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…
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.
- “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:
- 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”);
- The laws and their corollaries have been invoked to establish several theories involving the motions of bodies; and
- 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.
Kirsten Walsh writes…
In my last few posts, I have been discussing the nature of observations and experiments in Newton’s Opticks. In my first post on this topic, I argued that Newton’s distinction between observation and experiment turns on their function. That is, the experiments introduced in book 1 offered individual, and crucial, support for particular propositions, whereas the observations introduced in books 2 and 3 only supported propositions collectively. In my next post, I discussed the observations in more detail, arguing that they resemble Bacon’s ‘experientia literata’, the method by which natural histories were supposed to be generated. At the end of that post, I suggested that, in contrast to the observations, Newton’s experiments look like Bacon’s ‘instances of special power’, which are particularly illuminating cases introduced to provide support for specific propositions. Today I’ll develop this idea.
Note, before we continue, that there are two issues here that can be treated independently of one another. One is establishing the extent of Bacon’s historical influence on Newton; the other is establishing the extent to which Bacon’s methodology can illuminate Newton’s. In this post I am doing the latter – using Bacon’s view only as an interpretive tool.
Identifying ‘instances of special power’ (ISPs) was an important step in the construction of a Baconian natural history. ISPs were experiments, procedures, and instruments that were held to be particularly informative or illuminative. 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. They included experiments that were supposed to be especially representative of a certain class of experiments, tools and experimental procedures that provided interesting shortcuts in the investigation, and model examples that came very close to providing theoretical generalisations. In some cases, a collection of ISPs constituted a natural history.
The following features were typical of ISPs. Firstly, they were considered to be particularly illuminating experiments, procedures or tools. For example, a crucial instance, or a particularly clear or informative experiment, or experimental procedure. Secondly, they were supposed to be replicated. On Bacon’s view, replication was not merely an exercise for verifying evidence; it was an exercise for the mind, ensuring that one had truly grasped the phenomenon. Thirdly, they were versatile, in that they could be used in several different ways. As we shall see, the experiments of book 1 display these essential features.
In book 1 of the Opticks, Newton employed a method of ‘proof by experiments’ to support his propositions. Each experiment was introduced to reveal a specific property of light, which in turn proved a particular proposition. We know that Newton conducted many experiments in his optical investigations, so why did he present the experiments as he did, when he did? When we consider Newton’s experiments alongside Bacon’s instances of special power, common features start to emerge.
Firstly, for each proposition he asserted, Newton introduced a small selection of experiments in support – those that he considered to be particularly illuminating or, in his own words, “necessary to the Argument”. Unlike in his first paper, in the Opticks, Newton did not label any experiments ‘experimentum crucis’. But his use of terms such as ‘necessary’ and ‘proof’ make it clear that these experiments were supposed to provide strong support: just like ISPs.
Secondly, Newton usually provided more than one experiment to support each proposition. These were listed in order of increasing complexity and were carefully described and illustrated. That Newton took this approach, as opposed to just reporting on their results, suggests that these experiments were supposed to be an exercise for the reader: they were about more than just proof or confirmation of the proposition. The reader was supposed either to be able to replicate the experiment, or at least to understand its replicability. Starting with the simplest experiment, Newton led his reader by the hand through the relevant properties of light, to ensure that they were properly grasped. Like Bacon’s ISPs, then, Newton’s experiments were intended to be replicated.
Thirdly, Newton’s experiments were recycled in a variety of roles in the Opticks. For example, the experiments he used to support proposition 2 part II were experiments 12 and 14 from part I. Newton introduced and developed these experiments in several different contexts to illuminate and support different propositions. Again, this is typical of Bacon’s ISPs.
And so, Newton’s experiments in the Opticks play a role analogous to Bacon’s instances of special power, and thinking of them as such explains why they are presented as they are. They are particularly illuminating cases that are introduced to provide support for specific propositions. Newton selected the experiments which best functioned as ISPs for inclusion in the Opticks. Moreover, seen in this light, the seemingly disparate set of experiments start to look like a far more cohesive collection, or a natural history.
Many commentators have emphasised the ways that Newton deviated from Baconian method. Through this sequence of posts, I have argued that the Opticks provides a striking example of conformity to the Baconian method of natural history.
Peter Anstey writes …
It is not entirely clear when Robert Boyle (1627–1691) first used the term ‘experimental philosophy’, but what is clear is that his views on this new approach to natural philosophy began to form in the early 1650s, some years before the term came into common use.
