Kirsten Walsh writes…
Lately, I’ve been thinking about Newton’s work on the tides. In the Principia Book 3, Newton identified the physical cause of the tides as a combination of forces: the Moon and Sun exert gravitational pulls on the waters of the ocean which, together, cause the sea levels to rise and fall in regular patterns. This theory of the tides has been described as one of the major achievements of Newtonian natural philosophy. Most commentators have focussed on the fact that Newton extended his theory of universal gravitation to offer a physical cause for the tides—effectively reducing the problem of tides to a mathematical problem, the solution of which, in turn, provided ways to establish various physical features of the Moon, and set the study of tides on a new path. But in this post, I want to focus on the considerable amount of empirical evidence concerning tidal phenomena that underwrites this work.
Let’s begin with the fact that, while Newton’s empirical evidence of tidal patterns came from areas such as the eastern section of the Atlantic Ocean, the South Atlantic Sea, and the Chilean and Peruvian shores of the Pacific Ocean, Newton never left England. So where did these observational records come from?
Newton’s data was the result of a collective effort on a massive scale, largely coordinated by the Royal Society. For example, one of the earliest issues of the Philosophical Transactions published ‘Directions for sea-men bound for far voyages, drawn up by Master Rook, late geometry professour of Gresham Colledge’ (1665: 140-143). Mariners were instructed “to keep an exact Diary [of their observations], delivering at their return a fair Copy thereof to the Lord High Admiral of England, his Royal Highness the Duke of York, and another to Trinity-house to be perused by the R. Society”. With respect to the tides, they were asked:
“To remark carefully the Ebbings and Flowings of the Sea, in as many places as they can, together with all the Accidents, Ordinary and Extraordinary, of the Tides; as, their precise time of Ebbing and Flowing in Rivers, at Promontories or Capes; which way their Current runs, what Perpendicular distance there is between the highest Tide and lowest Ebb, during the Spring-Tides and Neap-Tides; what day of the Moons age, and what times of the year, the highest and lowest Tides fall out: And all other considerable Accidents, they can observe in the Tides, cheifly neer Ports, and about Ilands, as in St. Helena’s Iland, and the three Rivers there, at the Bermodas &c.”
This is just one of many such articles published in the early Philosophical Transactions that articulated lists of queries concerning sea travel, on which mariners, sailors and merchants were asked to report. In its first 20 years, the journal published scores of lists of queries relating to the tides, and many more reports responding to such queries. This was Baconian experimental philosophy at its best. The Royal Society used its influence and wide-ranging networks to construct a Baconian natural history of tides: using the method of queries, they gathered observational data on tides from all corners of the globe which was then collated and ordered into tables.
Newton’s engagement with these observational records is revelatory of his attitudes and practices relating to Baconian experimental philosophy. Firstly, especially in his later years, Newton was regarded as openly hostile towards natural histories. However, here we see Newton explicitly and approvingly engaging with natural histories. For example, in his discussion of proposition 24, he drew on observations by Samuel Colepresse and Samuel Sturmy, published in the Philosophical Transactions in 1668, explicitly offered in response to queries put forward to John Wallis and Robert Boyle in 1665:
“Thus it has been found by experience that in winter, morning tides exceed evening tides and that in summer, evening tides exceed morning tides, at Plymouth by a height of about one foot, and at Bristol by a height of fifteen inches, according to the observations of Colepress and Sturmy” (Newton, 1999: 838).
I have argued previously that Newton was more receptive to natural histories than is usually thought. The case of the tides offers additional support for my argument. Newton’s notes and correspondence show that, from as early as 1665, he was heavily engaged in the project of generating a natural history of the tides, although he never contributed data. And eventually, he was able to use these empirical records to theorise about the cause of the tides. This suggests that Newton didn’t object to using natural histories as the basis for theorising. Rather, he objected to treating natural histories as the end goal of the investigation.
Secondly, I have previously discussed the fact that Newton seldomly reported ‘raw data’. The evidence he provided for Phenomenon 1, for example, included calculated average distances, checked against the distances predicted by the theory. Newton’s empirical evidence on the tides, as reported in the Principia, was similarly manipulated and adjusted with reference to his theory. Commentators have largely either condemned or ignored this ‘fudge factor’, but such adjustments are ubiquitous in Newton’s work, suggesting that they were a key aspect of his practice. Newton recognised that ‘raw data’ had limited use: to be useful, data needed to be analysed and interpreted. In short, it needed to be turned into evidence. The Baconians appear to have recognised this: queries guide the collection of data, which is then ordered into tables in order to reveal patterns in the data. As this case makes clear, however, Newton’s theory-mediated manipulation of the data went beyond basic ordering, drawing on causal assumptions to reveal phenomena from the data.
Thirdly, this case emphasises Newton’s science as embedded in rich social, cultural and economic networks. The construction of this natural history of tides was an organised group effort. That Newton had access to data collected from all over the world was the result of hard work from natural philosophers, merchants, mariners and priests who participated in the accumulation, ordering and dissemination of this data. Further, the capacities of that data to be collected itself followed the increasingly global trade networks reaching to and from Europe. Newton’s work on the tides was the very opposite of a solitary effort.
On this blog, we have noted in passing, but not explored in depth, the crucial roles played by travellers’ reports and information networks in Baconian experimental philosophy. Newton’s study of the tides is revelatory of the attitudes and practices of early modern experimental philosophers with respect to such networks. I shall discuss these in my next post.
Kirsten Walsh writes…
In my last few posts, I’ve discussed some of the lesser-known aspects of Newton’s work. In my first post on this topic, I talked generally about how we might consider Newton’s chymistry, theology and Church history to be methodologically continuous with the experimental philosophy of the Principia and the Opticks. And in my second post I considered Newton’s alchemical tract, now referred to as ‘Of Natures obvious laws and processes in vegetation’, and identified several features that seem to highlight Newton’s early (albeit tacit) commitment to experimental philosophy.
In today’s post, I’ll begin to discuss an important but relatively understudied aspect of Newton’s work: his theological methodology. Since this blog is primarily concerned with early modern experimental philosophy, I’m going to start with the famous passage from the General Scholium to the Principia: “to treat of God from phenomena is certainly a part of natural philosophy”. The meaning of the first part of the statement is clear: we have epistemic access to God via our observations of the world. And so, from the phenomena, we can learn about God’s nature and divine will—in the same way that we can learn about, say, gravity. But in what sense is this ‘a part of natural philosophy’? That is, how does this statement fit with Newton’s stated views regarding that topic?
