Skip to Navigation Skip to Content Skip to Search Skip to Site Map

Tag Archives: Newton

Emilie du Châtelet and experimental philosophy I

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. [1][2]

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 [3], du Châtelet had reservations about Charles du Fay’s attempt to reduce the seven primitive colours to three.[4]

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… [5]


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 [6].

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. [7]

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. [8]

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 [9] and opts for Peter van Musschenbroek‘s interpretation [10][11].

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. [12]

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. [13]

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 [14] 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 [15]. 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. [16]


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. [17]

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.


  1. 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.
  2. 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.)
  3. Dissertation, p. 69.
  4. 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.
  5. Les lettres de la Marquise du Châtelet, ed. Theodore Besterman [Genève: Institut et Musée Voltaire, 1958], vol. 1, pp. 273–274.
  6. Dissertation, pp. 70–71.
  7. Letter 63. To Francesco Algarotti, in Cirey, the 20th [of April 1736], Les lettres de la Marquise du Châtelet, vol. 1, p. 112.
  8. Trans. I. Bour and J. P. Zinsser; Du Châtelet, Selected Philosophical…, p. 71.; Dissertation, p. 17.
  9. Hermannus Boerhaave, “De artis theoria,” in: Elementa chemiae, Tomus primus, editio altera [Parisiis: Apud Guillelmum Cavelier, 1733], p. 193 ff.
  10. Petrus van Musschenbroek, Elementa physicæ conscripta in usus academicos, editio prima Veneta [Venetiis: Apud Joannem Baptistam Recurti, 1745], p. 323 ff.
  11. 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.
  12. 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.
  13. Voltaire, “Essai sur la nature du feu,” Recueil, p. 180.
  14. 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.
  15. Dissertation, p. 24, 33 ff.
  16. Trans. I. Bour and J. P. Zinsser; Du Châtelet, Selected Philosophical…, p. 80; Dissertation, p. 40.
  17. Trans. I. Bour and J. P. Zinsser; Du Châtelet, Selected Philosophical…, pp. 84–85; Dissertation, p. 52.


How general was Newton’s experimental philosophy?

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 PrincipiaI. 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!

Locke and the Newtonian Achievement

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.

Understanding Newton’s Principia as part of the Baconian Tradition

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!

Voltaire: Experimental Philosopher

Voltaire, détail du visage (château de Ferney)

Voltaire, détail du visage (château de Ferney)

Peter Anstey writes …

The French Philosophe Voltaire played an important role in the transmission of experimental natural philosophy to France in the 1730s. That Voltaire regarded the emergence of experimental philosophy as a pivotal moment in history is seen in his history of The Age of Louis XIV (1751). In the Introduction to this work he speaks of the Italians of the Renaissance being ‘in possession of everything that was beautiful, excepting music, which was then in but a rude state, and experimental philosophy, which was everywhere unknown’.

The decisive moment came in the early seventeenth century in the writings of Francis Bacon. For, in his Letters Concerning the English Nation (Oxford, 1994) that appeared in English and French in 1734, Voltaire credits Bacon with being the first experimental philosopher:

He is the Father of experimental philosophy … no one, before the Lord Bacon, was acquainted with experimental Philosophy, nor with the several physical Experiments which have been made since his Time. (pp. 51–2)

But did Voltaire himself take up experimental philosophy or was he merely a herald and conduit for this movement to the French reading public?

Two works suggest that Voltaire fully embraced the new experimental philosophy that he had encountered in England in the 1720s. The first is his Treatise on Metaphysics that he wrote in 1734, the year in which his Letters appeared but which was published posthumously. This work bears the marks of someone who had imbibed the methodological position of the new experimental philosophy both in its rejection of speculative philosophy and hypotheses and the priority it gives to observation and experiment. For example, he says:

It is clear that one should not make hypotheses. We ought not to say ‘Let us begin by inventing some principles with which we will try to explain everything’, but we ought to say, ‘Make an exact analysis of things and then we will try with great diffidence whether they are related to certain principles’.

