‘F = MA’ and the Newtonian Revolution: An Exit from Religion Through Religion

Newton Isaac , Philosophiae naturalis principia mathematica (London, 1687). The third edition (London, 1726) is reproduced with comments in Isaac Newton's Principia, ed. by Koyré A. Cohen I. B. (2 vols, Cambridge, 1972). Page numbers given here refer to the third edition. Motte's translation has generally been used, with slight modifications when needed.

Einstein Albert , Mein Weltbild (Amsterdam, 1934), 210.

For a good example of this, see Feynman Richard P. , Lectures on physics (3 vols, Reading, Mass., 1965). See also Eisenbud Leonard , “On the classical laws of motion”, American journal of physics, xxvi (1957), 144–9; Weinstock R. , “The laws of classical motion: What's F? what's m? what's a?”, American journal of physics, xxix (1961), 698–702; Arnol'd V. I. , Huygens & Barrow, Newton & Hooke (Basel, 1990); Chandrasekhar S. , “Confronting the final limit”, Scientific American, cclxx (1994), 16–17.

On the traditional historiography of Newton's law, see Maltese G. , La Storia di «F=ma» (Florence, 1992).

For the starting point of this re-examination, see Dijksterhuis J. , De Mechanisering van het Wereldbeeld (Amsterdam, 1950); German transl., Die Mechanisierung des Weltbildes (Berlin, 1956), 298ff; English transl., The mechanization of the world picture (Oxford, 1961). See also Ellis Brian D. , “Newton's concept of motive force”, Journal of the history of ideas, xxiii (1962), 273–8.

Truesdell C. , “A program toward rediscovering the rational mechanics in the Age of Reason”, Archive for history of exact sciences, i (1960), 3–36; Hankins Thomas L. , “The reception of Newton's second law of motion in the eighteenth century”, Archives internationales d'histoire des sciences, xx (1967), 43–65; Truesdell C. , “Reaction of the Late Baroque Mechanics to success, conjecture and failure in Newton's Principia“, in Essays in the history of mechanics (Berlin, 1968), 138–83; Meli D. Bertoloni , Equivalence and priority: Newton versus Leibniz (Oxford, 1993).

The correspondence of Isaac Newton, ed. by Turnbull H. R. Scott J. F. Hall A. R. Tilling L. (7 vols, Cambridge, 1967–91), iv, 391.

“Mutationem motus proportionalem esse vi motici impressae, et fieri secundum lineam rectam qua vis illa imprimitur”, Principia (ref. 1), 13. From this text as from others, it is seen that the use of vectorial notation to re-express Newton's geometrical formulations is justified.

See for instance Buchdahl Gerd , “Science and logic: Some thoughts on Newton's second law of motion in classical mechanics”, The British journal for the history of science, ii (1952), 217–52; Jammer Max , Concepts of force (Cambridge, 1961), 124.

See ref. 5.

See Perl Margula R. , “Newton's justification of the Laws of Motion”, Journal of the history of ideas, xxvii (1966), 585–92; Gabbey Alan , “The case of mechanics: One revolution or many?”, in Reappraisals of the Scientific Revolution, ed. by Lindberg D. C. Westmann R. S. (Cambridge, 1990), 493–526; Nicholas J. M. , “Newton's extremal Second Law”, Centaurus, xxii (1978), 108–30.

In addition to the above quoted references (ref. 5), see Cohen I. Bernard , “Newton's Second Law and the concept of force in the Principia”, The Texas quarterly, x (1967), 127–57; idem, Introduction to Newton's ‘Principia’ (Cambridge, 1971); idem, The Newtonian Revolution (Cambridge, 1980), 172; Westfall Richard S. , Force in Newton's physics (London, 1971), 471; Barthélemy Georges , “De la force accélératrice dans les Principia”, Revue d'histoire des sciences, xl (1987), 273–80; Maltese , La storia (ref. 4), 22; Blay Michel , Les Raisons de l'infini (Paris, 1993), 79; Pierson Stuart , “Corpore cadente…: Historians discuss Newton's Second Law”, Perspectives on science, i (1993), 627–58.

See The mathematical papers of Isaac Newton , ed. by Whiteside D. T. (8 vols, Cambridge, 1967–81), vi, 539; Westfall Richard S. , Never at rest: The biography of Isaac Newton (Cambridge, 1985), 408–35; Nauenberg Michael , “Newton's early computational method for dynamics”, Archive for history of exact sciences, xlvi (1994), 221–52. Yet drafts are drafts, however interesting they may be from an historical point of view.

Dolby R. G. A. , “A note on Dijksterhuis' criticism”, Isis, lvii (1966), 108–15.

Maxwell James Clerk , Matter and motion (London, 1877).

Not checking systematically the Motte-Cajori translation with respect to Newton's Latin original, Dolby was misled in commenting a well-known quotation of the scholium of the laws (“corpore cadente …”, Principia (ref. 1), 21). As pointed out by Cohen I. B. , “Newton's use of ‘force’, or Cajori versus Newton: A note on translations of the ‘Principia’”, Isis, lviii (1967), 226–30, this entailed an error concerning a minor point of the whole case (which becomes even stronger when the original text is used, as will be seen below).