Boyle’s earliest datable use of the term is from his Spring of the Air published in 1660. The reason for the lack of clarity about Boyle’s first use of the term arises from the fact that what appears to be a very early usage survives only in a fragment published by Thomas Birch in his ‘Life of Boyle’ in 1744: no manuscript version is extant. The context of Boyle’s reference to experimental philosophy in this text suggests that this fragment is associated with his ‘Essay of the Holy Scriptures’ composed in the mid-1650s. Boyle speaks of:
those excellent sciences, the mathematics, having been the first I addicted myself to, and was fond of, and experimental philosophy with its key, chemistry, succeeding them in my esteem and applications …
(Works of Robert Boyle, eds Hunter and Davis, London, vol. 12, p. 356)
However, the question of the precise dating of Boyle’s use of the term is hardly as significant as the formation of his views on his distinctive form of natural philosophy. And on this point we have some fascinating and chronologically unambiguous evidence, namely, Boyle’s outline of a work ‘Of Naturall Philosophie’ which dates from around 1654. This short manuscript in Boyle’s early hand survives among the Royal Society Boyle Papers in volume 36, folios 65–6. (It is transcribed in full in Michael Hunter, Robert Boyle 1627–1691: Scrupulosity and Science (Woodbridge, 2000), 30–1.)
In it Boyle outlines the two ‘Principles of naturall Philosophie’. They are Sense and Reason. As for Sense, in addition to its fallibility, Boyle stresses that:
it is requisite to be furnished with observations and Experiments.
Boyle then proceeds to give a set of seven ‘Directions concerning Experiments’. These directions provide an early adumbration of his later experimental methodology. They include the following:
1. Make all your Experiments if you can your selfe [even] though you be satisfyed beforehand of the Truth of them.
3. Be not discouraged from Experimentinge by haveing now & then your Expectation frustrated
5. Get acquainted with Experimentall Books & Men particularly Tradesmen.
7. After you have made any Experiment, not before, reflect upon the uses & Consequences of it either to establish truths, detect Errors, or improve some knowne or give hints of some new Experiment
As for the principle of Reason, Boyle gives five considerations concerning it. What is striking here is that each of them concerns the relation between Reason and experiments:
- That we consult nature to make her Instruct us what to beleeve not to confirme what we have beleeved
- That a perfect account of noe Experiment is to be looked for from the Experiment it selfe
- That it is more difficult then most men are aware of to find out the Causes of knowne effects
- That it is more difficult then men thinke to build principles upon or draw Consequences from Experiments
- That therefore Reason is not to be much trusted when she wanders far from Experiments & Systematical Bodyes of naturall Philosophie are not for a while to be attempted
Note here the caution about the difficulty of building natural philosophical principles from experiments and the warning about wandering from experiments and premature system building, points that were to become key motifs of the experimental philosophy that blossomed in the 1660s.
It may well be that the movement of experimental philosophy did not emerge until the early 1660s, but the conceptual foundations of its most able exponent were laid nearly a decade before.
Are there any parallel cases of natural philosophers who worked out an experimental philosophy in the early 1650s or was Boyle the first?
Kirsten Walsh writes…
In a recent post, I considered Newton’s use of observation and experiment in the Opticks. I suggested that there is a functional (rather than semantic) difference between Newton’s ‘experiments’ and ‘observations’. Although both observations and experiments were reports of observations involving intervention on target systems and manipulation of independent variables, experiments offered individual, and crucial, support for particular propositions, whereas observations only supported propositions collectively.
At the end of the post, I suggested that, if we view them as complex, open ended series’ of experiments, the observations of books 2 and 3 look a lot like what Bacon called ‘experientia literata’, the method by which natural histories were supposed to be generated. In this post, I’ll discuss this suggestion in more detail, following Dana Jalobeanu’s recent work on Bacon’s Latin natural histories and the art of ‘experientia literata’.
The ‘Latin natural histories’ were Bacon’s works of natural history, as opposed to his works about natural history. A notable feature of Bacon’s Latin natural histories is that they were produced from relatively few ‘core experiments’. By varying these core experiments, Bacon generated new cases, observations and facts. The method by which this generation occurs is called the art of ‘experientia literata’. Experientia literata (often referred to as ‘learned experience’) was a late addition to Bacon’s program, developed in De Augmentis scientiarum (1623). It is a tool or technique for guiding the intellect. By following this method, discoveries will be made, not by chance, but by moving from one experiment to the next in a guided, systematic way.