He goes on to claim ‘when we can help ourselves with neither the compass of mathematics, nor the torch of experiment and natural philosophy, it is certain that we are not able to do anything’ (ibid., p. 301).

The second work is his ‘Essay on the nature of fire and its propagation’, an essay he submitted for the Académie des sciences prize in 1738. As things turned out Leonhard Euler’s essay won the prize, but Voltaire’s submission and that of Madame du Châtelet were published alongside Euler’s winning essay in the Recueil des pieces qui ont remporté le prix de l’Académie royale des sciences in 1739. This is Voltaire’s only serious foray into experimental natural philosophy.

In the Part One of the essay, the part that addresses the nature of heat, he uses the experiments of others to argue for an Aristotelian theory of heat as an element. In doing so he cites the experimental work of Boyle, Newton and Boerhaave. However, in the second article of Part Two of the essay, on the subject of how fire acts on other bodies, Voltaire relates a whole series of experiments that he had performed himself. This is with a view to establishing certain laws by which fire acts, the second of which purported laws is an inverse square law analogous to Newton’s law of gravitational attraction! (p. 201) At one point he tells us:

the comparative degrees of heat of fluids of minerals and of vegetables can, I believe, be known with the aid of a single thermometer constructed on the principles of Mr de Réaumur.

There is only one precaution to take, and this is that the spirit of wine should not boil in the thermometer. To achieve this I plunged only up to half of the ball of the thermometer in the boiling liquors. (p. 207)

Much more could be said about this fascinating essay, but the key point of interest here is that it is a demonstration of Voltaire’s commitment to and practice of experimental natural philosophy.

He may never have experimented again, yet he continued to refer to experimental philosophy, alluding to his essay on heat in his Metaphysics of Newton (La métaphysique de Neuton, Amsterdam, 1740, p. 49) and, most famously, referring to experimental philosophy in his literary works, including Candide (1759) and Micromégas (1752).


Baconian Induction in the Principia

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?

Crucial Instances in the Principia

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:

  1. Specify the explanandum;
  2. Consider the competing explanations (these are assumed to exhaust the possibilities);
  3. Derive a consequence from one explanation that is incompatible with the other explanation(s);
  4. 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?


Newton the empiricist?

Kirsten Walsh writes…

Recently, Zvi Biener and Eric Schliesser’s long-awaited volume, Newton and Empiricism, appeared on the shelves. The book is an excellent collection of papers, which makes a significant new contribution to the field. Today I want to focus on one aspect of this volume: the decision to frame the collection in terms of empiricism rather than experimental philosophy.

Over the last four years, we have provided many arguments for the superiority of the ESD over the RED. An important line of argument has been to show that ‘experimental philosophy’ and ‘speculative philosophy’ were the key terms of reference used by the actors themselves, and that they characterised their own work in terms of this division. For example, I have argued here, here, here and here that Newton is best understood as an experimental philosopher.

In their introduction, Biener and Schliesser explain their decision. They acknowledge the ‘Otago School’, and argue that, while in general there may be some good reasons to prefer the ESD to the RED, they see various problems with labelling Newton an ‘experimental philosopher’. Their concerns amount to the following: labelling Newton an ‘experimental philosopher’ obscures the idiosyncrasies of his approach to natural philosophy. They argue, firstly, that the label belies the significant influence of non-experimental philosophers on Newton’s methodology, for example those who influenced his mathematical focus. Secondly, that the label unhelpfully groups Newton with Boyle and Locke, when many features of his work support a different grouping. For example, Newton’s mathematical-system building suggests that his work should be grouped with Descartes’. Thirdly, they argue that the fact that Newton did not employ the label himself until after the publication of the first edition of the Principia suggests that he did not fully identify with the label.

These are important issues about the ESD and Newton’s place in it. So today I want to reflect on the broad problem of Newton’s idiosyncratic position. I argue that Newton’s divergence from Baconian tradition of the Royal Society is best seen as a development of experimental philosophy.

