Abstract
In this essay, I attempt to assess Henk de Regt and Dennis Dieks recent pragmatic and contextual account of scientific understanding on the basis of an important historical case-study: understanding in Newton’s theory of universal gravitation and Huygens’ reception of universal gravitation. It will be shown that de Regt and Dieks’ Criterion for the Intelligibility of a Theory (CIT), which stipulates that the appropriate combination of scientists’ skills and intelligibility-enhancing theoretical virtues is a condition for scientific understanding, is too strong. On the basis of this case-study, it will be shown that scientists can understand each others’ positions qualitatively and quantitatively, despite their endorsement of different worldviews and despite their convictions as what counts as a proper explanation.
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Notes
In private communication Henk De Regt has confirmed that this criterion is intended only to account for the first step in the process of understanding of a theory (19 May 2007, Leusden).
On CUL 3968, f. 584r [ca. 1712–1713], Newton wrote that is was his intention of writing the above quote was to remain “silent about the cause of gravity, there occurring no experiments or phænomena by wch he might prove what was the cause thereof: And this he hath abundantly declared in his Principles neare the beginning thereof in these words; Virium causas et sedes Physicas jam non expendo. And a little after: Voces attractionis, impulsus vel propensionis cujusque in centrum indifferenter & pro se mutuo promiscue usurpo, has vires non physice sed mathematice tantum considerando. Unde caveat Lector ne per hujusmodi voces cogitet me speciem vel modum actionis, causamve aut rationem physicam alicubi definire, vel centris (quæ sunt puncta Mathematica) vires vere et physice tribuere, si forte aut centra trahere aut vires centrarum esse dixero.”
See Leibniz’ defence of a mechanical ether composed of bullae in his Hypothesis Physica Nova (1671) in: Gerhardt (1849–1863, VI, pp. 17–59), his Tentamen de motuum coelestium causæ (1689), in ibid., VI, pp. 144–187, and his De causa gravitatis, et defensio sententiæ authoris de veris naturæ legibus contra Cartesianos (1690), in ibid., VI, pp. 193–203. In an unpublished letter addressed to the editor of The Memoirs of Literature (ca. May 1712) Newton defended himself as follows to Leibniz’s critique: “Because they do not explain gravity by a mechanical hypothesis, he charges them with making it a supernatural thing, a miracle and a fiction invented to support an ill-grounded opinion and compares their method of philosophy to that of Mr. de Roberval’s Aristarchus, which is all one as to call it romantic [i.e. fictional]. They show that there is a universal gravity and that all phenomena of the heavens are the effect of it and with the cause of gravity they meddle not but leave it to be found out by them that can explain it, whether mechanical or otherwise. […] And therefore if any man should say that bodies attract one another by a power whose cause is unknown to us, or by a power seated in the frame of nature by the will of God, or by a power seated in a substance in which bodies move and float without resistance and which has therefore no vis inertiae but acts by other laws than those that are mechanical: I know not why he should be said to introduce miracles and occult qualities and fictions into the world.” (Janiak 2005, pp. 115–116).
Author’s translation of: “Alias nullum omnino phaenomenon ↓per causam suam↓ recte explicari posset nisi causa
↓hujus↓ causae, & causa 
causae prioris redderetur & sic deinceps usque donec ad causam primam deventum sit.”Cohen’s translation of: “Qui leges et effectus Virium electricarum pari successu et certitudine eruerit, philosophiam multum promovebit, etsi ↓forte↓ causam harum Virium ignoraverit. Nam Phaenomena ↓observanda↓ primo ↓
↓ 
↓sunt↓, dein horum causae proximae, & postea causae causarum 
eruenda; ac tandem a causis ↓supremis causarum↓ per phaenomena stabilitis, ad ↓causas↓ caus 
↓eorum effectus↓, ↓
↓ argumentando a priori, descendere licebit. 
Philosophia naturalis non in opinionibus Metaphysicis, sed in Principiis propijs fundanda est; & haec [end of text]” (CUL Add. Ms. 3970, f. 109v ).“A priori” here means what comes first in the order of nature; “a posteriori” means what comes first in the order of knowing.
Which states: “A body acted on by [two] forces acting jointly describes the diagonal of a parallelogram in the same time in which it would describe the sides if the forces were acting separately.” (Newton 1999 [1726], p. 417).