The following features were typical of the experientia literata:
- The series of observations was built around a few core experiments;
- New observations were generated by the systematic variation of experimental parameters;
- The variation could continue indefinitely, so the observation sequence was open-ended;
- The experimental process itself could reveal things about the phenomena, beyond what was revealed by a collection of facts;
- The trajectory of the experimental series was towards increasingly general facts about the phenomena; and
- The results of the observations were collated and presented as tables. These constituted the ‘experimental facts’ to be explained.
Now let’s turn to Newton’s observations. For the sake of brevity, my discussion will focus on the observations in book 2 part I of the Opticks, but most of these features are also found in the observations of book 2 part IV, and in book 3 part I.
The Opticks book 2 concerned the phenomenon now known as ‘Newton’s Rings’: the coloured rings produced by a thin film of air or water compressed between two glasses. Part I consisted of twenty-four observations. Observation 1 was relatively simple: Newton pressed together two prisms, and noticed that, at the point where the two prisms touched, there was a transparent spot. The next couple of observations were variations on that first one: Newton rotated the prisms and noticed that coloured rings became visible when the incident rays hit the prisms at a particular angle. Newton progressed, step-by-step, from prisms to convex lenses, and then to bubbles and thin plates of glass. He varied the amount, colour and angle of the incident light, and the angle of observation. The result was a detailed, but open ended, survey of the phenomena. Part II consisted of tables that contained the results of part I. These constituted the experimental facts to be explained in propositions in part III. In part IV, Newton described a new set of observations, which built on the discussions of propositions from part III.
When we consider Newton’s observations alongside Bacon’s experientia literata, we notice some common features.
Firstly, the series of observations was built around the core experiment involving pressing together two prisms to observe the rings that appeared.
Secondly, new observations were generated by the variation of experimental parameters: i.e. new observations were generated, first by varying the obliquity of the incident rays, then by varying the glass instruments, then by varying the colour of the incident light, and so on.
Thirdly, the sequence of observations was open-ended. Newton could have extended the sequence by varying the medium, or some other experimental parameter. Moreover, at the end of the sequence, Newton noted further variations to be carried out by others, which might yield new or more precise observations.
Fourthly, the experimental process itself revealed things about the phenomenon, beyond what was revealed by a collection of facts. For example, in observation 1, Newton noticed that increasing the pressure on the two prisms produced a transparent spot. The process of varying the pressure, and hence the thickness of the film of air between the two prisms, suggested to Newton a way of learning more about the phenomenon of thin plates. He realised he could quantify the phenomenon by introducing regularly curved object glasses, which would make the variation in thickness regular, and hence, calculable.
Fifthly, the trajectory of the experimental series was towards increasingly general facts about the phenomenon. Newton began by simply counting the number of rings and describing the sequence of colours under specific experimental parameters. But eventually he showed that the number of rings and their colours was a function of the thickness and density of the film. Thus, he was able to give a much broader account of the phenomenon.
Finally, these general results were collated and presented as tables in part II. Thus, the tables in part II constituted the facts to be explained by propositions in part III.
Many commentators have emphasised the ways that Newton deviated from Baconian method. However, when viewed in this light, book 2 of the Opticks provides a striking example of conformity to the Baconian method of natural history: Newton led the reader from observations in part I, to tables of facts in part II, to propositions in part III. Moreover, it ended with a further series of observations in part IV, emphasising the open-endedness of the art of experientia literata.
In contrast to the observations in book 2, Newton’s experiments in book 1 look like Bacon’s ‘instances of special power’, which are particularly illuminating cases introduced to provide support for specific propositions. I’ll discuss this next time. For now, I’d like to hear what our readers think of my Baconian interpretation of Newton’s observations.
Peter Anstey writes…
In my last post I introduced Roger Cotes’ famous Preface to the second edition of Newton’s Principia in order to show its importance as an expression of a commitment to experimental philosophy. In that post I focused on Cotes’ critique of the Cartesian vortex theory and the manner in which this attack on the archetypal speculative philosophy formed the bookends of the Principia. In this post I will discuss the role of experiment in Cotes’ comments on experimental philosophy.
The Preface is actually quite a complex essay that has both polemical and expository agendas. On the one hand, Cotes uses it to give a summary of the main theses of the Principia centred around Newton’s theory of gravity. On the other hand, Cotes uses it to defend the theory of gravity against the charge that it is an occult quality, to defend Newton’s system of the world against the Cartesian vortex theory, and to defend the methodology of the work against rival approaches.