On this blog, I have sketched many features of Newton’s natural philosophical methodology. I have argued that, if we look at Newton from within the framework of the ESD, he can be neatly and easily identified as an experimental philosopher. His use of queries, his cautious approach to hypotheses, and his many methodological statements decrying the construction of metaphysical systems, suggest that this is a label that Newton would have been comfortable with. However, there is an important caveat to note: while Newton was clearly influenced by the Baconian experimental tradition, he did not consider himself a Baconian experimental philosopher.

In the earliest statements of his mathematico-experimental approach, Newton set up his position in opposition to the Baconian experimental philosophers. In these passages, one feature of Newton’s methodology stands out in explicit rejection of the Baconian method: his claims to certainty. This feature, in itself, is not very significant – many experimental philosophers believed that, in the end, natural philosophy would be a form of scientia, i.e. a system of knowledge demonstrated from certain axioms. Indeed, Bacon shared this ideal of certainty. He thought that his method of induction could get around the problems usually associated with ampliative inference and deliver knowledge of the essences of things. Thus, Bacon’s method of natural history was ultimately supposed to provide the axioms on which scientia could be founded. The challenge, which everyone agreed on, was to discover those axioms on which the system would be built.

Newton and the Baconians seem to diverge on their responses to this challenge. Baconian experimental philosophers recommended that one should have all the facts before formulating generalisations or theories. In contrast, Newton thought that a few, or even just one, well-constructed experiment might be enough – provided you used it in the right way. This shows that Newton took a different view of the role of evidence in natural philosophy. This divergence amounts to three key differences between Newton and the Baconian experimental philosophers:

  1. Where the Baconian experimental philosophers advocated a two-stage model, in which construction of natural histories preceded theory construction, Newton appeared to reject this two-stage approach. Newton commenced theory-building before his knowledge of the facts was complete.
  2. Related to (1), the Baconian experimental philosophers conceived of phenomena as immediate facts, acquired via observation, and hence pre-theoretic. In contrast, Newton’s phenomena were generalised regularities, acquired via mediation between observation and theory.
  3. For the Baconian experimental philosophers, queries were used to give direction and define the scope of the inquiry. But Newton’s queries were more focussed on individual experiments.

There is strong textual evidence that the ESD was operative in Newton’s early natural philosophical work. We have good reason to suppose that Newton regarded his natural philosophical pursuits as experimental philosophy. This becomes clearer in Newton’s later work. For instance, in the General Scholium to the Principia (1713), Newton explicitly described his work as ‘experimental philosophy’ – indeed, Peter Anstey has noted that Roger Cotes also recognised this feature of Newton’s work. We also have good reason to suppose that, in important ways, Newton saw his work as aligned with the Royal Society and, by extension, with the Baconian movement. But Newton was also a mathematician, and he saw a role for mathematical reasoning in experimental philosophy. In many ways, it was this mathematical approach that led to his divergence from the Baconian experimental philosophy.

Biener and Schliesser are right to draw attention to the ways in which Newton’s position diverged from the experimental tradition of the Royal Society. However, they fail to recognise that Newton’s position diverged in a way that should be viewed as a development of this tradition. Indeed, the ‘Newtonian experimental philosophy’ eventually replaced the experimental philosophy of Boyle, Hooke and the other early members of the Royal Society.  The label ’empiricism’ has no such historical relevance.  But, more on this another time…

‘Epistemic amplification’ and Newton’s laws


Kirsten Walsh writes…

In my last post, I considered the experimental support Newton offers for his laws of motion. In the scholium to the laws, Newton argues that his laws of motion are certainly true. However, in support he only cites a handful of experiments and the agreement of other mathematicians. I suggested that the experiments discussed do support his laws, but only in limited cases. This justifies their application in Newton’s mathematical theory, but does not justify Newton’s claims to certainty. In this post, I will speculate that the laws of motion were in fact better established than Newton’s discussion suggests. I introduce the notion ‘epistemic amplification’ – suggesting that Newton’s laws gain epistemic status by virtue of their relationship to the propositions they entail. That is, by reasoning mathematically from axioms to theorems, the axioms obtained higher epistemic status, and so the reasoning process effectively amplified the epistemic status of the axioms.