I refer here to the difference between the vis inertiae and the vis impressa inside the Newtonian framework; and to the contrast between Newton's various forces and Leibniz's vis viva: See The Leibniz-Clarke correspondence , ed. by Alexander H. (Manchester, 1956), 121–5; and Laudan L. , “The vis viva controversy: A post-mortem”, Isis, lix (1968), 131–43. I shall assume, here and below, that Newton had an active share role in that controversy: See Koyré Alexandre Cohen I. Bernard , “Newton & the Leibniz-Clarke correspondence”, Archives internationales d'histoire des sciences, xv (1968), 63–126.

I must admit that I was convinced beforehand, having developed the approach presented below before reading Dolby's paper and, when finishing the present paper, Maxwell's considerations on the impressed force signalled by Cohen I. Bernard , “The review of the first edition of Newton's Principia in the Acta eruditorum”, in The investigation of difficult things , ed. by Harman P. M. Shapiro A. E. (Cambridge, 1992), 323–53.

Bechler Zev , “The essence and soul of seventeenth-century scientific revolution”, Science in context, i (1987), 87–101, reassessing the scientific revolution. Gabbey Alan , “Force and inertia in seventeenth-century dynamics”, Studies in history and philosophy of science, ii (1971), 1–67, chopping it up. Jardine Nicholas , “Writing off the scientific revolution”, Journal of the history of astronomy, xxii (1991), 311–18, and Cunningham Andrew , “How the Principia got its name; or, taking natural philosophy seriously”, History of science, xxix (1991), 377–92, writing it off.

For the religious context surrounding the Principia, see Hoskin M. A. , “Newton, providence and the universe”, Journal for the history of astronomy, viii (1977), 77–101; Jacob Margaret J. Jacob James R. , “The Anglican origins of modern science”, Isis, lxxi (1980), 251–67; Funkenstein Amos , Theology and the scientific imagination (Princeton, 1986), 89–91; Deason G. B. , “Reformation theology and the mechanistic conception of nature”, in: God and nature , ed. by Lindberg D. C. Numbers R. L. (Berkeley, 1986), 167–91; Schaffer Simon , “Godly men and mechanical philosophers: Souls and spirits in restoration natural philosophy”, Science in context, i (1987), 58–85; Force James E. Popkin Richard H. , Essays on the context, nature and influence of Isaac Newton's theology (Dordrecht, 1990); Dobbs Betty J. T. , The Janus faces of genius (Cambridge, 1991); Cunningham , “How the Principia got its name” (ref. 19); Verlet Loup , La Malle de Newton (Paris, 1993); Baillon Jean-Francois , “Newtonianisme et idéologie dans l'Angleterre des lumières”, Thesis, Université de Paris IV-Sorbonne, 1995. On the politico-religious consequences of the Principia, see Jacob Margaret C. , The Newtonians and the English Revolution 1689–1720 (Ithaca, 1976); Shapin Steven , “Of gods and kings: Natural philosophy and politics in Leibniz-Clarke disputes”, Isis, lxxii (1981), 187–215; Gascoigne John , “From Bentley to the Victorians: The rise and fall of British Newtonian natural theology”, Science in context, ii (1988), 219–56; Baillon Jean-François , “La réformation permanente: Les newtoniens et le dogme trinitaire”, Le Christ entre Orthodoxie et Lumières, ed. by Petassi M.-C. (Geneva, 1994), 123–37.

Verlet , La Malle de Newton (ref. 20).

Hazard Paul , Crise de la conscience européenne, 1680–1715 (3 vols, Paris, 1935).

For further developments, see Verlet , La Malle de Newton (ref. 20), especially chap. V. On the traditional religious order and the transition to individualism, see Dumont Louis , Homo hierarchicus (Paris, 1966), English transl., Homo hierarchicus (Chicago, 1970); Dumont Louis , Homo aequalis I (Paris, 1976); Gauchet Marcel , Le Désenchantement du monde (Paris, 1965). Laslett Peter , The world we have lost — Further explored (London, 1983), and Wrightson Keith , English society, 1580–1680 (London, 1982), give vivid descriptions of the traditional English society.

The “cultural revolution” in the scientific realm has been studied in Verlet , La Malle de Newton (ref. 20), 97–223, à propos the reception of the Newtonian theory of colours; two remarkable texts may help to characterize this revolution: The furious attack on Cartesian physics led by the influential Jesuit Louis de La Ville (R.P. Le Valois, S.J.), Sentiments de M. Descartes touchant l'essence et les propriétés du corps opposés à la doctrine de l'Église et conformes aux erreurs de Calvin sur le sujet de l'Eucharistie, avec une dispute sur la prétendue possibilité des choses impossibles (Paris, 1690); and the report made by Gauger Nicolas , Lettre sur les différentes réfrangibilités des rayons de la lumière et l'immutabilité de leurs couleurs (Paris, 1728), on a public repetition of Newton “crucial experiment”.