On this latter point, Cotes begins by claiming that Newton’s method is ‘based upon experiment’ (The Principia, eds I.B. Cohen and A. Whitman, Berkeley: University of California Press, 1999, p. 386). One might expect here that Cotes will give a list of the sorts of experimental results that Newton achieved or some reference to crucial experiments, but instead he introduces another set of methodological notions: phenomena, principles, hypotheses, analysis and synthesis. It is only later when appealing to various laws, principles and axioms in his summary of Newton’s system of the world that Cotes refers to experiments.
Here is a summary of Cotes’ account of the method of the Principia. Natural philosophy attempts to derive the causes of all things from the simplest of principles and not from contrived hypotheses. These principles are derived from the phenomena by a two-step process of analysis and synthesis. From select phenomena the forces and simpler laws of these forces are ‘deduced’ by analysis. Then by synthesis ‘the constitution of the rest of the phenomena’ is given. In the case of the Principia the relevant force is gravitational attraction and the relevant law is the inverse square law. Though Cotes throws in the laws of planetary motion claiming that ‘it is reasonable to accept something that can be found by mathematics and proved with the greatest certainty’ (p. 389). He also claims, after presenting a summary of the system of the world, ‘the preceding conclusions are based upon an axiom which is accepted by every philosopher, namely, that effects of the same kind –– that is, effects whose known properties are the same –– have the same causes, and their properties which are not yet known are also the same’. Indeed, ‘all philosophy is based on this rule’ (p. 391).
Where then do experiments fit in this picture? The first mention of experiments is in relation to the law of fall. Cotes refers here to pendulum experiments and to Boyle’s air-pump. Next, Huygens’ pendulum experiments are referred to in the discussion of the determination of the centripetal force of the moon towards the centre of the Earth (p. 389). They then appear in the elaboration of the ‘same effect, same cause’ axiom and its application to the attribution of gravity to all matter. Cotes says ‘[t]he constitution of individual things can be found by observations and experiments’ and from these we make universal judgments (p. 391). Thus, ‘since all terrestrial and celestial bodies on which we can make experiments or observations are heavy, it must be acknowledged without exception that gravity belongs to all bodies universally. … extension, mobility, and impenetrability of bodies are known only through experiments’ and so too is gravity. Finally, in recapping the Newtonian method near the conclusion of the Preface Cotes repeats that ‘honest and fair judges will approve the best method of natural philosophy, which is based on experiments and observations’ (p. 398).
What are we to make of the role of experiments here? First, notice how experiments are appealed to in the establishment of laws and the ‘same effect, same cause’ axiom. Second, it is worth pointing out that the ‘same effect, same cause’ axiom is Newton’s second rule of philosophizing: indeed, Cotes uses the very same example as Newton, namely, the falling of stones in America and Europe (see p. 795). Third, notice how without any explanation Cotes extends experiments to experiments and observations. He begins by saying that there are those ‘whose natural philosophy is based on experiment’ and he ends by saying that ‘the best method of natural philosophy, … is based on experiments and observations’. This is not an equivalent expression and while it is consistent with many other methodological statements by experimental philosophers, it still calls out for explanation.
Has Cotes really given an adequate summary of the method of experimental philosophy and has he captured the manner in which experiments are used in Newton’s reasoning in the Principia? In my view he has not. I’d be interested to hear your views?
Kirsten Walsh writes…
In my last post, my analysis of the phenomena in Principia revealed a continuity in Newton’s methodology. I said:
- In the Opticks, Newton isolated his explanatory targets by making observations under controlled, experimental conditions. In Principia, Newton isolated his explanatory targets mathematically: from astronomical data, he calculated the motions of bodies with respect to a central focus. Viewed in this way, Newton’s phenomena and experiments are different ways of achieving the same thing: isolating explananda.
In this post, I’ll have a closer look at Newton’s method of isolating explananda in the Opticks. It looks like Newton made a distinction between experiment and observation: book 1, contained ‘experiments’, but books 2 and 3, contained ‘observations’. I’ll argue that the distinction in operation here was not the standard one, which turns on level of intervention.
In current philosophy of science, the distinction between experiment and observation concerns the level of intervention involved. In scientific investigation, intervention has two related functions: isolating a target system, and creating novel scenarios. On this view, experiment involves intervention on a target system, and manipulation of independent variables. In contrast, the term ‘observation’ is usually applied to any empirical investigation that does not involve intervention or manipulation. This distinction is fuzzy at best: usually level of intervention is seen as a continuum, with observation nearer to one end and experiment nearer to the other.