In the General Scholium, Newton explains that, while the laws of motion explain why celestial bodies move in Keplerian orbits, they cannot explain how celestial bodies come to be in their present orbits. And so, he writes, “This most elegant system of the sun, planets, and comets could not have arisen without the design and dominion of an intelligent and powerful being”. Prima facie, examples such as this don’t fit with Newton’s natural philosophical method. He seems to employ non-empirical background assumptions about the nature of God’s intervention to plug gaps in his theory. This looks dangerously close to feigning hypotheses. Moreover, from these assumptions, he seems to leap right to the first cause, blocking further scientific inquiry, and contradicting the ‘satis est’ attitude he adopts in his natural philosophy.
I think, however, that Newton’s treatment of God from phenomena is more consistent with his method of natural philosophy than it first appears. But to recognise this, we need to look more closely at how Newton approaches God from the phenomena. In fact, Newton treats of God from phenomena in several different ways. One approach is to move directly from the phenomena to the nature of God’s interactions with the world. For example, in the General Scholium, Newton notes that all celestial bodies move in regular orbits, which tells us that neither planets nor comets encounter any kind of resistance in their orbits. Newton uses the lack of resistance to argue that celestial bodies do not move through vortices but through empty space. However, this phenomenon also reveals that, while God is omnipresent and substantial, he is not material:
God is one and the same God always and everywhere. He is omnipresent not only virtually but also substantially; for action requires substance. In him all things are contained and move, but he does not act on them nor they on him. God experiences nothing from the motions of bodies; the bodies feel no resistance from God’s omnipresence (Principia, Cohen & Whitman translation, pp. 941-942).
Another way Newton approaches God is to ask after the nature of his interventions. Here, Newton identifies explanatory gaps between phenomena and theory, and asks whether God could be acting, and if so, what is the nature of that action? For example, in a letter to Bentley Newton notes that that his theory of universal gravitation can explain the motions of the planets, but not their original sizes or positions in the solar system. The latter, he concludes, can only be explained by divine intervention. That God works to achieve such perfect balance in the system of the world tells us that he is “not blind and fortuitous, but very well skilled in mechanics and geometry”. Here, the insight is that gravity can destabilise the system of the world—and so the physical world constantly tends towards decay. Thus, God is required to use his skills of design and maintenance to prevent this from happening.
Neither approach looks like ‘feigning hypotheses’. For one thing, Newton doesn’t allow his thinking about God to justify or constrain his theorising. Rather, God is introduced after the physical theory has been established to see what it can teach us about the nature of his intervention. And for another thing, Newton’s ideas about God don’t result from speculation, but from rigorous study of both scripture and the natural world, and the careful application of reason. It is from our post-Enlightenment perspective that rigorous study of scripture seems to fall outside of natural philosophy.
Moreover, Newton’s introduction of God doesn’t stop inquiry. Rather, it raises further questions about how and why God intervenes on the system of the world. And these, in turn, lead back to physical inquiry. For example, Newton’s discussions about God’s role in the sizing and positioning of the planets leads to a fruitful inquiry about the specific compositions of the planets and why the biggest planets are furthest from the Sun. That the inquiry continues highlights the fact that Newton doesn’t view the cause of a given phenomenon as either natural or supernatural: every phenomenon is generated by both natural and supernatural causes. That is, physical objects act on one another as natural causes, subject to physical and mathematical laws, but God is the first-cause, and hence, behind all actions. And so, when Newton treats of God from phenomena, the inquiry doesn’t end there.
Finally, as a good experimental philosopher, Newton knows that we only have direct epistemic access to the evidence of our senses, so our knowledge of God is necessarily limited. However, as he makes clear in query 28 of the Opticks, we mustn’t be put off by our inability to discover the first cause directly. Instead, we must work to uncover intermediate causes—proximate causes—and work slowly to uncover deeper and deeper levels of causes until we come to the first cause. And, importantly, these intermediate causes can also reveal the nature of God:
And these things being rightly dispatch’d, does it not appear from Phænomena that there is a Being incorporeal, living, intelligent, omnipresent, who in infinite Space, as it were in his Sensory, sees the things themselves intimately, and thoroughly perceives them, and comprehends them wholly by their immediate presence to himself… And though every true Step made in this Philosophy brings us not immediately to the Knowledge of the first Cause, yet it brings us nearer to it, and on that account is to be highly valued (Optics, Dover edition, p. 370).
Kirsten Walsh writes…
In my last post, I started thinking about the lesser-known aspects of Newton’s work—his chymistry, theology and Church history—in order to learn more about his methodology. In particular, I wondered what kinds of methodological continuity, if any, there are across his many projects. In this post, I’ll focus on a tract, now referred to as ‘Of Natures obvious laws and processes in vegetation’, from Newton’s alchemical corpus. Newton probably wrote this piece in 1672—the year that he wrote his ‘New Theory of Light and Colour’. The piece represents Newton’s attempt to give a synopsis of his early alchemical reading and to come up with, essentially, a ‘theory of everything’.
There is a great deal to interest us in this tract, including an early mechanical-æthereal theory of gravity and a discussion of the nature of God. But here, I’ll focus on one idea: Newton’s distinction between mechanical processes and vegetative processes. Where ‘vegetation’ is the generative process through which animals, plants and minerals grow, putrefy and regenerate themselves, ‘mechanical’ processes involve adding, subtracting and rearranging parts (described as “a gross mechanical transposition of parts” (5r)). Newton considers these processes to be exhaustive: “Natures actions are either vegetable or purely mechanical” (5r).
Newton’s discussion of this idea highlights several methodological continuities. I’ll discuss two of them here.
The first concerns the way Newton infers physical processes from observed phenomenal patterns. Drawing comparisons across the ‘three kingdoms of nature’—animal, vegetable and mineral—Newton notes that some metals grow, putrefy and regenerate within the Earth, much in the way that trees grow out of the earth, suggesting that some metals and minerals ‘vegetate’. In contrast, some salts and minerals appear to generate by the simple combining and arranging of parts. And so Newton proposes that there are two distinct processes at work in nature: vegetative and mechanical. The postulated distinction in turn guides further exploration of natural phenomena, enabling him to unify some patterns of generation and to differentiate others. The phenomena he explores go well beyond the initial cluster of metals and salts, eventually including organic life, heat and flame, and gravitation. And these phenomena, in turn, offer further clues about nature’s hidden processes. In short, observed phenomena illuminate underlying processes, which, in turn, guide further exploration of phenomena.