The change from divine to limited rights of kings was especially sudden in Great Britain; it may be appreciated through the question of the healing power of kings, vigorously exercised by Charles II and commonly laughed at a few decades afterwards: Bloch Marc , Les Rois thaumaturges (Paris, 1961); Hill Christopher , Some intellectual consequences of the English Revolution (London, 1980).

Filmer Robert , Patriarcha (London, 1680). As is well known, the first of Locke's Two treatises is meant as a refutation of Filmer's book.

As shown by Polanyi Karl , The great transformation (New York, 1944), this transition is exemplified by the evolution of the ideas concerning poverty: The idea of the abandonment of the poor to a self-regulating market seems to appear with Daniel Defoe, Giving alms no charity and employing the poor a grievance to the nation (London, 1714), and de Mandeville Bernard , The fable of the bees, or private vices, publick benefits (London, 1727); these pamphleteers foretell the replacement of the hand of the Providence by the “invisible hand of the market”: Smith Adam , An inquiry into the nature and causes of the wealth of nations (2 vols, London, 1776).

The evocation of the ultimate Principle holding the socio-political order is meant as an allusion to the important work of Legendre Pierre , Dieu au miroir (Paris, 1994) and references therein. See also Verlet , La Malle de Newton (ref. 20), 144ff.

It should be noted with some regret that, because they are socially shared and institutionally entrenched, these viewpoints may leave little leeway for independent thinking.

Whiteside Derek T. , “Newtonian dynamics”, History of science, v (1966), 104–17; idem, “Before the Principia: The maturing of Newton's thoughts on dynamical astronomy, 1664–1684”, Journal for the history of astronomy, i (1970), 5–19; idem, “The mathematical principles underlying Newton's Principia mathematica”, idem, i (1970), 116–38; above all, his editorial work in The mathematical papers (ref. 13).

Cunningham , “How the Principia got its name” (ref. 19).

By rational knowledge, I do not mean only and primarily theoretical knowledge. Our prehistorical ancestors, who, as far as we know, found in their mythological repertoire the ‘explanation’ of any significant element of their surrounding, possessed a rational practical knowledge concerning fire, hunting, flint cutting, etc.: If not, we would not be there wondering about their enchanted world.

Gauchet , Le Désenchantement du monde (ref. 23).

Verlet , La Malle de Newton (ref. 20), 225–79. One of the referees insists on finding equivalents to Gauchet's book that would be written in English, and he or she refers to Funkenstein , op. cit. (ref. 20) and to Brooke John , Science and religion (Cambridge, 1991). Although both these books present us with valuable contributions to Max Weber's programme concerning the Entzauberung der Welt, they differ considerably in scope, content, and emphasis from Le Désenchantement du monde which gives an essential role to the historical variations on the theme of the Incarnation. This may be seen by consulting the original or its English translation which, I understand, is about to be published.

As Descartes admitted, the highly speculative physics of the Principia philosophiae rests on the Meditations where God is the necessary link between the cogito and the world. That God was harshly denounced by the Augustinian Pascal as “le Dieu des philosophes et des savants”.

Principia (ref. 1), 528.

On Calvin's possible influence on Newton, see Deason , “Reformation theology” (ref. 20); Verlet , La Malle de Newton (ref. 20); and Section II of the present paper.

As Leibniz sneeringly remarked in a letter to Bernoulli J. , The correspondence (ref. 7), vi, 355.

This quotation and the following one are taken from Newton's letters to Bentley , The correspondence (ref. 7), iii, 244 and 253.

Principia (ref. 1), 386.

If only for the following reason: An “ultimate theory” supposed to solve the cosmological paradox cannot contain a meta-theorem proving its ultimate character.

See Manuel Frank E. , The religion of Isaac Newton (Oxford, 1974), 61f.

Addressing his illustrious predecessor, Einstein writes: “Newton, forgive me! You found the only way which in your age was just about possible for a man with the highest powers of thought and creativity. The concepts which you created are guiding our thinking in physics even today, although we know now that they will have to be replaced by others farther removed from the sphere of immediate experience, if we aim at a profounder understanding of relationships” (quoted in Schilpp P. A. , Albert Einstein: Philosopher-scientist (New York, 1949), 684).

According to such eminent scientists as Einstein and Chandrasekhar (ref. 3).

See Arnol'd , Huygens & Barrow, Newton & Hooke (ref. 3); Nauenberg Michael , “Hooke, orbital motion and Newton's Principia”, American journal of physics, lxii (1994), 331–50.

The discovery of a new frame-theory is a leap over a logical chasm, which involves the active involvement of a creative subject. Yet the frequent simultaneity of important discoveries (see Merton R. K. , The sociology of science (Chicago, 1973); Kuhn Thomas , The essential tension (Chicago, 1977)) cannot be accounted for if those discoveries were not floating in the air du temps, ready to be seized and worked out by sensitive and creative individuals. Such was the case for quantum mechanics, in marked contrast to general relativity which was very much the work of a single author. The Newtonian revolution occupies a position somewhere in between these two contemporary revolutions.

The term ‘myth’ is used here positively. It is defined following Plato (Timaeus 29d): When we come to make sense of the foundation, we have to resort, because of our “human nature”, to an account that appears as if it were true. The myth thus defined is very near to Einstein's fiction (see below): The founding principles of theoretical physics may be seen as condensed myths.