If Newton was working with this sort of distinction, then we should find that the experiments in book 1 involve a higher level of intervention than the observations in books 2 and 3. That is, in contrast to the experiments in book 1, the observations should involve fewer prisms, lenses, isolated light rays, and artificially created scenarios. However, this is not what we find. Instead we find that, in every book of the Opticks, Newton employed instruments to create novel scenarios that allowed him to isolate and identify certain properties of light. It is difficult to quantify the level of intervention involved, but it seems safe to conclude that Newton’s use of the terms ‘observation’ and ‘experiment’ doesn’t reflect this distinction.
To understand what kind of distinction Newton was making, we need to look at the experiments and observations more closely. In Opticks book 1, Newton employed a method of ‘proof by experiments’ to support his propositions. Each experiment was designed to reveal a specific property of light. Consider for example, proposition 1, part I: Lights which differ in Colour, differ also in Degrees of Refrangibility. Newton provided two experiments to support this proposition. These experiments involved the use of prisms, lenses, candles, and red and blue coloured paper. From these experiments, Newton concluded that blue light refracts to a greater degree than red light, and hence that blue light is more refrangible than red light.
In the scholium that followed, Newton pointed out that the red and blue light in these experiments was not strictly homogeneous. Rather, both colours were, to some extent, heterogeneous mixtures of different colours. So it’s not the case, when conducting these experiments, that all the blue light was more refrangible than all the red light. And yet, these experiments demonstrate a general effect. This highlights the fact that, in book 1, Newton was describing ideal experiments in which the target system had been perfectly isolated.
Book 2 concerned the phenomenon now known as ‘Newton’s Rings’: the coloured rings produced by a thin film of air or water compressed between two glasses. It had a different structure to book 1: Newton listed twenty-four observations in part I, then compiled the results in part II, explained them in propositions in part III, and described a new set of observations in part IV. The observations in parts I and IV explored the phenomena of coloured rings in a sequence of increasingly sophisticated experiments.
Consider, for example, the observations in part I. Observation 1 was relatively simple: Newton pressed together two prisms, and noticed that, at the point where the two prisms touched, there was a transparent spot. The next couple of observations were variations on that first one: Newton rotated the prisms and noticed that coloured rings became visible when the incident rays hit the prisms at a particular angle. But Newton steadily progressed, step-by-step, from prisms to convex lenses, and then to bubbles and thin plates of glass. He varied the amount, colour and angle of the incident light, and the angle of observation. The result was a detailed, but open ended, survey of the phenomena.
I have argued that Newton’s experiments and observations cannot be differentiated on the basis of intervention, but there are two other differences worth noting. Firstly, whereas the experiments described in book 1 were ideal experiments, involving perfectly isolated explanatory targets, the observations in books 2 and 3 were not ideal. Rather, through a complex sequence of observations, as the level of sophistication increased, the explanatory target was increasingly well isolated. When viewed in this way, the phenomena of Principia seem to have more in common with the experiments of book 1 than the observations of books 2 and 3.
Secondly, the experiments of book 1 were employed to support particular propositions, and so, individually, they were held to be particularly relevant and informative. In contrast, the observations of books 2 and 3 were only collectively relevant and informative. Moreover, the sequence of observations was open ended: there were always more variations one could try.
What are we to make of these differences between observation and experiment in the Opticks? I have previously argued that, while Newton never constructed Baconian natural histories, his work contained other features of the Baconian experimental philosophy, such as experiments, queries and an anti-hypothetical stance. However, in viewing them as complex, open ended series’ of experiments, I now suggest that the observations of books 2 and 3 look a lot like what Bacon called experientia literata, the method by which natural histories are generated. I’ll discuss this in my next post, but in the mean time, I’d like to hear what our readers think.
Peter Anstey writes …
In two previous posts I examined an early teacher of experimental philosophy, John Theophilus Desaguliers and a later one, George Adams. In this post I turn to a third teacher of experimental philosophy, Francis Hauksbee the Elder (1660–1713). (He was called ‘the Elder’ to differentiate him from his nephew of the same name who also taught experimental philosophy.) Hauksbee was one of the two most important first-generation pedagogues. (We will examine the other, John Keill, in my next post.)
He was a gifted instrument maker who not only developed a new much improved design of Robert Boyle’s air-pump, but also conducted a series of very important new experiments using this instrument. Many of these were published in the Philosophical Transactions. As a result of his proficiency with experimental apparatus he became a kind of de facto curator of experiments at the Royal Society in c. 1704 after Robert Hooke’s death. In addition he seconded James Hodgson FRS to carry out public lectures on experimental philosophy in London while he acted as the demonstrator.