We see Newton engaging in similar inferential patterns in both the Principia and the Opticks. In the Principia, from the observed Keplerian orbits of the planets, Newton infers the inverse-square centripetal force. The inverse-square force, in turn, guides Newton’s exploration of other celestial phenomena, allowing him to calculate the motions of comets, the shapes of planets, and also to correct for perturbations of orbits. Similarly, in the Opticks, from the phenomena of the unequal refraction of light, Newton infers the heterogeneity of white light. The heterogeneity of white light, in turn, guides Newton’s exploration and theorising of other optical phenomena, including the colours of thin plates, thick plates and coloured fringes. In other words, this inferential feedback loop between phenomena and processes appears to be a standard feature of Newton’s methodology. In Query 31 of his Opticks, Newton describes this in terms of the joint methods of ‘analysis’ and ‘composition’. ‘Of Natures obvious laws’ might be considered an early manifestation of this method.
A second feature worth considering is the way Newton operationalised the concept of vegetation in order to develop a quantitative test for such processes. The term ‘vegetative’ was familiar to those concerned with the study of life and vitalism, and Newton was happy to speculate on the nature of this process:
The principles of her vegetable actions are noe other than the seeds or seminal vessels of things those are her onely agents, her fire, her soule, her life (5r).
But such a qualitative description of the process wasn’t very helpful for establishing which phenomena were generated by which processes. Especially since, as he noted, some natural phenomenon might appear to have been generated through vegetative processes, but in fact be produced mechanically. The way to distinguish between the two kinds of effects was to analyse them—i.e. break the entity down into its parts—and then try to put it back together again. If the recomposition was successful, then this indicated mechanical processes, if it wasn’t, then vegetative processes were operative. And so the methods of resolution and composition, or analysis and synthesis, provided him with a way of testing for vegetative processes. And thus ‘vegetation’ was effectively operationalised: the concept was defined through the operations which tested for it.
We see Newton engaging in a similar practice in his study of interference phenomena. His hypothesis on the nature of light postulated a hypothetical cause for the observed pattern of coloured rings: an æthereal ‘pulse’. Operationalising the concept of a pulse gave Newton a unit of measurement and, eventually, a way of formalising and abstracting the explanation. I have argued that Newton’s hypotheses played sophisticated supporting roles in his optical investigations. The role performed by the hypothesis of vegetation in this alchemical tract, and the way Newton links it to observation and experiment, looks similarly rich and sophisticated.
This feature helps me to say something more specific about, what I have termed, Newton’s ‘rhetorical style’. As I have noticed in previous posts, Newton took familiar terms and stretched them to fit his methodology. It is well-known that he did this with physical concepts such as ‘force’ and ‘mass’, and I have shown, on this blog, that he did this with methodological concepts such as ‘query’, ‘hypothesis’ and ‘principle’. Bill Newman has demonstrated that Newton also borrowed the concepts of ‘analysis’, ‘synthesis’ and ‘redintegration’ from chymistry and adapted them to his optical work—massaging them to fit his own needs. But Newton’s use of ‘vegetation’ highlights a particular feature of his rhetorical style: Newton took common terms with imprecise, qualitative meanings and defined them in terms of methods which measure, quantify or detect certain processes. And so what was really innovative in this case wasn’t that Newton used analysis and synthesis to investigate salts and metals, but rather, that he defined mechanical and vegetative processes in terms of that kind of intervention. In other words, Newton’s rhetorical style involved operationalising concepts—turning them into tools of measurement.
I closed my last post by pointing out that Newton’s efforts to pass off his published work as experimental philosophy may well have been politically motivated: by describing his work as ‘experimental philosophy’, he was signalling his commitment as much to the Royal Society as to observation- and experiment-based theorising. Newton’s chymical papers were circulated much more privately and so, presumably, the same political motivations didn’t apply. Moreover, Newton did not describe himself as an ‘experimental philosopher’ in his published work until 1713. So it is not surprising that we find no explicit mention of experimental philosophy or the methods of the Royal Society in this tract, which predates that explicit declaration by at least 40 years. However, the two features I’ve identified highlight Newton’s commitment to observation- and experiment-based theorising. That this commitment is evident, absent of any political pressure, suggests that it was genuine.
A guest post by Hanna Szabelska.
Hanna Szabelska writes …
Gabrielle Émilie le Tonnelier de Breteuil, la Marquise du Châtelet (1706–1749), ambitious femme savante and Voltaire’s muse had an unusual penchant for physics and mathematics, which pushed her towards conducting and discussing experiments.
By way of an example, to show that heat and light, as opposed to rarefaction – the distinctive property of fire – are nothing but its modes that do not necessarily accompany each other, she made use of the phenomenon of bioluminescence while imitating René-Antoine Ferchault de Réaumur’s experiment:
Dails [pholads] and glowworms are luminous without giving off any heat, and water does not extinguish their light. M. Réaumur even reports that water, far from extinguishing it, revives the light of dails [pholads]. I have verified this on glowworms, I have plunged some in very cold water, and their light was not affected. 
Since she held Newton’s experimental precision in the Opticks in high esteem, to the point that she acquired knowledge to do experiments about different degrees of heating among primitive colours on her own , du Châtelet had reservations about Charles du Fay’s attempt to reduce the seven primitive colours to three.
The following passages are characteristic of her reliance on experiments. Letter 152. To Pierre Louis Moreau de Maupertuis [about the first of December 1738]
I know the Optics by Mr Newton nearly by heart and I must confess that I did not think it possible to call into question his experiments on refrangibility.
A tremendous series of experiments [une furieuse suite d’expériences] is necessary to undermine the truth that Mr Newton seems to have felt with all his senses. However, since I have not seen du Fay’s experiments I suspend my judgement… 
However, as much as she was fascinated by the potential of experimental philosophy, du Châtelet had an acute awareness of her own limitations and those of available apparatus. For example, she ventures the generalization that the tactile sensations of various colours differed analogically from the visual ones but admits her inability to conduct a decisive experiment and confides this task to the judges of her essay on fire .
Moreover, one can detect irony in her remarks about a defective camera obscura designed for optical experiments. In a letter to Algarotti she complains that:
The abbé Nollet has sent me my camera obscura, more obscure than ever; he claims that you have found it very clear in Paris: the sun of Cirey must be, therefore, unfavourable to it. 
Imperfect instruments could distort the results of experiments but so could an experimenter’s understanding of them if, like Locke or Leibniz, one takes the camera obscura as a metaphor of both visual perception and ideas based on it. Such epistemological doubts were also preying on du Châtelet’s mind, giving her natural philosophy a metaphysical depth. Thus, having enumerated some great names of experimental philosophy, she comes to the conclusion that:
It seems that a truth that so many competent natural philosophers have not been able to discover is not to be known by humanity. With regard to first principles, only conjectures and probabilities are within our reach. 
Interestingly, for Voltaire, this amalgam of the experimental and the speculative, imbued with the venustas muliebris of style, as Cicero would put it, was just the Marquise’s way of life, expression of her complex personality, philosophical to the backbone, but not easy to deal with.