Maxwell , Matter and motion (ref. 15).

Dolby , “A note” (ref. 14).

Kutschmann Werner , Die Newtonsche Kraft: Metamorphose einer wissenschaflischen Begriff (Wiesbaden, 1983), who appreciated the importance of the qualifier ‘impressed’ when referring to the force, misinterpreted the symmetric qualifier ‘generated’. Reading carefully Law II, Françoise Balibar, Galilée, Newton lus par Einstein (Paris, 1984) realized that the “motive force impressed” should be F δt rather than F, but she unfortunately chose ‘motive’ and not ‘impressed’ as the relevant qualifier: This is clearly an inconsistent choice.

The religious meaning of this distinction has already been pointed out above: It contrasts the “inanimate brute matter” ruled by the (Cartesian) vis inertiae with the animating motion which may be seen as “impressed” by “the divine arm”. This distinction is probably inherited from More Henry , “Antidote against atheism”, A collection of several philosophical writings (London, 1662), 36. More may have been inspired by Plotin's Enneads (II, 2): See Verlet , La Malle de Newton (ref. 20), 56.

In the Introduction to the Principia, Newton tries to relate the very abstract principles he introduces with the familiar experience of the reader: See Ludwig Berndt , “What is Newton's law of inertia about?”, Science in context, v (1992), 139–64.

This distinction is very clearly set in the opening section of the early manuscript “De gravitatione” (Unpublished scientific papers of Isaac Newton, ed. by Hall A. R. Hall M. B. (Cambridge, 1962), 89–156, p. 90).

See e.g. Republic, VII, 522b-531c. This structural homology does not imply the identity of Plato's and Newton's views on the role of mathematics. It may be have been inspired by Newton's familiarity with the Cambridge neo-platonist philosophers. Let us note that Newton had two versions of Plato's Republic in his library: John Harrison, The library of Isaac Newton (Cambridge, 1978), 218.

Sir Isaac Newton: Theological manuscripts, ed. by McLachlan H. M. (Liverpool, 1950), 58.

See Shapin Steven , A social history of truth (Chicago, 1994).

Well-known quotations illustrate that point. Bentley Addressing , The correspondence (ref. 7), iii, 233, Newton states that, when writing the Principia, he “had an eye upon such principles as might work with considering men for the belief of a Deity”. And, in the general Scholium (Principia (ref. 1), 529), he asserts that “to discourse of [God] from the phenomena does belong to natural philosophy”.

Concerning this accusation, see Austin William H. , “Isaac Newton on science and religion”, Journal of the history of ideas, xxxi (1969), 521–42. It may be argued using this statement concerning God: “We know him only by his properties and attributes, by his most wise and excellent contrivances of things and final causes, and we admire him for his perfections” (Principia (ref. 1), 529).

Some of the historians quoted in ref. 12, who specialized in the first sections of the Principia, argue rightly that, in order to study the motion of bodies in conic sections, Newton did not use Law II, but followed the indirect route of Proposition 6 which defines the so-called dynamics ratio (see Brackenridge J. Bruce , “Newton's mature dynamics: Revolutionary or reactionary?”, Annals of science , xlv (1988), 451–76). They are then able, within that restricted reading of the Principia, to credit Newton with an important discovery and at the same time to pretend that he made a gross error concerning Law II.

Dealing with finite geometrical elements, Newton can insist that he is proceeding under the aegis of Euclid, Appolonius, and Pappus. The Principia is supposedly written in the language of ancient geometry, but Whiteside , “The mathematical principles” (ref. 30), has convincingly shown that, beneath the “Grecian scaffolding”, the mathematical edifice built by Newton “is, in its essentials, neither classically inspired nor classically built”. The geometrical language of the Principia refers to proportions (as may be seen from the wording of Law II quoted above), where, since Viète, the algebraic language writes equalities: When Newton's commentators substitute without any word of caution an equality sign for the proportionality ratio explicitly stated in Law II, they obviously take for granted that the proportionality constant which is evident in Newton's geometrical reasoning is otherwise veiled under the sequences of equations and is finally recovered, as a multiplicative constant, in the definition of the force.

Principia (ref. 1), 28 and 37.

Letter from Newton to Oldenburg, February 1672, The correspondence (ref. 7), i, 92.

See Westfall , Never at rest (ref. 13), for a relation of the quarrel and Verlet , La Malle de Newton (ref. 20), 97–223 for a proposed interpretation.

The correspondence (ref. 7), ii, 110.

Such a concealment was not frequent, but certainly not unheard of. For the war between Newton and Leibniz, see Hall A. Rupert , Philosophers at war (Cambridge, 1980).

Whiteside , “The mathematical principles” (ref. 30), 125.

Newton Isaac , Chronology of ancient kingdoms amended (London, 1728).

See Manuel Frank E. , Isaac Newton historian (Cambridge, 1963).

Westfall , Never at rest (ref. 13), 815.