By 1709 he himself was lecturing on experimental philosophy and continued this until his death in 1713. In 1709 he published a compilation volume of his air-pump experiments entitled Physico-Mechanical Experiments … touching Light and Electricity. This volume, in many ways, mimicked Boyle’s ground-breaking New Experiments Physico-mechanical touching the Spring of the Air (1660). (Even the titles are similar.) Hauksbee clearly saw himself as working in a tradition of experimental natural philosophy that extended back to Boyle.
The work gives us an interesting insight into how he viewed natural philosophy. He begins by telling us that:
The Learned World is now almost generally convinc’d, that instead of amusing themselves with Vain Hypotheses, which seem to differ little from Romances, there’s no other way of Improving Natural Philosophy, but by Demonstrations and Conclusions founded upon Experiments judiciously and accurately made. (Preface)
By now our readers should recognize the standard tropes of the experimental philosopher: the decrying of hypotheses; the likening of them to romances; the appeal to the necessity of experiment for the improving of natural philosophy.
Hauksbee goes on in the Preface to mention ‘The Honourable and most Excellent Mr. Boyle’ and ‘the … Incomparable Sir Isaac Newton’ implying that he himself is engaged in the same natural philosophical project. It is interesting to note, however, that there is no mention of the method of natural history as practised and promoted by Boyle in the Preface or in Hauksbee’s work. Hauksbee’s experimental practice was a natural extension of Boyle’s work, but at the same time methodologically discontinuous with it.
Hauksbee was also much quicker than Boyle to draw natural philosophical conclusions from his experiments. He did not, however, apply mathematics to his discoveries and he was later criticized by Desaguliers in his Course of Experimental Philosophy (1734) in so far as his experiments
were only shewn and explain’d as so many curious Phaenomena, and not made Use of as Mediums to prove a Series of philosophical Propositions in a mathematical Order, they laid no such Foundation for true Philosophy. (vol. 1, Preface)
Hauksbee may not have had developed views on the methodology of natural philosophy or much aptitude in mathematics, but he was a gifted experimenter and a keen promoter of experimental philosophy.
Juan Gomez writes…
Some time ago I wrote a post regarding David Fordyce’s Elements. This text was used almost in its entirety as the entry for moral philosophy in the Encyclopædia Britannica from the first edition in 1771 and until the seventh edition where it was modified and the replaced by an essay on the topic by William Alexander. I want to refer to the Encyclopædia again, this time to trace the description of four terms, namely ‘empiric,’ ‘experimental philosophy,’ ‘rational’ and ‘rationalism,’ and ‘speculative.’ I will focus on the first two terms in today’s post.
The word ‘empiric’ appears in the first eight editions (1771 to 1898 when the ninth edition appeared). It is a very short entry and it restricts its use to method in medicine:
It is clear from the definition that the word had a different use than the one implied by the modern term ‘empiricism,’ which appeared for the first time in the eleventh edition(1910) of the Encyclopædia. In such editions the writer of the entry tells us that the term refers “in philosophy, [to] the theory that all knowledge is derived from sense-given data. It is opposed to all forms of intuitionalism, and holds that the mind is originally an absolute blank.” The last paragraph of the entry refers to the restricted definition of the term ‘empiric’ given in previous editions that I quoted above.
This term can be found in the first eight editions as well and disappears from the ninth edition onwards. The following is the definition from the first edition of the Encyclopædia:
However, the definition for Experimental Philosophy was substantially expanded for editions two to six, and then reduced to one small paragraph in the eighth edition. From 1778 (second edition) to 1823 (sixth edition) the entry consists in a general description and refers to seventeen items that form “the foundations of the present system of experimental philosophy.” The items are basic definitions of the object of study of experimental philosophy: natural bodies and their properties, extension, arrangement of particles, law of gravity, properties of light, and so on. For the seventh edition the entry was reduced to this:
The entry is the same for the eighth edition but from the ninth edition onwards there is no entry for ‘experimental philosophy.’
As far as the Encyclopædia Britannica is concerned, we can see that the terms used in the eighteenth and nineteenth centuries are better explained by using the ESD framework instead of the RED. The contrast between the meaning of the term ’empiric’ in the medical context and the later twentieth century entry on ’empiricism’ illustrates this nicely. As we will see in my next post, the way the terms ‘speculative’ and ‘rational’ were used gives us more evidence to prefer the ESD framework for interpreting the early modern period.