The Marquise’s experimental inclination, under the spell of Leibnizian speculative philosophy, gave rise to sophisticated arguments, that often elude the language of modern physics. The devil is, as usual, in the details so let’s analyse some of them.
One of the most instructive stories is du Châtelet’s disagreement with Voltaire on the nature of fire, in particular on the question of its weight. While assisting with his experiments (cf. Peter Anstey’s post), she came to different conclusions and started working on her own essay in secret.
Voltaire evidently tried hard to interpret his results through the lens of a Newtonian experimentalist: to show that fire has weight and is subject to the force of gravity. Therefore, he downplays Herman Boerhaave’s reservations concerning the acquisition of weight by heated bodies  and opts for Peter van Musschenbroek‘s interpretation .
I visited an iron forge to do an experiment [exprès] and whilst I was there I had all the scales replaced. The [new] iron scales were fitted with iron chains instead of ropes. After that I had both the heated and the cooled metal within the range of one pound to two thousand pounds weighed. As I never found the smallest difference in their weights I reasoned as follows: the surface of these enormous masses of heated iron had been enlarged due to their dilation, therefore they must have had less specific gravity. So I can conclude – even from the fact that their weight stays the same irrespective of whether they are hot or cool – that fire had penetrated the masses of iron adding precisely as much weight as dilation made them lose, and consequently, fire has real weight. 
To save his Newtonian face, Voltaire jumps to hypotheses in a rather non-Newtonian manner:
However, although no experiment to date seems to have shown beyond any doubt the gravity and impenetrability of fire, it is apparently impossible not to assume them. 
Despite his efforts, Voltaire’s conclusion remains caught in a limbo between mere hypothesis and a proposition deduced from phenomena and generalized by induction.
Of course, Newton would not have been himself had not his rejection of hypotheses been nuanced  but even so the leap in Voltaire’s reasoning seems a hidden thorn in his Newtonian flesh.
The conceptualization of Boerhaave’s experiment offered by du Châtelet is, on the contrary, more consistent with the data than that of her companion . But on the other hand, it opens the way for establishing fire as one of the grand metaphysical principles of the Universe:
…but claiming that fire has weight is to destroy its nature, in a word, to take away its most essential property, that by which it is one of the mainsprings of the Creator. 
The action of fire, whether it is concealed from us or perceptible, can be compared to force vive [living force] and force morte [dead force]; but just as the force of bodies is perceptively stopped without being destroyed, so fire conserves in this state of apparent inaction the force by which it opposes the cohesion of the particles of bodies. And the perpetual combat of this effort of fire and of the resistance bodies offer to it, produces almost all the phenomena of nature. 
The passages above are to be found in both versions of du Châtelet’s essay on fire: the original (1739, reprinted in 1752 by the Academy) and the revised one from 1744 (published by the Marquise’s own assumption by Prault, fils). However, it is worth noting that her conceptual framework became more consistently Leibnizian with time. It is this development that I will discuss in my next post.
- Trans. Isabelle Bour and Judith P. Zinsser; Du Châtelet, Selected Philosophical and Scientific Writings, ed. J. P. Zinsser, Chicago: University of Chicago Press, 2009, p. 64.
- Dail is an obsolete French term for pholade, pholas dactylus. (Du Châtelet, Dissertation sur la nature et la propagation du feu, Paris: Chez Prault, Fils,1744, p. 4.)
- Dissertation, p. 69.
- du Fay, Observations physiques sur le meslange de quelques couleurs dans la teinture, “Histoire de l’Académie royale des sciences … avec les mémoires de mathématique & de physique,” 1737, p. 267.
- Les lettres de la Marquise du Châtelet, ed. Theodore Besterman [Genève: Institut et Musée Voltaire, 1958], vol. 1, pp. 273–274.
- Dissertation, pp. 70–71.
- Letter 63. To Francesco Algarotti, in Cirey, the 20th [of April 1736], Les lettres de la Marquise du Châtelet, vol. 1, p. 112.
- Trans. I. Bour and J. P. Zinsser; Du Châtelet, Selected Philosophical…, p. 71.; Dissertation, p. 17.
- Hermannus Boerhaave, “De artis theoria,” in: Elementa chemiae, Tomus primus, editio altera [Parisiis: Apud Guillelmum Cavelier, 1733], p. 193 ff.
- Petrus van Musschenbroek, Elementa physicæ conscripta in usus academicos, editio prima Veneta [Venetiis: Apud Joannem Baptistam Recurti, 1745], p. 323 ff.
- cf. Bernard Joly, “Voltaire chimiste: l’influence des théories de Boerhaave sur sa doctrine du feu,” Revue du Nord 77, No 312 (1995): 817–843.
- Voltaire, “Essai sur la nature du feu et sur sa propagation,” in Recueil des pièces qui ont remporté le prix de l’Académie royale des Sciences en 1738, par M. Rouillé de Meslay [Paris: de l’Imprimerie Royale, 1739], p. 176.
- Voltaire, “Essai sur la nature du feu,” Recueil, p. 180.
- cf. e.g. William L. Harper, Isaac Newton’s Scientific Method: Turning Data into Evidence about Gravity and Cosmology (Oxford: Oxford University Press, 2011), p. 44.
- Dissertation, p. 24, 33 ff.
- Trans. I. Bour and J. P. Zinsser; Du Châtelet, Selected Philosophical…, p. 80; Dissertation, p. 40.
- Trans. I. Bour and J. P. Zinsser; Du Châtelet, Selected Philosophical…, pp. 84–85; Dissertation, p. 52.
Kirsten Walsh writes…
Newton is often taken to have spawned two important, but different, sciences: an experimental science exemplified in the Opticks, and a mathematical science exemplified in the Principia. I. Bernard Cohen and George Smith, for example, write:
There is, perhaps, no greater tribute to the genius of Isaac Newton than that he could thus engender two related but rather different traditions of doing science.
Like many commentators, they emphasise the differences between the austere, formal mathematism of Newton’s so-called ‘rational mechanics’ and the complex and sophisticated experimentalism of his work on light and colour. And so, the two works are typically taken to exemplify very different methodologies.
In contrast, on this blog, I have emphasised the common features, rather than the differences—presenting a more integrated account of Newton’s methodology. For example, I have argued that his claim, that the Principia is a work of experimental philosophy, is something we should take seriously. And so the mathematico-experimental method is a feature of both the Opticks and the Principia. Moreover, I have argued that Newton’s mathematico-experimental method can be broadly characterised by an epistemic triad: a three-way epistemic division between theories, hypotheses and queries. The epistemic triad drives Newton’s optical work and his rational mechanics in a trajectory from experiment to certainty, using mathematical reasoning.