Can, however, a continuous force be approximated by as a limit of discontinuous impulsive force as the time interval shrinks to zero? This point has often been debated. D.T. Whiteside and E.J. Aiton dismissed its validity (Whiteside 1991, p. 30; Aiton 1972, pp. 103–104). However, an adequate assessment of the situation is not solely contingent on whether we grant Newton’s assumption that a continuous force can be approximated as a limit of discontinuous impulsive force: for even if we grant Newton this, his limiting procedure does not prove what he claimed it proved, namely that all centripetal forces produce orbits that lie in a fixed plane, as Pourciau has shown (Pourciau 2003). First of all, Newton could not independently prove the impulse assumption and the claim that areas involved lie on the same plain (the one is required to establish the other and this observations holds for any polygonal approximation) (ibid., esp. the reconstruction of Newton’s proof on pp. 277–279). Thus, Newton could only have established that the areas, which bodies made to move in orbits describe radii drawn to an unmoving center of forces and which lie in unmoving planes, are proportional to the times. Furthermore, and even more seriously, Newton’s arguments for Proposition I clearly involves impulse motions and limits of impulse motions; however, the conclusion is supposed to be valid for all centripetal forces (impulse and continuous ones). However, Newton’s proof of Proposition I can be restored by introducing some additional conditions on the smoothness of a specific curve (see ibid., pp. 291–295).
Proposition II also required the assumption that the resting deflections in the limit motion are directed toward the central point whenever every vertex of every polygonal motion has a resting deflection directed toward the central point (Pourciau 2009, pp. 23–24). A restored proof of Proposition II can be found on ibid., pp. 26–27.
Which states “When bodies are enclosed in a given space, their motions in relation to one another are the same whether the space is at rest or whether it is moving uniformly straight forward without circular motion.” (Newton 1999 [1726], p. 423).
In fact, when working on De Motu, Newton already realised that the true motions of celestial bodies are immensely complicated and far from being exactly Keplerian. Simultaneously taking in account all causes of planetary motion “exceeds the force of any human mind” (Whiteside 1967–1981, VI, p. 78).
Which states: “If bodies are moving in any way whatsoever with respect to one another and are urged by equal accelerative forces along parallel lines, they will all continue to move with respect to one another in the same way as they would if they were not acted by such forces. For those forces, by acting equally (in proportion to the quantities of the bodies to be moved) and along parallel lines, will (by law 2) move all the bodies equally (with respect to velocity), and so will never change their positions and motions with respect to one another (Newton 1999 [1726], p. 423).
Cf. CUL Add. Ms. 3965, f. 269r [ca. 1694], where Newton wrote: “Nam Planetæ […] non […] ↓petent se mutuo↓ vi ↓aliqua↓ gravitates neque ullo modo agent in se invicem nisi mediante principio aliquo activo quod utrumque intercedat, et per quod vis ab utroque in alterum propagetur.” [italics added].
Given Newton’s addition “whether this Agent be material or immaterial”, it seems that Newton, during the first years after the publication of the Principia still left open the possibility that gravity was produced by an extremely subtle mechanical ether. However, this would change shortly after 1692/3. In material related to the Classical Scholia (ca. 1694), Newton wrote: “[Hoc medium ex mente veterum non erat corporeum cum corpora universa ex essentia sua gravia esse dicerent, atque atomos ↓ipsos vi æterna↓ naturæ suæ absque aliorum corporum impulse per spatia vacua in terram cadere.]” (CUL Add. Ms. 3965, f. 269r). This change was rendered explicit in the General Scholium to second edition of the Principia. The ethers Newton introduced in The Opticks (and related manuscript material) were clearly non-mechanical: they required non-material interaction of micro-level forces (see infra).
Note that De Regt and Dieks discuss Newton’s theory of universal gravitation but—quite ironically—mentioned that apparently “Newton had difficulty with the metaphysics now associated with Newtonian theory: there was no room for actio in distans in the corpuscularist worldview to which he adhered” and that he “did not accept it as a tool for scientific understanding” (de Regt and Dieks 2005, p. 161).
Newton’s account of gravitation as being produced by “the elastick force” of mutually repellent small particles occurs in Query 21 (Newton 1979 [1730], pp. 350–352).
This observation is entirely correct, for if Newton thought otherwise we would be led to accept the conclusion that he tried to explain action at a distance at the macro-level away by reintroducing it at the micro-level.