As Westfall , Never at rest (ref. 13), 346–8, has shown, the problem of the reconstruction of the Temple's plan was important for Newton and gave rise to a significant amount of unpublished papers. But, as pointed out by Westfall, Newton nowhere states explicitly the reason for his interest which has to be reconstructed: His contention that the Ancients knew about the Copernican system and the action at a distance (see McGuire J. E. Rattansi P. M. , “Newton and the pipes of Pan”, Notes and records of the Royal Society, xxi (1966), 108–43), and his belief that the pristine possessors of the Prisca sapientia were the Hebrews makes it likely that he was searching for signs of the primitive knowledge embedded in the Temple's plan.

Principia (ref. 1), 387.

The demonstration of the most important Proposition 41 is examined in detail by Whiteside , “The mathematical principles” (ref. 30). Proposition 39, reviewed by Westfall , Never at rest (ref. 13), 409, refers to a one-dimensional case and is therefore easily grasped.

Principia (ref. 1), 294. I took the liberty of adding between brackets symbols that fix the context.

See Cohen , “Newton's Second Law” (ref. 12); Cohen , Introduction to Newton's ‘Principia’ (ref. 12), 163.

Whiteside (ed.), The mathematical papers (ref. 13), vii, 540.

The example of the first corollary of the laws is here instructive. This corollary concerns the composition of the motions generated by the conjoined action of two forces acting “in a given time”. The action of the forces being localized in space and time, they should be considered as impressed forces. The qualifier ‘impressed’, missing in the first edition of the Principia, was subsequently added: See Principia (ref. 1), 14; and Costabel Pierre , “Les Principia de Newton et leurs colonnes d'Hercule”, Revue d'histoire des sciences, 1 (1987), 251–71.

Leibniz took the point in each of his five letters to Clarke (The Leibniz-Clarke correspondence (ref. 17)). Newton's original suggestion that space should be considered “as if it were” the Sensorium Dei figures in Queries 28 and 31 of Isaac Newton, Opticks (third edition, London, 1721). See also Koyré Alexandre Cohen I. Bernard , “The case of the missing Tanquam”, Isis, cii (1961), 555–66.

The religious connotation of Newton's absolute space is well-known: See Metzger Hélène , Attraction universelle et religion naturelle chez quelques commentateurs anglais de Newton (Paris, 1938); Fierz Markus , “Ueber der Ursprung und Bedeutung der Lehre Isaac Newton's vom absoluten Raum”, Gesnerus, xi (1954), 62–129; Koyré Alexandre , From the closed world to the infinite universe (Baltimore, 1957); McGuire J. E. , “Existence, actuality and necessity: Newton on space and time”, Annals of science, xxxv (1978), 436–508. In the Scholium generale Newton says of God that “by existing always and everywhere, he constitutes duration and space” (Principia (ref. 1), 528).

Principia (ref. 1), 11.

As stated by Newton in his preface: “mathesis, quatenus ea ad philosophiam spectat”.

According to Newton's own words, “Moses, accommodating his words to the gross conception of the vulgar, describes things much after the manner as one of the vulgar would have inclined to do”, The correspondence (ref. 7), ii, 333. For Calvin's doctrine, see Calvin Jean , Institution de la religion chrétienne (Geneva, 1560), I, VI, 1 and I, VIII, 1; Latin transl., Institutio Christianae religio (Geneva, 1561); English transl., The institution of the Christian religion (London, 1562), which has been quoted here with a modern spelling. The above three numbers refer respectively to the book, chapter and section; Commentaries on Genesis (quoted by Deason , “Reformation theology” (ref. 20), 171): “Moses wrote in a popular style which, without instruction, all ordinary persons endued with common sense, are able to understand; but astronomers investigate with great labour whatever the sagacity of the human mind can comprehend.”.

This quotation is extracted, as the following ones, from Yahuda Ms. 1, as reproduced in Appendix A of Manuel, The religion (ref. 42), 123ff.

Ibid., 109.

Ibid., 108.

Ibid., 124.

For some considerations closely related to the ones presented here, see the conclusion of Rob Iliffe, “Apocalyptic hermeneutics and the sociology of Christian idolatry”, in Force J. E. Popkin R. H. (eds), The Books of Nature and Scripture (Dordrecht, 1994), 55–88.

Manuel , The religion (ref. 42), 123.

Yahuda Ms. 15, 1, 11, quoted by Manuel, The religion (ref. 42), 54.

And that, more and more clearly as time passes on: See Manuel , The religion (ref. 42), 102.

Principia (ref. 1), 11.

As a concrete realization of Newton's thoughts on that matter, we may think about Foucault's pendulum.

Principia (ref. 1), 12.

Yahuda Ms. 21, 2, quoted by Westfall , Never at rest (ref. 13), 355.

It should be remembered that Augustine's God was explicitly a synthesis, within the Christian theology, of the supremely intelligent Being of the Neo-platonists and of the free, ever-acting, and sovereign God of the Bible (see Taylor Charles , Sources of the self (Cambridge, 1989), 127); through the Reformation, Newton inherited from that synthesis.

The correspondence (ref. 7), iii, 235.

Whiteside (ed.), The mathematical papers (ref. 13), vii, 289.