While the Opticks and the Principia represent two fields to which Newton made important contributions, these impressive tomes do not signify the entirety of his research output—nor even the bulk. During his lifetime, Newton produced vast quantities of written work on chymistry, theology and Church history, as well as mathematics. Over several posts, I plan to explore some of this less well-known work in order to learn more about Newton’s methodology. In particular, I want to see what kinds of methodological continuity, if any, there are between his many projects.
This may seem like a fool’s errand. Indeed, these lesser-known parts of Newton’s research have a poor reputation. One idea, floated by Jean-Baptiste Biot in his 1829 biography, was that Newton’s intellectual life divided naturally in two: prior to his mental breakdown in 1692, Newton’s life was sane, rational and scientific, but afterwards was mad, irrational and religious. And so Newton’s alchemical and theological manuscripts are often dismissed as the half-baked musings of an old man. In more recent times, however, commentators such as Betty Jo Teeter Dobbs, William R. Newman, Rob Iliffe and Sarah Dry (to name just a few!) have aimed to redress this situation. They have demonstrated that Newton’s alchemical and theological pursuits were as much a part of his intellectual life as the optics, rational mechanics and mathematics, for which he is famous. So, firstly, if there was any kind of cleavage, it was not along disciplinary lines, and secondly, these intellectual pursuits should be counted as serious scholarship—not simply to be swept under the proverbial rug.
So what sorts of continuities should we expect to find? In the remainder of this post, I’ll offer a few preliminary suggestions.
One striking feature of Newton’s published scientific work is how methodologically reflective it was. Perhaps we should expect similar reflections in his manuscripts on chymistry, theology or Church history. Indeed, a cursory look at the collection shows that Newton approached chymistry, theology and Church history with the same persistence and vigour that we find in his other work. Moreover, we can recognise several of the same methodological and foundational concerns. For example, Newton’s interest in the restoration of an ancient tradition of knowledge that has been lost or corrupted, and the view that reason, hard work and disciplined empirical research are always preferable to speculation.
Another feature of Newton’s work that I have discussed on this blog is what I call his ‘rhetorical style’: Newton borrowed familiar terms and bent them to his own needs. He is, moreover, best characterised as a methodological omnivore—he read widely on different methodologies and approaches, and selected from among them the best tools for the job. We might expect to find the same thing in his chymistry and theology. Again, my preliminary reading offers some support. Newton appears to have been interested in all aspects of chymistry—a heavily experimental discipline, often with a pragmatic eye to profit, as much about developing chemical technologies and pharmaceuticals as it is about turning base metals into gold. However, while Newton worked on the typical alchemist’s project of deciphering ancient myths, he doesn’t seem to have drunk the Kool-Aid. He appears to have been much more concerned with linking his chymical research to his more mainstream science—for example, his matter theory. In short, in these manuscripts, we can recognise the same desire to penetrate appearances and arrive at the fundamental truths of nature that we find in his physics.
Following on from this, we might also expect to find a concern for unification: the idea that Newton’s many topics of investigation are in fact part of a larger project. For example, in Query 31 of the Opticks, Newton argues for both ontological and methodological unification. Again, looking briefly at some of his alchemical manuscripts, we see a similar preoccupation. Newton’s discussions of the ‘vegetative spirit’, for example, offer insight into the ways in which the various strands of his scholarly endeavours, including chymistry and theology, were united under one grand scheme.
When understanding the development of Newton’s thought, I often find it helpful to distinguish between Public-Newton and Private-Newton. I have argued that there are important methodological differences between the work that Newton published (and hence, was willing to assert and defend) and the work he kept private. While the former conforms, in some sense, to the experimental philosophy, the latter is typically much more speculative. The distinction is particularly useful when considering Newton’s optical work, where we find stark differences between draft material and the final published version. But I suspect it won’t be so useful once we turn to his chymistry, theology and Church history, where many of Newton’s unpublished manuscripts were in circulation—some only among his closest circle of like-minded friends, and others, much more widely. And yet, this raises one final issue. Newton’s efforts to pass off his published work as experimental philosophy may well have been politically motivated: by describing his work as ‘experimental philosophy’, he was signalling his commitment as much to the Royal Society as to observation- and experiment-based theorising. His chymical, theological and Church history manuscripts were circulated much more privately—and presumably the same political motivations did not apply. When working outside the jurisdiction of the Royal Society, did Newton conform to the experimental philosophy?
I’d love to hear your thoughts on this!
Kirsten Walsh writes…
In the Principia, Newton claimed to be doing experimental philosophy. Over my last three posts, I’ve wondered whether we can interpret his so-called ‘experimental philosophy’ as Baconian. In the first two posts, I identified methodological similarities between Bacon and Newton: first, the use of crucial instances; second, the use of Baconian induction. In each case, I concluded that, without some sort of textual evidence clearly tying Newton’s method to Bacon’s, such similarities don’t demonstrate influence. In my third post, I tried a different approach: I considered Mary Domski’s claim that Newton’s Principia should be considered Baconian because members of the Royal Society recognised, and responded to, it as part of the Baconian tradition. While Domski’s argument was fruitful in helping us better to understand what’s at stake in discussions of influence, I raised several concerns with her narrative. In this post, I shall address those concerns in more detail.
Let’s focus on Domski’s account of how Locke reacted to Newton’s Principia. Domski argues that Locke regarded Newton’s mathematical inference as the speculative step in the Baconian program. That is, building on a solid foundation of observation and experiment, Newton was employing mathematics to reveal forces and causes. In short, Domski suggests that we read Locke’s Newton as a ‘speculative naturalist’ who employed mathematics in his search for natural causes. Last time, I expressed two concerns with this account. Firstly, ‘speculative naturalist’ looks like a contradiction in terms (I have discussed the concept of ‘speculative experimental science’ here), and surely neither Locke nor Newton would have been comfortable with the label. Secondly, there’s a difference between being part of the experimental tradition founded by Bacon, and being Baconian. Domski’s discussion of the reception of the Principia establishes the former, but not necessarily the latter.
We can get more traction on both of these concerns by considering Peter Anstey’s account of how the Principia influenced Locke. Anstey argues that Newton’s achievement forced Locke to revise his views on the role of principles in natural philosophy. In the Essay, Locke offers a theory of demonstration—the process by which one can reason from principles to certain truths via the agreement and disagreement of ideas. In the first edition, Locke argued that this method of reasoning was only possible in mathematics and moral philosophy, where one could reason from certain principles. Due to limitations of human intellect, such knowledge was not possible in natural philosophy. Instead, one needed to follow the Baconian method of natural history which provided, at best, probable truths. However, Anstey shows us that, by the late 1690s, Locke had revised his account of natural philosophy to admit demonstration from ‘principles that matter of fact justifie’ (that is, principles that were discovered by observation and experiment).