In Janiak 2007, Janiak did not refer to Henry’s work. He does so in Janiak 2008, p. 53, footnote 53. There Henry’s views are quickly dismissed on the basis of an excerpt wherein Henry (incorrectly) wrote that gravity is “a superadded inherent property” (Henry 1994, p. 141; note however, that in Henry, 2007 this mistake is corrected). In any case, Henry’s slip should not detract us from the important points he made: that the ether theories did not originate in Newton’s dissatisfaction with action at a distance per se, and that Newton accepted action at a distance in his optical work and in his work on the cause of gravity. In his subsequent discussion (Janiak 2008, pp. 53–65), Janiak does not consider these two points.
This conclusion was also reached in McMullin 1978, p. 144, footnote 13 and p. 151, footnote 210.
Newton’s “phenomena” are inductive generalizations based on a large number of singular astronomical observations and their complex mathematical processing. Here I shall not further discuss how these astronomical observations were obtained. Instead I refer the reader to Densmore 1995, pp. 242–282.
I.e., here, as in the rest of the Principia, Newton considered relative motions.
For the secondary planets Newton’s application of Corollary 6 is no surprise, since he assumes that the orbits of the circumjovial planets, e.g., do “not differ sensibly from circles concentric with Jupiter” (Newton 1999 [1726], p. 797). Newton presupposes a circular approximation here.
While Newton came to accept the empirical validity of Kepler’s harmonic rule from quite early on, it was only shortly before the composition of De motu that Newton came to accept the area rule when John Flamsteed’s astronomical observations indicated a fairly accurate confirmation of it (ca. 1684). See Whiteside 1964 and 1970, Russell 1964, Thoren 1974 and Wilson 1974 for further discussion.
Here Newton rejected geocentrism.
At this point, Newton leaves open the possibility of the Tychonic theory. It is only in Proposition XII of Book III that Newton established that the sun is the common centre of gravity of all planets (Newton 1999 [1726], p. 817).
On Newton’s apsidal precession theorem, see furthermore Valluri et al. 1997.
In commenting on Proposition VI, Newton noted: “Actually, the motion of the moon is somewhat perturbed by the force of the sun, but in these phenomena I pay no attention to minute errors that are neglegible.” (Newton 1999 [1726], p. 801).
A translation more close to the original is: “which in each revolution is only three degrees and three minutes in consequentia [i.e., in an easterly direction forward]”.
This is the value Newton had calculated in Corollary 1 to Proposition XLV (Newton 1999 [1726], pp. 802–803, p. 544).
This force differs 4/243 from the inverse-square proportion and 239/243 from the inverse-cube proportion. By dividing the difference from the cube proportion, 239/243, by the difference from the inverse-square proportion, 4/243, we arrive at 593/4.
Newton, first of all, decomposed the sun’s perturbing force on the moon into a radial and a transradial component. Given the mathematical properties of a three-body system based on Proposition LXVI of Book I—which takes the moon’s orbit to be circular—and by an application of Corollary 17 to Proposition LXVI, Book I (cf. Proposition XXV, Book III (Newton 1999 [1726], p. 840)), Newton calculated the average value of the radial component of the sun’s perturbing force that draws the moon away from the earth—here he abstracted from the sun’s transversal component—is to the acceleration of the moon to the earth as ½(T M/T E)², i.e. as ½((27d7h43m = 39,343 min)/(365d6h9m = 525,969 min))², which yields a ratio of ca. 1 to 357.45 (Wilson 1989, p. 264).
The computation based on Corollary 2 to Proposition XLV, Book I, was added in the second edition.
The line “Apsis Lunæ est duplo velocior circiter.” was added in the third edition.
This value remained unchanged in all editions.
Ptolemy’s name was added in the third edition.
Huygens’ name was added in the third edition.
With respect to Tycho’s value, Newton observes: “But Tycho and all those who follow his table of refractions, by making the refractions of the sun and moon (entirely contrary to the nature of light) be greater than those of the fixed stars—in fact greater by about four or five minutes—have increased the parallax of the moon by that many minutes, that is, by about a twelfth or fifteenth of the whole parallax. Let that error by corrected, and the distance will come to be roughly 601/2 terrestrial semidiameter, close to the value that has been assigned by others” (Newton 1999 [1726], pp. 803–804). In the first edition Newton corrected Tycho’s value as to result in 61 terrestrial semi-diameters; in the second edition he corrected Tycho’s value as to result in 601/2 terrestrial semidiameters.