See Umberto Eco, La ricerca della lingua perfetta nella cultura europa (Rome, 1994); Herrenschmidt Clarisse , “Le Tout, l'énigme et l'illusion”, Le Débat, lxii (1990), 95–118.

Gauchet , Le Désenchantement du monde (ref. 23).

Whence the importance of the controversies on transubstantiation in the seventeenth century: See Redondi Pietro , Galileo eretico (Turin, 1983); English transl., Galileo heretic (Princeton, 1987); and Verlet , La Malle de Newton (ref. 20), 97–223.

For the distinction between general and special revelation, see Stauffer Richard , Dieu, la Création et la Providence dans la prédication de Calvin (Berne, 1978), and references therein. This distinction is tailored after the scholastic distinction between general and special Providence, between potentia Dei ordinata et absoluta.

I am aware that this is a dangerously imprecise word, but it is difficult to do without it when brevity is required. In addition to the references given in Verlet , La Malle de Newton (ref. 20), 116ff, see Trevor-Roper Hugh , Religion, the Reformation and social change (London, 1984); Hill Christopher , Society and Puritanism in pre-revolutionary England (Harmondsworth, 1986); White P. , “Calvinism and the English church 1570–1635”, Past and present, cxiv (1987), 32–76; and references therein.

A plate in Harrison , The library (ref. 54), shows the fly-leaf of Calvin's Institutio (ref. 81) with Newton's signature and the date 1661.

A large fraction of them (but not Newton: Force Popkin , Essays (ref. 20), 119–41)) can be labelled as Latitudinarians. For a recent and valuable reappraisal of the Latitudinarian movement, see Kroll Richard Ashcraft Richard Zagorin Perez (eds), Philosophy, science, and religion in England, 1640–1700 (Cambridge, 1992).

On the Anglican reaction to enthusiasm, see Cragg Gerald. R. , The church and the Age of Reason 1648–1789 (Harmondsworth, 1960); Jacob Jacob , “The Anglican origins” (ref. 20); Heyd Michael , “The reaction to enthusiasm in the seventeenth century: Towards an integrative approach”, The journal of modern history, ciii (1981), 258–80; Shapin Steven Schaffer Simon , Leviathan and the air pump (Princeton, 1985). On a broad definition of Calvinism, see Hall B. , “Calvin against the Calvinists”, in John Calvin , ed. by Duffield G. E. (Abingdon, 1966), 19–37. On Locke's religion, see Dunn John , The political thought of John Locke (Cambridge, 1969); Taylor , Sources of the self (ref. 94), 234–47. On Boyle's religion, see Jacob James R. , Robert Boyle and the English Revolution (New York, 1977); Shapin , A social history of truth (ref. 56), 156–70.

See Stauffer , Dieu (ref. 100); Deason , “Reformation theology” (ref. 20); and Verlet , La Malle de Newton (ref. 20), 333–41.

Calvin , The institution (ref. 81), I, V, 1.

Ibid., II, I, 8.

Ibid., I, V, 11.

Ibid., I, IV, 1.

Ibid., I, XVII, 2.

Ibid., I, XVI, 1.

Ibid., I, XVI, 3.

References to Newton's own writings: For tenet 1, ref. 58 and ref. 93, p. 17; for tenet 2, ref. 88, p. 17; for tenet 3, an important text (David Gregory MS. 245) discovered by McGuire J. E. , “Force, active principles, and Newton's invisible realm”, Ambix, xv (1968), 154–208, which is concomitant with the exchange with Bentley, states that “God is an entity … freely willing good things; by his will effecting things possible …; and constantly cooperating with all things according to accurate laws, as being the foundation and cause of the whole of nature, except where it is good to act otherwise”; for tenet 4, see below. An appropriate illustration of these four tenets may be found in the General Scholium of the Principia.

Principia (ref. 1), 33.

Newton's adhesion to the doctrine of Prisca sapientia ( McGuire Rattansi , op. cit. (ref. 70)) tended to protect his Geometry, developed under the patronage of the Ancients, from the “errors” of modern Analysis. The measuring instruments, which shielded the observer from fallacious fantasying ( Verlet , La Malle de Newton (ref. 20), 81), should correct “the fallen nature of humanity” through “the use of artificial aids”: See Schaffer Simon , “The body of natural philosophers in seventeenth century England”, in Knowledge incarnate: The physical presentation of intellectual ideas , ed. by Lawrence C. Shapin S. (Chicago, forthcoming); see also Schaffer Simon , “Comets & idols: Newton's cosmology and political theology”, in Action and reaction, ed. by Theerman P. Seef A. F. (Newark, 1993), 206–31.

Dobbs , The Janus faces (ref. 20).

See Fisch Harold , “The scientist as a priest: A note on Robert Boyle's natural philosophy”, Isis, xliv (1953), 252–65, for a portrait of Robert Boyle as a priest who devoted his chaste life to the quest for the world's Creator. The same can be maintained about Newton, but this is only half of the story. As the author of the Principia, that awesome model of self-denying rhetoric, and as the imperial and austere President of the Royal Society, Newton passed on to his heirs the socialized do's and don't's which ensure the conformity of the public expression of science to its ideal of objectivity and which prevent the untimely surge of ‘private’ beliefs and opinions.