I now draw your attention to two features of this account. Firstly, Newton’s scientific achievement—his theory of universal gravitation—as opposed to his successful development of a new natural philosophical method per se forced Locke to revise his position on demonstration from principles. (A while ago, Currie and I noted that this situation is to be expected, if we take the ESD seriously.) This feature should make us suspicious of Domski’s claim that Newton’s Principia was taken to exemplify the speculative stage of Baconian natural philosophy. Locke did not see Newton’s achievement as a system of speculative hypotheses, but as genuinely empirical knowledge, demonstrated from principles that are justified by observation and experiment. Newton had not constructed a Baconian natural history, but nor had he constructed a speculative system. Rather, Locke recognised Newton’s achievement as something akin to a mathematical result—one which his epistemological story had better accommodate. This forced him to extend his theory of demonstration to natural philosophy. And so, by the late 1690s, we find passages like the following:
“in all sorts of reasoning, every single argument should be managed as a mathematical demonstration; the connection and dependence of ideas should be followed, till the mind is brought to the source on which it bottoms, and observes the coherence all along” (Of the Conduct of the Understanding).
Secondly, Anstey emphasises that Locke didn’t regard Newton’s mathematico-experimental method as Baconian, but only as consistent with his, Locke’s, theory of demonstration. (Anstey also claims that Locke never fully integrated the revisions required to his view of natural philosophy in the Essay.) On this blog, we have suggested that, in the 18th century, a more mathematical experimental natural philosophy displaced the natural historical approach. And Anstey has offered a sustained argument for this position here. He argues that the break was not clean cut, but in the end in Britain mathematical experimental philosophy trumped experimental natural history. That this break was not clean cut helps to explain why experimental moral philosophers, such as Turnbull, thought they were pursuing both a Baconian and a Newtonian project, and were quite comfortable with this.
Notice that I’ve shifted from the vexed question of the extent to which Bacon influenced Newton, to a perhaps more fruitful line of enquiry: how Newton influenced Locke and others. This is no non sequitur. The members of the Royal Society strove to understand Newton in their terms—namely, in terms of Baconianism and the experimental philosophy. Here, it seems that two conclusions confront us. Firstly, we (again) find that Newton was taken as legitimately developing experimental philosophy by emphasising both the role of experimentally-established principles of natural philosophy and the capacity of mathematics to carry those principles forward. These aspects are, at best, underemphasised in Bacon and certainly missing from the Baconian experimental philosophy adopted by many members of the Royal Society. Secondly, we see that Newton’s influence on Locke was due, at least in part, to his scientific achievements. Newton did not argue directly with Locke’s epistemology or method, nor did Locke take Newton’s methodology as a replacement for his own. Rather, Locke took Newton’s scientific success as an example of demonstration from ‘principles that matter of fact justifie’. This, in turn, necessitated modifications of his own account.
Kirsten Walsh writes…
Lately I have been examining Baconian interpretations of Newton’s Principia. First, I demonstrated that Newton’s Moon test resembles a Baconian crucial instance. And then, I demonstrated that Newton’s argument for universal gravitation resembles Bacon’s method of gradual induction. This drew our attention to some interesting features of Newton’s approach, bringing the Principia’s experimental aspects into sharper focus. But they also highlighted a worry: Newton’s methodology resembling Bacon’s isn’t enough to establish that Newton was influenced by Bacon. Bacon and Newton were gifted methodologists—they could have arrived independently at the same approach. One way to distinguish between convergence and influence is to see if there’s anything uniquely or distinctively Baconian in Newton’s use of crucial experiments and gradual induction. Another way would be if we could find some explicit references to Bacon in relation to these methodological tools. Alas, so far, my search in these areas has produced nothing.
In this post, I’ll consider an alternative way of understanding Baconianism in the Principia. I began this series by asking whether we should regard Newton’s methodology as an extension of the Baconian experimental method, or as something more unique. In answering, I have hunted for evidence that the Principia is Baconian insofar as Newton applied Baconian methodological tools in the Principia. But you might think that whether Newton was influenced by Bacon isn’t so relevant. Rather, what matters is how the Principia was received by Newton’s contemporaries. So in this post, I’ll examine Mary Domski’s argument that the Principia is part of the Baconian tradition because it was recognised, and responded to, as such by members of the Royal Society.
Domski begins by dispelling the idea that there was no place for mathematics in the Baconian experimental tradition. Historically, Bacon’s natural philosophical program, centred on observation, experiment and natural history, was taken as fundamentally incompatible with a mathematical approach to natural philosophy. And Bacon is often taken to be deeply distrustful of mathematics. Domski argues, however, that Bacon’s views on mathematics are both subtler and more positive. Indeed, although Bacon had misgivings about how mathematics could guide experimental practice, he gave it an important role in natural philosophy. In particular, mathematics can advance our knowledge of nature by revealing causal processes. However, he cautioned, it must be used appropriately. To avoid distorting the evidence gained via observation and experiment, one must first establish a solid foundation via natural history, and only then employ mathematical tools. In short, Bacon insisted that the mathematical treatment of nature must be grounded on, and informed by, the findings of natural history.
Domski’s second move is to argue that seventeenth-century Baconians such as Boyle, Sprat and Locke understood and accepted this mathematical aspect of Bacon’s methodology. Bacon’s influence in the seventeenth century was not limited to his method of natural history, and Baconian experimental philosophers didn’t dismiss speculative approaches outright. Rather, they emphasised that there was a proper order of investigation: metaphysical and mathematical speculation must be informed by observation and experiment. In other words, there is a place for speculative philosophy after the experimental stage has been completed.
Domski then examines the reception of Newton’s Principia by members of the Royal Society—focusing on Locke. For Locke, natural history was a necessary component of natural philosophy. And yet, Locke embraced the Principia as a successful application of mathematics to natural philosophy. Domski suggests that we read Locke’s Newton as a ‘speculative naturalist’ who employed mathematics in his search for natural causes. She writes:
[O]n Locke’s reading, Newton used a principle—the fundamental truth of universal gravitation—that was initially ‘drawn from matter’ and then, with evidence firmly in hand, he extended this principle to a wide store of phenomena. By staying mindful of the proper experimental and evidentiary roots of natural philosophy, Newton thus succeeded in producing the very sort of profit that Sprat and Boyle anticipated a proper ‘speculative’ method could generate (p. 165).
In short, Locke regarded Newton’s mathematical inference as the speculative step in the Baconian program. That is, building on a solid foundation of observation and experiment, Newton was employing mathematics to reveal forces and causes.
