by Pierre Coste (Amsterdam: Henri Schelte). Locke, J. (1714) The works of John Locke Esq. (3 vols.) (London: Printed for John Churchill and Sam. Manship). Locke, J. (1975 [1690]) An essay concerning human understanding, edited by Peter H. Nidditch (Oxford: Clarendon Press). Maas, A. (2012) The Man who erased himself, Willem ‘s Gravesande and the Enlightenment, in Jorink and Maas (eds.), 2012, pp. 113-137. Mandelbrote, S. (ed.) (2004) Newton and Newtonianism, Special issue of Studies in History and Philosophy of Science, vol. 35(3). Mandelbrote, S. and Pulte, H. (eds.) (forthcoming) The Reception of Newton in Europe (London, Continuum). Metzger, H. (1930) Newton, Stahl, Boerhaave et la doctrine chimique (Paris: Albert Blanchard). Molhuysen, P. C. (1910-1924) Bronnen tot de geschiedenis der Leidsche Universiteit, 1574-1811 (7 vols.) (’sGravenhage, Martinus Nijhoff). Newton, I. (1952 [1704]) Opticks, or a treatise of reflections, refractions, inflections and colours of light (New York, Dover). Newton, I. (1999) The Principia, Mathematical principles of natural philosophy, A new translation by I. Bernard Cohen and Anne Whitman, assisted by Julia Budenz, Preceded by a guide to Newton’s Principia by I. Bernard Cohen (Berkeley: University of California Press). Nieuwentijt, B. (1720a [1715]) Het regt gebruik der werelt beschouwingen ter overtuiginge van ongodisten en ongelovigen (3rd edition) (Amsterdam: Joannes Pauli). Nieuwentijt, B. (1720b) Gronden van zekerheid, Of de regte betoogwyse der wiskundigen (Amsterdam: Joannes Pauli). Porter, Roy (2003) Introduction, in: R. Porter (ed.), The Cambridge History of Science, Volume 4: Eighteenthcentury Science (Cambridge: Cambridge University Press), pp. 1-20 Roberts, L. (1999) Going Dutch: Situating science in the Dutch Enlightenment, in: W. Clark, J. Golinsky, and S. Schaffer (eds.), The sciences in Enlightened Europe (Chicago: Chicago University Press), pp. 350-388. Ruestow, E. G. (1973) Physics at seventeenth and eighteenth-century Leiden: Philosophy and the new science in the university, Series: International archives of the history of ideas, vol. 11 (The Hague: Martinus Nijhoff). Sassen, F. (1959) Geschiedenis van de wijsbegeerte in Nederland tot het einde der negentiende eeuw (Amsterdam: Elsevier). Schaffer, S. (1995) The show that never ends: Perpetual motion in the early eighteenth century, The British journal for the history of science, 28(2), pp. 157-189. Schliesser, E. (2011) Newton’s challenge to philosophy: A programmatic essay, HOPOS: The journal of the international society for the history of philosophy of science, 1(1), pp. 101-128. Schofield, R. E. (1970) Mechanism and materialism: British natural philosophy in the Age of Reason (Princeton: Princeton University Press). Schofield, R.E. (1978) An evolutionary taxonomy of eighteenth-century Newtonianisms’, Studies in eighteenthcentury culture, 7, pp. 175-192. Schuurman, P. (2004) Ideas, mental faculties and method, The logic of ideas of Descartes and Locke and its reception in the Dutch Republic, 1630-1750 (Leiden: Brill). Schuurman, P. (2010) ‘Thou knowest not the works of God’: Gisbertus Voetius (1589-1676) and John Locke on learned ignorance’, Westminster theological journal, 72(1), pp. 59-69. Shank, J. B. (2008) The Newton wars and the beginning of the French Enlightenment (Chicago: The University of Chicago Press). Shapiro, B. J. (1983) Probability and certainty in seventeenth-century England (Princeton: Princeton University Press). Stewart, L. (1992) The rise of public science: Rhetoric, technology, and natural philosophy in Newtonian Britain, 1660–1750 (Cambridge: Cambridge University Press). Thackray, A. (1970) Atoms and Powers: An Essay on Newtonian Matter-theory and the Development of Chemistry (Cambridge (Mass.): Harvard University Press). van Berkel, K. (1999) Academics and Aristocrats, 1620-1700, in: K. van Berkel, A. van Helden and L. Palm (eds.), A History of Science in the Netherlands, Survey, Themes and Reference (Leiden: Brill), pp. 37-67 van Bunge, W. (unpublished manuscript) Dutch Cartesian empiricism and the advent of Newtonianism. van der Wall, E. G. E. (2004) Newtonianism and Religion in the Netherlands, Studies in History and Philosophy of Science, 35(3), pp. 493-514. Van Leeuwen, H. G. (1963) The problem of certainty in English thought 1630–1690 (The Hague: Martinus Nijhoff) Vermij, R. H. (1991) Secularisering en natuurwetenschap in de zeventiende en achttiende eeuw: Bernard Nieuwentijt, Series: Nieuwe Nederlandse bijdragen tot de geschiedenis der geneeskunde en der natuurwetenschappen, vol. 38 (Amsterdam-Atlanta: Rodopi). Vermij, R. H. (2003) The formation of the Newtonian philosophy: The case of the Amsterdam mathematical amateurs, The British journal for the history of science, 36(2), pp. 183-200. Wiesenfeldt, G. (2002) Leerer Raum in Minervas Haus: Experimentelle Naturlehre and der Universitët Leiden, 1675-1715, Series: History of science and scholarship in the Netherlands, vol. 2 (Amsterdam/Berlin and Diepholz: Koninklijke Nederlandse Akademie van Wetenschappen/Verlag für Geschichte der Naturwissenschaften und der Technik). Wigelsworth, J. R. (2003) Competing to popularize Newtonian philosophy, John Theophilus Desaguliers and the preservation of reputation, Isis, 94(3), pp. 435-455. Wilson, C. (2003) Astronomy and cosmology, in: R. Porter (ed.), The Cambridge History of Science, Volume 4: Eighteenth-century science (Cambridge: Cambridge University Press). Fig. 1. Jacob Houbraken’s (1968-1780) portrait of W. J. ‘s Gravesande at the time at which the latter was professor of mathematics and astronomy at the University of Leiden. Source: Leiden University Library, Digital Special Collections. Fig. 2. Anonymous portrait of W. J. ‘s Gravesande at the time at which he was professor professor totius philosophiae at the University of Leiden. Source: Leiden University Library, Digital Special Collections.

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