The average of the five values Newton provided in the third edition is ca. 60,047. In the first edition, the average is ca. 60,567 terrestrial semi-diameters. In the second edition, it is ca. 59,958 terrestrial semi-diameters.
One Paris foot equals 1.066 English feet (Densmore 1995, p. 299).
In the first edition Newton wrote 151/12 Paris feet tout court; in the second edition he wrote “pedum Parisiensium 151/12 circiter”. It is worth mentioning Shinko Aoki’s conclusion on the accuracy of the moon test: “Newton believed he had shown the inverse-square law to be more exactly verified than was in fact the case. If in the Moon-test an accuracy of one part in 6000 was [implicitly] required, in Newton’s opinion, to provide an empirical basis for the structure of the Principia, then Newton failed in his effort, because he mistook the calculations necessary for this purpose. He would have done better to remain content with the accuracy obtained in the first edition of Proposition IV of Book III; this was reasonably given because the observational data Newton used were poorly determined. It would not then have been necessary to consider sophisticated correction factors in verifying the inverse-square law; these were superfluous, or it was at least premature to take them into account.” (Aoki 1992, p. 169).
Here I have calculated this value from the route Newton suggested via Corollary 9 to Proposition IV of Book I. For the route via Proposition 36 of Book I using the versed sine, see Spencer 2004, pp. 779–780.
On the actual value given by Huygens and its derivation, see Aoki 1996, p. 394.
In opting for 60 earth semi-diameters as the moon-earth distance Newton made the computation to the best advantage as to the numbers in terms of accuracy (cf. Westfall 1973, p. 755). Nevertheless, the correlation Newton established was quite strong: William L. Harper has correctly indicated that if we neglect from Newton’s 1/178.25 correction and take each of the lunar distances cited in the third edition of the Principia separately, Huygens’ value is still well within the error bounds of 14.612–15.47 Paris feet (Harper 2002a, p. 182).
1 “line” is a twelfth of an inch.
Since (60 × 60 × 151/12 Paris feet)/(60s)² = 151/12 Paris feet/(1s)².
In the first and second edition Newton gave 151/12 tout court Paris feet for Huygens’ value.
On the regulae philosophandi see 4.3.
The same point holds for the accelerative force of the primary planets on their satellites, the accelerative force of the sun, and the accelerative force of all bodies universally.
Corollary 1 was slightly different in the first edition. The difference is, however, not relevant to our present discussion.
Corollary 2 was identical in all editions.
I.B. Cohen pointed out that the effect Newton was looking for was too small to be detected with the instruments available at the time (Newton 1999 [1726], p. 211).
Corollary 3 was added in the second edition and remained unchanged in the third.
Rule IV was added in the third edition of the Principia: “In experimental philosophy, propositions gathered from phenomena by induction should be considered [haberi debent] either exactly or very nearly true notwithstanding any contrary hypotheses, until yet other phenomena make such propositions either more exact or liable to exceptions [accuratiores reddantur aut exceptionibus obnoxiæ]. This rule should be followed so that arguments based on induction may not be nullified [tollatur] by hypotheses.” (Newton 1999 [1726], p. 796).
In the second edition, Newton changed “sufficiunt” into “sufficiant” and added the sentence “Dicunt utique philosophi (…) potest per pauciora.” (Koyré et al. 1972, vol. II, pp. 550–551).
This has some truth to it, for Newton obviously did not measure the equality of the active gravitational mass and the passive gravitational mass, a point forcefully made in Harper 2002b, pp. 92–94.
For the reader’s convenience I provide the relevant extract from the letter that Cotes received: “[T]he Difficulty you mention wch lies in these words [Et cum Attractio omnis mutua sit] is removed by considering that as in Geometry the word Hypothesis is not taken in so large a sense as to include Axiomes & Postulates, so in experimental Philosophy it is not to be taken in so large a sense as to include the first Principles or Axiomes wch I call the laws of motion. These Principles are deduced from Phænomena & made general by Induction: wch is the highest evidence that a Proposition can have in this philosophy. And the word Hypothesis is here used by me to signify only such a Proposition as is not a Phænomena nor deduced from any Phænomena but assumed or supposed wthout experimental proof. Now the mutual & mutually equal attraction of bodies is a branch of the third Law of motion & how this branch is deduced from Phænomena you may see in the end of the Corollaries of ye Laws of Motion, p. 22. If a body attracts another body contiguous to it & is not mutually attracted by the other: the attracted body will drive the other before it & both will go away together wth an accelerated motion in infinitum, as it were by a self moving principle, contrary to ye first law of motion, whereas there is no such phænomena in all nature.” (Newton to Cotes, 28 March 1713, Turnbull et al. (1959–1977), vol. V, pp. 396–399, pp. 396–397).