I am not arguing that epistemic amplification captures Newton’s thinking. In fact, Newton explicitly stated that epistemic gain was not possible. For him, the best one could achieve was avoiding epistemic loss. (I have discussed Newton’s aims of certainty and avoiding epistemic loss here and here.) I suggest that, objectively speaking, the epistemic status of Newton’s laws increases over the course of the Principia.

To begin, recall that Newton has two projects in relation to the laws:

  1. The specification of the laws as the axioms of a mathematical system; and
  2. The justification of laws as first principles in natural philosophy.

Let’s consider the first project. In addition to the support of mathematicians and the experiments that Newton cites, it is plausible that the epistemic status of the laws increases by virtue of their success in the mathematical system: in particular, by entailing Keplerian motion. Kepler’s rules and Newton’s laws of motion have independent evidence: as we have seen, Newton’s laws are weakly established by localised experiments and the ‘agreement of mathematicians’; Kepler’s rules are established by observed planetary motion and were widely accepted by astronomers prior to the Principia. Newton’s laws entail Kepler’s rules, which boosts Newton’s justification for his laws. Moreover, Newton’s laws provide additional support for Kepler’s rules, by telling us about the forces required to produce such motions. The likelihood of the two theories is coupled: evidence for one carries over to the other. So Newton’s laws also boost the justification for Kepler’s rules. Thus, Newton achieves epistemic gain: the epistemic status of the laws, qua mathematical axioms, has increased by virtue of their relationship to Kepler’s rules.

Now let’s consider the second project – the application of the laws to natural philosophy. Again, the discussion in the scholium justifies their use, but not their certainty. I now suggest that these laws, as physical principles, gain epistemic status through confirmation of Newton’s theory. This occurs in book 3, when Newton explicitly applies his mathematical theory to natural phenomena. As I have previously discussed, the phenomena (i.e. the motions of the planets and their moons) are employed as premises in Newton’s argument for universal gravitation. However, the phenomena also support the application of the mathematical theory to the physical world: they show that the planets and their moons move in ways that approximate Keplerian motion. As we saw above, the laws of motion entail Kepler’s rules. So, since the phenomena support Kepler’s rules, they also support the laws of motion. So this is a straightforward case of theory-confirmation.

There is also scope for theory-testing in book 1. Each time Newton introduces a new factor (e.g. an extra body, or a resisting medium), the mathematical theory is tested. For instance, the contrasting versions of the harmonic rule in one-body and two-body model systems provides a test: it allows the phenomena to empirically decide between two theories, one involving singly-directed central forces, the other involving mutually-interactive central forces. Similarly, the contrasting two-body and three-body mathematical systems provide a test: they allow the phenomena to select between a theory involving pair-wise interactions and a theory involving universal mutual interaction. Moreover, in the final section of book 2, Newton shows that, unlike his theory, Cartesian vortex theory does not predict Keplerian motion. Thus, the phenomena seem to support his theory, and by extension the laws of motion, and to refute the theory of vortices. Again, the laws seem to gain support by virtue of their relationship to the propositions they entail.

To summarise, Newton claims that his laws are certainly true, but the support he gives is insufficient. Here, I have sketched an account in which Newton’s laws gain epistemic status by virtue of their relationship to the propositions they entail. ‘Epistemic amplification’ is certainly not something which Newton himself would have had truck with, but the term does seem to capture the support actually acquired by Newton’s laws in the Principia.  What do you think?



Are Newton’s Laws Experimentally Confirmed?

Kirsten Walsh writes…

Previously on this blog, I have argued that the combination of mathematics, experiment and certainty are an enduring feature of Newton’s methodology.  I have also highlighted the epistemic tension between experiment and mathematical certainty found in Newton’s work.  Today I shall examine this in relation to Newton’s ‘axioms or laws of motion’.