In summary, Domski makes a good case for viewing the mathematico-experimental method employed in the Principia as part of the seventeenth-century Baconian tradition. I have a few reservations with her argument. For one thing, ‘speculative naturalist’ is surely a term that neither Locke nor Newton would have been comfortable with. And for another thing, although Domski has provided reasons to view Newton’s mathematico-experimental method as related to, and a development of, the experimental philosophy of the Royal Society, I’m not convinced that this shows that they viewed the Principia as Baconian. That is to say, there’s a difference between being part of the experimental tradition founded by Bacon, and being Baconian. I’ll discuss these issues in my next post, and for now, I’ll conclude by discussing some important lessons that I think arise from Domski’s position.
Firstly, we can identify divergences between Newton and the Baconian experimental philosophers. And these could be surprising. It’s not, in itself, his use mathematics and generalisations that makes Newton different—Domski has shown that even the hard-out Baconians could get on board with these features of the Principia. The differences are subtler. For example, as I’ve discussed in a previous post, Boyle, Sprat and Locke advocated a two-stage approach to natural philosophy, in which construction of natural histories precedes theory construction. But Newton appeared to reject this two-stage approach. Indeed, in the Principia, we find that Newton commences theory-building before his knowledge of the facts was complete.
Secondly, the account highlights the fact that early modern experimental philosophy was a work in progress. There was much variation in its practice, and room for improvement and evolution. Moreover, its modification and development was, to a large extent, the result of technological innovation and the scientific success of works like the Principia. Indeed, it was arguably the ability to recognise and incorporate such achievements that allowed experimental philosophy to become increasingly dominant, sophisticated and successful in the eighteenth century.
Thirdly, the account suggests that, already in the late-seventeenth century, the ESD framework was being employed to guide, and also to distort, the interpretation and uptake of natural philosophy. By embracing the Principia as their own, the early modern experimental philosophers intervened on and shaped its reception, and hence, the kind of influence the Principia had. This raises an interesting point about influence.
As I have already noted, it is difficult to establish a direct line of influence stretching from Bacon to Newton. But, by focusing on how Bacon’s program for natural philosophy was developed by figures such as Boyle, Sprat and Locke, we can identify a connection between Bacon’s natural philosophical program and Newton’s mathematico-experimental methodology. That is, we can distinguish between influence in terms of actual causal connections—Newton having read Bacon, for instance—and influence insofar as some aspect of Newton’s work is taken to be related to Bacon’s by contemporary (or near-contemporary) thinkers. Indeed, Newton could have been utterly ignorant of Bacon’s actual views on method, but the Principia might nonetheless deserve to be placed alongside Bacon’s work in the development of experimental philosophy. Sometimes what others take you to have done is more important than what you have actually done!
Kirsten Walsh writes…
Recently, I have been looking for clear cases of Baconianism in the Principia. In my last post, I offered Newton’s ‘moon test’ as an example of a Baconian crucial instance, ending with a concern about establishing influence between Bacon and Newton. Newton used his calculations of the accelerations of falling bodies to provide a crucial instance which allowed him to choose between two competing explanations. However, one might argue that this was simply a good approach to empirical support, and not uniquely Baconian. In this post, I’ll consider another possible Baconianism: Steffen Ducheyne’s argument that Newton’s argument for universal gravitation resembles Baconian induction.
Let’s begin with Baconian induction (this account is based on Ducheyne’s 2005 paper). Briefly, Bacon’s method of ampliative inference involved two broad stages. The first was a process of piecemeal generalisation. That is, in contrast to simple enumerative induction, shifting from the particular to the general in a single step, Bacon recommended moving from particulars to general conclusions via partial or mediate generalisations. Ducheyne refers to this process as ‘inductive gradualism’. The second stage was a process of testing and adjustment. That is, having reached a general conclusion, Bacon recommended deducing and testing its consequences, adjusting it accordingly.
Ducheyne argues that, in the Principia, Newton’s argument for universal gravitation proceeded according to Baconian induction. In the first stage, Newton’s argument proceeded step-by-step from the motion of the moon with respect to the Earth, the motions of the moons of Jupiter and Saturn with respect to Jupiter and Saturn, and the motions of the planets with respect to the Sun, to the forces producing those motions. He inferred that the planets and moons maintain their motions by an inverse square centripetal force, and concluded that this force is gravity—i.e. the force that causes an apple to fall to the ground. And, in a series of further steps (still part of the first stage), Newton established that, as the Sun exerts a gravitational pull on each of the planets, so the planets exert a gravitational pull on the Sun. Similarly, the moons exert a gravitational pull on their planets. And finally, the planets and moons exert a gravitational pull on each other. He concluded that every body attracts every other body with a force that is proportional to its mass and diminishes with the square of the distance between them: universal gravitation. Moving to the second stage, Newton took his most general conclusion—that gravity is universal—and examined its consequences. He demonstrated that the irregular motion of the Moon, the tides and the motion of comets can be deduced from his theory of universal gravitation.
Ducheyne notes that Newton didn’t attribute this method of inference to Bacon. Instead, he labelled the two stages ‘analysis’ and ‘synthesis’ respectively, and attributed them to the Ancients. However, Ducheyne argues that we should recognise this approach as Baconian in spirit and inspiration.
This strikes me as a plausible account, and it illuminates some interesting features of Newton’s approach. For one thing, it helps us to make sense of ‘Rule 4’:
In experimental philosophy, propositions gathered from phenomena by induction should be considered either exactly or very nearly true notwithstanding any contrary hypotheses, until yet other phenomena make such propositions either more exact or liable to exceptions.
Newton’s claim that, in the absence of counter-instances, we should take propositions inferred via induction to be true seems naïve when interpreted in terms of simple enumerative induction. However, given Newton’s ‘inductive gradualism’, Rule 4 looks less epistemically reckless.
Moreover, commentators have often been tempted to interpret this rule as an expression of the hypothetico-deductive method, in which the epistemic status of Newton’s theory is sensitive to new evidence. Previously, I have argued that, when we consider how this rule is employed, we find that it’s not the epistemic status of the theory, but its scope, that should be updated. Ducheyne’s Baconian interpretation supports this position—and perhaps offers some precedent for it.
Ducheyne’s suggestion also encourages us to re-interpret other aspects of Newton’s argument for universal gravitation in a Baconian light. Consider, for example, the ‘phenomena’. Previously, I have noted that these are not simple observations but observed regularities, generalised by reference to theory. They provide the explananda for Newton’s theory. In Baconian terms, we might regard the phenomena as the results of a process of experientia literata—they represent the ‘experimental facts’ to be explained. This, I think, ought to be grist for Ducheyne’s mill.