In the original “described” is preceded by “
” (CUL Add. Ms. 3984.14, f. 1r).In the original “rational” is preceded by “
” (ibid.).This was the point Newton made in a letter to Leibniz: “For since celestial motions are more regular than if they arose from vortices and observe other laws, so much so that vortices contribute not to the regulation but to the disturbance of the motions of planets and comets; and since all phenomena of the heavens and of the sea follow precisely, so far as I am aware, from nothing but gravity acting in accordance with the laws described by me; and since nature is very simple, I have myself concluded that all other causes are to be rejected and that the heavens are to be stripped as far as may be of all matter, lest the motions of planets and comets be hindered or rendered irregular [ipse causas alias omnes abdicandas judicavi et cælos materia omni quantum fieri licet privandos ne motus Planetarum et Cometarum impediantur out reddantur irregulares].” (Newton to Leibniz, 16 October 1693, Turnbull et al. (1959–1977), vol. III, pp. 285-289, p. 287 [italics added]).
In other words, Newton was clearly of the ampliative nature of inductive generalizations.
For a recent reconstruction of Newton’s experiments, see Wilson 1999.
Proposition XXIV of Book II established that m 1/m 2 :: (Fm1 × t1²)/(Fm2 × t 2²) obtains for swinging bodies. Since the times are equal, we derive m 1/m 2 :: Fm1/ Fm2 (Corollary 1).
As Harper points out: “Absence of such orbital polarization counts as a phenomenon measuring the equality of ratios of mass to weight toward the Sun at equal distances.” (Harper 2002a, p. 189).
In the second edition of the Principia, Rule III—which has often baffled interpreters—was introduced: “Those qualities of bodies that cannot be intended and remitted [i.e., qualities that cannot be increased and diminished] [intendi & remitti nequeunt] and that belong [competent] to all bodies on which experiments can be made should be taken [habendæ sunt] as qualities of all bodies universally (Newton 1999 [1726], p. 795). At the end of the text to Rule III, Newton noted that gravity “diminishes as bodies recede from the earth” (ibid., p. 796). It may then be objected that Newton seems to be contradicting himself by claiming, on the one hand, that gravity cannot be increased and diminished (and therefore is a universal property), and, on the other hand, that gravity diminishes as a body recedes from the earth. However, the apparent contradiction on Newton’s part easily disappears once we consider relevant manuscript material (post-1713, pre-1717): “All bodies here below are heavy towards ye Earth in proportion to the quantity of matter in ↓each of↓ them. Their gravity ↓in proportion to their matter↓ is not intended or remitted ↓in the same region of the earth by any variety of ↓forms↓ & therefore it cannot be taken away
(…)” (CUL Add. Ms. 3970, f. 243v [italics added], cf. f. 253r). In order to get further understanding of the meaning of “qualities that cannot be intended or remitted”, it is useful to contrast them with qualities that can be intended and remitted. After having discussed the “vertue or disposition” of Island Crystal to produce double refraction, Newton noted: “And as magnetism may be intended & remitted, & and is found only in the Magnet & in iron: so this vertue of refracting the perpendicular rays is greater in Island Crystal less in Crystal of the rock & is not yet found in other bodies.” (CUL Add. Ms. 3970, f. 258r [post 1713, pre-1717]). Rule III instructs us to consider such qualities as qualities that pertain to all bodies universally.The argument based on Rule III as well as the reference to Aristotle and Descartes were added in the second edition and remained unaltered in the third edition.
In the first edition, the first sentence of Corollary 3 was “Itaque Vacuum necessariò datur”.
This final sentence to Corollary 4 was added in the second edition and remained unchanged in the third edition.
Corollary 5 in the second and third edition correspond to Corollary 4 in the first edition.
This corollary was identical in the second and third editions.