In the scholium to the laws, Newton argues that his laws of motion are certainly true.  In support, however, he cites a handful of experiments and the agreement of other mathematicians: surprisingly weak justification for such strong claims!  In this post, I show how Newton’s appeals to experiment justify the axioms’ inclusion in his system, but not with the certainty he claims.

Newton begins:

    “The principles I have set forth are accepted by mathematicians and confirmed by experiments of many kinds.”

Newton expands on this claim, discussing firstly, Galileo’s work on the descent of heavy bodies and the motion of projectiles, and secondly, the work conducted by Wren, Wallis and Huygens on the rules of collision and reflection of bodies.  He argues that:

  1. The laws and their corollaries have been accepted by mathematicians such as Galileo, Wren, Wallis and Huygens (the latter three were “easily the foremost geometers of the previous generation”);
  2. The laws and their corollaries have been invoked to establish several theories involving the motions of bodies; and
  3. The theories established in (2) have been confirmed by the experiments of Galileo and Wren (which, in turn confirms the truth of the laws).

These claims show us that Newton regards his laws as well-established empirical propositions.  However, Newton recognises that the experiments alone are not sufficient to establish the truth of the laws.  After all, the theories apply exactly only in ideal situations, i.e. situations involving perfectly hard bodies in a vacuum.  So Newton describes supplementary experiments that demonstrate that, once we control for air resistance and degree of elasticity, the rules for collisions hold.  He concludes:

    “And in this manner the third law of motion – insofar as it relates to impacts and reflections – is proved by this theory [i.e. the rules of collisions], which plainly agrees with experiments.”

This passage suggests that the rules of collisions support a limited version of law 3, “to any action there is always an opposite and equal reaction”, and that the rules themselves appear to hold under experimental conditions.  However, this doesn’t show that law 3 is universal: which Newton needs to establish universal gravitation.  This argument is made by showing how the principle may be extended to other cases.

Firstly, Newton extends law 3 to cases of attraction.  He considers a thought experiment in which two bodies attract one another to different degrees.  Newton argues that if law 3 does not hold between these bodies the system will constantly accelerate without any external cause, in violation of law 1, which is a statement of the principle of inertia.  Therefore, law 3 must hold.  As the principle of inertia was already accepted, this supports the application of law 3 to attraction.

Newton then demonstrates law 3’s application to various machines.  For example, he argues that two bodies suspended from opposite ends of a balance have equal downward force if their respective weights are inversely proportional to the distances between the axis of the balance and the points at which they are suspended.  And he argues that a body, suspended on a pulley, is held in place by a downward force which is equal to the downward force exerted by the body.  Newton explains that:

    “By these examples I wished only to show the wide range and the certainty of the third law of motion.”

What these examples in fact show is the explanatory power of the laws of motion – particularly law 3 – in natural philosophy.  Starting with collision, which everyone accepts, Newton expands on his cases to show how law 3 explains many different physical situations.  Why wouldn’t a magnet and an iron floating side-by-side float off together at an increasing speed?  Because, by law 3, as the magnet attracts the iron, so the iron attracts the magnet, causing them to press against one another.  Why do weights on a balance sometimes achieve equilibrium?  Because, by law 3, the downward force at one end of the balance is equal to the upward force at the other end of the balance.  These examples demonstrate law 3’s explanatory breadth.  But these examples do not give us a compelling reason to think that law 3 should be extended to gravitational attraction (which seems to require some kind of action, or attraction, at a distance).

Newton, clearly, is convinced of the strength of his laws of motion.  But this informal, discussion of the experiments he appeals to shows that he ought not be so convinced.  As I see it, Newton has two projects in relation to his laws:

1)      The specification of the laws as the axioms of a mathematical system; and

2)      The justification of laws as first principles in natural philosophy.

I suggest that the experiments discussed give strong support for the laws in limited cases.  This justifies their application in Newton’s mathematical model, but it does not justify Newton’s claims to certainty.  In modern Bayesian terms, we might say that Newton’s laws have high subjective priors.  In my next post, I shall sketch an account in which Newton’s laws gain epistemic status by virtue of their relationship to the propositions they entail.