Interpreting Newton’s argument for universal gravity in terms of Baconian induction brings the experimental aspects of the Principia into sharper focus. These aspects have often been overlooked for two broad reasons. The first is that the mathematical aspects of the Principia have distracted people from the empirical focus of book 3. I plan to examine this point in more detail in my next post. The second is that the Baconian method of natural history has largely been reduced to a caricature, which has made it difficult to recognise it when it’s being used. Dana Jalobeanu and others have challenged the idea that a completed Baconian natural history is basically a large storehouse of facts. Bacon’s Latin natural histories are complex reports containing, not only observations, but also descriptions of experiments, advice and observations on the method of experimentation, provisional explanations, questions, and epistemological discussions. We don’t find such detailed observation reports in the Principia, but we do find some of the features of Baconian natural histories.
So, Ducheyne’s interpretation of Newton’s argument for universal gravitation in terms of Bacon’s gradualist inductive method proves both fruitful and insightful. However, recall that, in my last post, I worried that the resemblance of Newton’s methodology to Bacon’s isn’t enough to establish that Newton was influenced by Bacon’s methodology. If Bacon was just describing a good, general, epistemic method, couldn’t Newton have simply come up with it himself? He was, after all, an exceptional scientist who gave careful thought to his own methodology. Is Ducheyne’s discussion sufficient to establish influence? What do you think?
Kirsten Walsh writes…
In the General Scholium, which concluded later editions of Principia, Newton described the work as ‘experimental philosophy’:
In this experimental philosophy, propositions are deduced from phenomena and are made general by induction. The impenetrability, mobility, and impetus of bodies, and the laws of motion and the law of gravity have been found by this method.
On this blog, I have argued that we should take this statement at face value. In support, I have emphasised similarities between Newton’s work in optics and mechanics. For example, I have considered the kind of evidence provided in each work, arguing that both the Principia’s ‘phenomena’ and the Opticks’s ‘experiments’ are idealisations based on observation, and that they perform the same function: isolating explananda. I have also emphasised Newton’s preoccupation in the Principia with establishing his principles empirically. Finally, I have suggested that this concern with experimental philosophy, in combination with his use of mathematics, made Newton’s method unique.
In my last blog post, I wondered if we should regard Newton’s methodology as an extension of the Baconian experimental method, or as something more unique. I have written many blog posts discussing the Baconian aspects of Newton’s optical work (for example, here, here and here), but the Baconian aspects of the Principia are less well-established. I can identify at least three possible candidates for Baconianism in the Principia. The first, suggested by Daniel Schwartz in recent conversation, is that book 3 contains what might be interpreted as Baconian ‘crucial instances’. The second, discussed by Steffen Ducheyne, is that Newton’s argument for universal gravitation resembles Bacon’s method of induction. The third, discussed by Mary Domski, is that the mathematical method employed in the Principia should be viewed as part of the seventeenth-century Baconian tradition. In this post, I’ll focus on Schwartz’s suggestion—the possibility there is a crucial instance in book 3 of the Principia—I’ll address the rest in future posts.
To begin, what is a ‘crucial instance’? For Bacon, crucial instances (instantiae crucis) were a subset of ‘instances with special powers’ (ISPs). When constructing a Baconian natural history, ISPs were experiments, procedures, and instruments that were held to be particularly informative or illuminative of aspects of the inquiry. These served a variety of purposes. Some functioned as ‘core experiments’, introduced at the very beginning of a natural history, and serving as the basis for further experiments. Others played a role later in the process. This included experiments that were supposed to be especially representative of a certain class of experiments, tools and experimental procedures that provided interesting investigative shortcuts, and model examples that came close to providing theoretical generalisations.
Crucial instances are part of a subset of ISPs that were supposed to aid the intellect by “warning against false forms or causes”. When two possible explanations seemed equally good, then the crucial instance was employed to decide between them. To this end, it performed two functions: the negative function was to eliminate all possible explanations except the correct one; the positive function was to affirm the correct explanation.
According to Claudia Dumitru, Bacon’s crucial instances have a clear structure:
- Specify the explanandum;
- Consider the competing explanations (these are assumed to exhaust the possibilities);
- Derive a consequence from one explanation that is incompatible with the other explanation(s);
- Test that consequence.
Are there any arguments in the Principia that look like crucial instances? I think there’s at least one: Newton’s famous ‘Moon test’. Let’s have a look at it.
In proposition 4 book 3, Newton used his Moon test to establish that “The moon gravitates toward the earth and by the force of gravity is always drawn back from rectilinear motion and kept in its orbit”. Here, Newton argued that the inverse-square centripetal force, keeping the moon in orbit around the Earth, is the same force that, say, makes an apple fall to the ground, namely, gravity. I think we can tease out the features of a Baconian crucial instance from Newton’s reasoning here.
Firstly, there is an explanandum: what kind of force keeps the Moon in its orbit and prevents it from flying off into space? Secondly, two possible explanations are provided: the force is either (a) the same force that that acts on terrestrial objects, namely, gravity; or (b) a different force. Thirdly, we have a consequence of (a) that is incompatible with (b): if the moon were deprived of rectilinear motion, and allowed to fall towards Earth, it would begin falling at the rate of 15 1/12 Paris feet in the space of one minute, accelerating so that at the Earth’s surface it would fall 15 1/12 Paris feet in a second. Finally, we see a test of that consequence: the calculations based on the size and motion of the Moon, and its distance from the Earth. The results are taken to support (a) and refute (b).
I have three concluding remarks to make.
Firstly, interpreting the Moon test as a crucial instance involves ‘rational reconstruction’. In the text, Newton starts by calculating the rate at which the Moon would fall, and shows that this supports proposition 4. But I think my reading of this as a crucial instance is supported by Newton’s concluding remarks:
For if gravity were different from this force, then bodies making for the earth by both forces acting together would descend twice as fast, and in the space of one second would by falling describe 301/6 Paris feet, entirely contrary to experience.
Here, Newton described the Moon test as a crucial instance: he used an observation to choose between two competing explanations of the explanandum.
Secondly, when looking for crucial instances in the Principia, it might be tempting to start with the phenomena, listed at the beginning of book 3. Elsewhere, I have argued that these resemble Newton’s experiments in the Opticks, which function as instances with special powers. But the label ‘crucial instance’ describes the function, not the content, of an empirical claim. And so, to see if they provide crucial instances, we need to consider how the phenomena are used. In fact, I think they do provide crucial instances for Newton’s rejection of Cartesian vortex theory in favour of universal gravitation, found at the end of book 2. But again, this requires rational reconstruction.
Finally, there is the issue of historical influence. I have shown that Newton employed the Moon test to decide between two competing explanations, and that this argument resembles one of Bacon’s crucial instances. However, one might think that this was simply a good approach to empirical support, and that Newton was using his common-sense. So perhaps we shouldn’t take this to indicate (direct or indirect) influence. And so I have a question for our readers: was this style of reasoning uniquely Baconian?