Newton noted: “If anyone objects that by this law all bodies on our earth would have to gravitate toward one another, even though gravity of this kind is by no means detected by our senses, my answer is that gravity toward these bodies is far smaller than what our senses could detect, since such gravity is to the gravity toward the whole earth as [the quantity of matter in each of] these bodies to the [quantity of matter in the] whole earth.” (Newton 1999 [1726], p. 811).
I refer to propositions of this type as micro inference-tickets, as they license conclusions about the inverse-square centripetal forces of the micro-particles that constitute a macroscopic body from the overall inverse-square centripetal force exerted by that body.
Huygens’ 1690 account of gravitation was a spherical-vortical account of gravitation which rejected Cartesian vortices. Cf.: “[…] je voudrais bien sçavoir si du depuis [i.e., since the publication of Newton’s Principia in 1687] vous n’avez rien changé à vostre Theorie, parce que vous y faites entrer les Tourbillons de Mr. des Cartes, qui à mon avis sont superflus, si on admet le Systeme de Mr. Newton où le mouvement des Planetes s’explique par la pesanteur vers le Soleil et la vis centrifuga, qui se contrebalancent. Outre que ces Tourbillons Cartesiens faisoient naitre plusieurs difficultés, comme vous verrez pas mes remarques et mesme sans elles vous ne pouviez pas l’ignorer.” (Huygens to Leibniz, 8 February 1690, Huygens 1888-1950, vol. IX, p. 368, cf. Huygens to Leibniz, 11 July 1692, ibid., vol. X, p. 297, cf. Huygens to Leibniz, 12 January 1693, ibid., vol. X, p. 385; for Huygens’ reservations against Cartesianism, see: Huygens to G. Meier, June 1691, ibid., vol. X, pp. 104–105; cf. Huygens 1690, pp. 472–473; cf. Snelders, 1989, pp. 215–219).
I shall refrain from going into the technical details of Newton’s propositions on the shape of the earth, which often contained hidden steps and mathematical results which Newton did not bother to spell out (Greenberg 2006).
For a systematic outline of the idea of trans-theoretical communication, see Batens 1985.
↓hujus↓ causae, & causa 
causae prioris redderetur & sic deinceps usque donec ad causam primam deventum sit.”
↓ 
↓sunt↓, dein horum causae proximae, & postea causae causarum 
eruenda; ac tandem a causis ↓supremis causarum↓ per phaenomena stabilitis, ad ↓causas↓ caus 
↓eorum effectus↓, ↓
↓ argumentando a priori, descendere licebit. 
Philosophia naturalis non in opinionibus Metaphysicis, sed in Principiis propijs fundanda est; & haec [end of text]” (CUL Add. Ms. 3970, f. 109v ).
” (CUL Add. Ms. 3984.14, f. 1r).
” (ibid.).
(…)” (CUL Add. Ms. 3970, f. 243v [italics added], cf. f. 253r). In order to get further understanding of the meaning of “qualities that cannot be intended or remitted”, it is useful to contrast them with qualities that can be intended and remitted. After having discussed the “vertue or disposition” of Island Crystal to produce double refraction, Newton noted: “And as magnetism may be intended & remitted, & and is found only in the Magnet & in iron: so this vertue of refracting the perpendicular rays is greater in Island Crystal less in Crystal of the rock & is not yet found in other bodies.” (CUL Add. Ms. 3970, f. 258r [post 1713, pre-1717]). Rule III instructs us to consider such qualities as qualities that pertain to all bodies universally.References
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Steffen Ducheyne is indebted to Eric Schliesser and George E. Smith to benefit from their forthcoming publication, to The Provosts and Syndics of Cambridge University Library for permission to quote from the Portsmouth and Maclessfield Collection, and to Helmut Pulte, Henk de Regt and the two anonymous referees of this journal for their valuable comments and suggestions. Convention for my transcriptions of Newton’s manuscripts: arrows pointing downwards (↓…↓) indicate that the text in between them was inserted above Newton’s original interlineation. Arrows pointing upwards (↑…↑) indicate that the text in between them was inserted under Newton’s original interlineation. All other text-editorial features are as in the original.
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Ducheyne, S. Understanding (in) Newton’s Argument for Universal Gravitation. J Gen Philos Sci 40, 227–258 (2009). https://doi.org/10.1007/s10838-009-9096-y
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DOI: https://doi.org/10.1007/s10838-009-9096-y