Letter to Fermat, in de Fermat Pierre , Oeuvres, ed. by Tannery P. Henry Ch. (5 vols, Paris, 1888–1922), ii, 36.

Letter to Mersenne (in Latin), April 1647, in René Descartes, Oeuvres, ed. by Adam Ch. Tannery P. , rev. by Costabel P. Rochot B. (13 vols, Paris, 1964–74), iv, 396.

The correspondence (ref. 7), iii, 254.

Often forgotten by Newton's successors or seen as if it represented merely Newton's personal opinion, this objection is compelling as long as one remains in the ‘classical’ framework.

The hypothesis of the aether was very much inspired by Newton's alchemical works. Although it was revived by Newton in his old age, it never led him anywhere. On Newton's attempts concerning a gravitational interaction mediated by the aether, see Rosenfeld Léon , “Newton and the law of gravitation”, Archive for history of exact science, ii (1965), 365–86. For the evolution of Newton's ideas concerning the cause of the gravitational force, see Dobbs , The Janus faces (ref. 20).

Bentley Richard , Eight sermons at the Hon. Robert Boyle's lectures (Cambridge, 1724), 253. One of the referees of this journal called my attention on John Henry's paper: “‘Pray do not Ascribe that Notion to me’: God and Newton's gravity”, in Force Popkin (eds) (ref. 86), 123–47. Henry's analysis, also based on the exchange between Bentley and Newton, comes to a conclusion which, on the face of it, seems to differ from the classic point of view presented here. Henry agrees that Newton's conception of gravity “dovetailed perfectly with his voluntary theology” (p. 141). But he states that, when Newton refers to an “immaterial Agent”, he has not in mind the continuous action of God's Finger lawfully “impressed” on inanimate matter, but the continuous impression on matter of “a property superadded by God”. This controversial property expresses God's Fiat: “Mysterious though it is, God could make matter act at a distance — To deny this was to deny God's omnipotence” (ibid.). This subtle distinction concerning the mode of God's real presence in the physical world runs parallel to the distinction between the realist and nominalist point of views in the theology of the Eucharist. Newton would probably not have been enthusiastic over such theological niceties, as may be seen from the quotation given just below (ref. 124).

Undated note from the Library of Lehigh University quoted by Guerlac Henry Jacob Margaret C. , “Bentley, Newton, and providence”, Journal of the history of ideas, xxx (1969), 307–19. The religious character of the action at a distance was clear to Daniel Bernoulli, who used it to persuade the Calvinist Euler that, “hat Gott können einem animam, deren Natur uns unbegreiflich ist, erschaffen, so hat er auch können eine attractionem universalem materiae imprimiren, wenn gleich solche attractio supra captum ist” ( Fuss P.-H. , Correspondance mathématique et physique de quelques célèbres géomètres du XVIII^e siècle (2 vols, St Petersbourg, 1843), ii, 541).

See Leibniz-Clarke, Correspondance, ed. by Robinet A. (Paris, 1957), 17. This letter was written before the debate with Clarke. The translation from the French is mine.

See the texts published by Westfall , Never at rest (ref. 13), 315 and 350; and by Manuel Frank E. , A portrait of Isaac Newton (Cambridge, Mass., 1968), 60 and 287. In an unpublished paper (Yahuda MS. 14, 20), Newton enumerates the “10 miracles” entailed “by saying this is my body” and he tries to prove, by common sense arguments, that these miracles are impossible. I tried to show in La Malle de Newton (ref. 20) that the fierce controversy about transubstantiation in Restoration England was a convenient cover for internal strife within the Anglican Church.

Principia (ref. 1), 528.

Tertullian , De carne Christi, V, 4. The translation is mine.

The term aporia, which designates an insurmountable contradiction, refers etymologically both to the difficulty of finding a way through the contradiction and to the effects of confusion and anxiety associated with an unescapable contradiction ( Verlet , La Malle de Newton (ref. 20), 297).

The cosmological paradox underlies Kant's cosmological antinomies. Some of its variants may be found in the literature. See for instance Harrison Edward , Cosmology (Cambridge, 1981), 115–16. The present section is an extremely condensed version of the last chapter of La Malle de Newton (ref. 20).

See Verlet , La Malle de Newton (ref. 20), 380.

Concerning the flexible epistemological position of “revolutionary” physicists: On Boltzmann, see Verlet , La Malle de Newton (ref. 20), 386, and Broda Engelbert , Ludwig Boltzmann (Vienna, 1955), 119; on Einstein, see Pais Abraham , “Subtle is the Lord” (Oxford, 1982), 13.

See next subsection and Rosenfeld , “Newton” (ref. 122).

See next subsection and Jürgen Mittelstrass, “The Galilean revolution: The historical fate of a methodological insight”, Studies in history and philosophy of science, ii (1972), 297–328. This interesting paper is somewhat marred, it seems to me, by the fact that the Galilean law of falling bodies and the Newtonian theory are put on the same plane, whereas the former is a specific theory which could be developed from an astutely chosen mathematical assumption while the latter is an all-encompassing frame-theory resting on an interlocking system of principles which could not be obtained without a deep meditation of the experimental situation (this does not mean, of course, that those principles were simply induced from experiment as Newton sometimes pretended).

Popper Karl , Unended quest (Glasgow, 1976), 37. See Popper Karl , Conjectures and refutations (London, 1969), 185, for the assertion that Kant believed Newton's theory to be true.

Popper Karl , Logik des Forschung (Vienna, 1934); English transl., The logic of scientific discovery (London, 1968).

Concerning “superb theories”, see Penrose Roger , The emperor's new mind (New York, 1989), 152ff. It is very likely that Newton anticipated, for religious reasons, the “superb” character of the frame-theories he designed. The question of the elegance of the theory has been discussed at the end of Section I. Explicitly stated, its universality is referred to the “dominion of One” (Principia (ref. 1), 528) who is the “Universal Ruler”. The precision of the theory appears all through Book III to have been a major concern for Newton: He took great pains to calculate observable effects, so far as he could with his inconvenient technique, thus leading to a comparison with measurements which were at the time becoming highly accurate.

Wigner Eugene , “The unreasonable efficiency of mathematics in the natural sciences”, Communications on pure and applied mathematics, i (1960), 1–14.

Taylor , Sources of the self (ref. 94), 127–42.

Principia (ref. 1), 527.

Hawking Stephen , A brief history of time (New York, 1988).

Schweber Sam , “Physics, community and the crisis in physical theory”, Physics today, xxxiv (1993), 34–40.

Hawking , A brief history (ref. 141), 169.

Eliott Ralph W. , “Isaac Newton's ‘Of An Universal Language’”, Modern language review, lii (1957), 11–18.

Eco, La ricerca (ref. 97).

Newton: Theological manuscripts (ref. 55), 119.

See Dobbs Betty J. , The foundations of Newton's alchemy (Cambridge, 1975).

Verlet , La Malle de Newton (ref. 20), 337.

Koyré Alexandre , Newtonian studies (Cambridge, Mass., 1965), 52.

Hall Hall (eds), Scientific papers (ref. 53), 91.

Koyré , Newtonian studies (ref. 149), 35.

Einstein , Mein Weltbild (ref. 2), 200. ‘Fictitious’ comes often from Einstein's pen to qualify the fundamental principles: See e.g. Pais , “Subtle is the Lord” (ref. 132), 460.

Verlet Loup , “Sous le masque de la raison”, Littératures classiques, xxv (1995), 243–69.

Einstein , Mein Weltbild (ref. 2), 42.

Verlet , La Malle de Newton (ref. 20), 284.

See Bateson Gregory , Steps to an ecology of mind (New York, 1972), for the psychical difficulty involved in a deep change of the internalized “epistemological premisses”.

Planck Max , Physikalische Abhandlungen und Vorträge (3 vols, Braunschweig, 1958), iii, 389.

Bateson , Steps (ref. 156), and Hofstadter Douglas , Gödel, Escher, Bach (New York, 1980), have independently attempted to give a logical characterization of the hierarchical modes of the human psychical functioning. Both these authors hold that the higher mode in the hierarchy is a paradoxical mode which, for most humans, can be sustained only intermittently. See also Verlet , La Malle de Newton (ref. 20), 281; and Winnicott Donald W. , Playing and reality (Harmondsworth, 1974).

Thus may be explained the coexistence, in Copernicus's thought, of a revolutionary celestial mechanics with an obsolete Aristotelian physics. Another example would be the persistence, in Freud's perpetually changing theoretical activity, of the strange theory of actual neuroses that provided a fixed and comforting link with biological science.

The recourse to an unusual frame of thought, used as a provisional scaffolding, can be found elsewhere. For a remarkable example of this, see Herrenschmidt Clarisse , “Entre Perses et Grecs I: Démocrite et le Mazdéisme”, to be published. Herrenschmidt's paper concerns Democritus, one of Newton's favourite figures. The father of atomism succeeded in thinking that there was a radical difference between the visible world around us and the invisible world composed of atoms, the colours of the visible bodies being unrelated to any ‘colours’ of invisible atoms. In order to perform that feat, he used as a scaffolding the Mazdean religious cosmology which left discernible marks in some of the fragments attributed to him.

Descartes was not unaware of the anthropological paradox as may be seen from his remarkable letter to Princess Elizabeth, dated 28 June ( Descartes , Oeuvres (ref. 119), iii, 690). See nevertheless Martin Heidegger, Nietzsche (2 vols, Pfullingen, 1961), 31–256, for a harsh critique of Descartes's philosophy regarded as inevitably leading to a complete objectivation of the mind's life.

Schaffer , “The body” (ref. 115).

Certain philosophical questions: Newton's Trinity notebook, ed. by McGuire P. M. Tamny M. (Cambridge, 1983), 397, 443 and 482.

Verlet , La Malle de Newton (ref. 20), 81.

The correspondence (ref. 7), iii, 152.

Westfall , Never at rest (ref. 13), 345.

Dobbs , The foundations (ref. 147), 161.

Winnicott , Playing and reality (ref. 158).