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Cotes’ Preface and Experiment

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?

Roger Cotes’ ‘Preface’ and the ESD

Peter Anstey writes…

One of the main tasks of this blog over the last three years has been to provide evidence for our claim that from the 1660s the distinction between experimental and speculative philosophy is crucial for an understanding of early modern natural philosophy and even the philosophy of this period in general. More specifically, we have been furnishing evidence that the self-styled experimental philosophers both emphasized the importance of experiment and observation for the acquisition of knowledge, and decried the use of speculation and hypotheses that made little or no appeal to observation. We have also claimed that a prime example of a speculative philosophy that came under attack from experimental philosophers was the Cartesian vortex theory.

It may be surprising, therefore, that hitherto little has been said on this blog about Roger Cotes’ Preface to the second edition of Newton’s Principia published 300 years ago in 1713. For, Cotes’ Preface contains one of the most forthright and sustained defenses of experimental philosophy to be found in the early eighteenth century and it prefaces what can only be described as the most important contribution to natural philosophy in the early modern period.

Cotes begins his Preface with a tripartite distinction between ‘the whole of the Scholastic doctrine derived from Aristotle and the Peripatetics’, (The Principia, 1999, 385) ‘those who take the foundation of their speculations from hypotheses’ and ‘those whose natural philosophy is based upon experiment’. Needless to say, it is this latter method that is ‘incomparably [the] best way of philosophizing’ and ‘which our most celebrated author [Newton] thought should be justly embraced in preference to all others’. (386) The rest of the Preface is a justification of this method of experimental philosophy. First, he elaborates on the method in more detail. He then proceeds to show how Newton’s thesis of universal gravity was established according to this method. Next, he argues against the Cartesian vortex theory and plenist accounts of the universe and, finally, he brings it to a close claiming: ‘Therefore honest and fair judges will approve the best method of natural philosophy, which is based on experiments and observations’. (398).

In this post I shall outline one of the interesting features of Cotes’ critique of the Cartesian vortex theory. In my next post I’ll examine his view of the experimental philosophy in more detail. According to Cotes the speculators ‘are drifting off into dreams, … are merely putting together a romance, elegant perhaps and charming, but nevertheless a romance’ (386) One such romance is the Cartesian vortex theory.

Cometary motion through the vortices of Descartes

Cometary motion through the vortices of Descartes

In the first edition of the Principia (1687) Newton had advanced a number of arguments against the vortex theory at the end of Book Two, such as the claim that planets moving in a vortex would speed up at the point most distant from the sun when, in fact, the observational evidence and Kepler’s area law showed that they slowed down at this point. But apart from this, little mention is made of the theory. By contrast, in the second edition of the Principia the critique of the vortex theory is a prominent theme. In addition to the arguments at the end of Book Two, the new ‘General Scholium’ appended to the book begins ‘The hypothesis of vortices is beset with many difficulties’ (939) and there follows a whole paragraph on the problems with the theory. The final two sentences deal with the motion of comets, claiming that their regular motion ‘cannot be explained by vortices and that their eccentric motions can only be explained if ‘vortices are eliminated’. These are not claims that Newton makes in the Principia but are rather summaries of arguments that Cotes presents in his Preface.

About one quarter of the Preface is given over to a critique of vortices. In this section, Cotes develops the arguments from cometary motion that are alluded to in Newton’s Scholium. First he claims that bodies in a vortex must move in the same direction and with the same velocity as the surrounding fluid and must have the same density as the fluid that surrounds them. But comets and planets orbit the sun with different velocities and different directions even when they are in the same region of the heavens. Therefore, ‘those parts of the celestial fluid that are at the same distances from the sun revolve in the same time in different directions with different velocities’. But this cannot be accounted for by one vortex, so there will have to be more than one vortex ‘going through the same space surrounding the sun’. It must be asked then ‘how these same vortices keep their integrity without being in the least perturbed through so many centuries by the interactions of their matter’. (394 ) Moreover, because ‘the number of comets is huge’ and they obey the same laws as the planets going ‘everywhere into all parts of the heavens and pass very freely through the regions of the planets, often contrary to the order of the signs … [t]here will be no room at all for the motions of the comets unless that imaginary matter [of the vortices] is completely removed from the heavens’. (395)

What is striking about these arguments is that they are, in effect, the bookends of the Principia. They don’t appear in the body of the work, but are a kind of polemical after thought, and most importantly, they are set within the context of a defense of experimental philosophy. What is it that accounts for the extraordinary fact that Cotes introduced this material in the opening preface and that Newton should allude to it at the end when the arguments are absent from the book? This is not merely a rhetorical question. I would value any comments you may have.

Experimental philosophy in France

Peter Anstey writes…

When did the French embrace experimental philosophy? There is no doubt that the early Académie des Sciences was committed to the use of experimental methods in natural philosophy from its inception in 1666. But there is little evidence of French natural philosophers self-identifying as experimental philosophers, of the teaching of experimental philosophy or of institutional recognition of experimental philosophy before the 1730s.

In 1735 Abbé Nollet offered the first course in experimental philosophy in France and two years later he published Programme ou idée générale d’un cours de physique expérimentale which was strongly influenced by John Theophilus Desaguliers whom he had met in England around 1734. By the late 1730s, however, it is not hard to find explicit endorsements of experimental philosophy and the deployment of the experimental/speculative distinction. The reviewer of Abbé Pluche’s Spectacle de la Nature in 1739 claims that Pluche rightly prefers experimental natural philosophy to speculative (Physique spéculative à laquelle il préfére avec raison la Physique) and that experimental philosophy is ‘so à la mode today’ (qui est aujourd’hui si à la mode).

By the early 1750s experimental philosophy is part and parcel of French natural philosophy. We have discussed this before on this blog in relation to Denis Diderot, but the following nice, clear, anonymous dictionary entry reinforces the point. In the Dictionnaire philosophique ou Introduction à la connoisance de l’homme, London (?), 1751 we find the following entry under ‘Physique’:

Natural philosophy is the knowledge of causes and effects of nature. It is experimental or conjectural. Experimental natural philosophy is certain knowledge; conjectural natural philosophy is often only ingenious. The one leads us to the truth, the other leads to error.

La Physique est la connoissance des causes & des effets de la nature: elle est expérimentale, or conjecturale. La Physique expérimentale est une connoissance certaine; la Physique conjecturale n’est souvent qu’ingénieuse: l’une nous conduit à la vérité, & l’autre nous mene à l’erreur.

The parallels with our oft-cited passage from John Dunton’s student manual in 1692 are striking:

Philosophy may be consider’d under these two Heads, Natural and Moral: The first of which, by Reason of the strange Alterations that have been made in it; may be again Subdivided into Speculative and Experimental.

… we must consider, the distinction we have made of Speculative and Experimental, and, as much as possible, Exclude the first, for an indefatigable and laborious Search into Natural Experiments, they being only the Certain, Sure Method to gather a true Body of Philosophy, for the Antient Way of clapping up an entire building of Sciences, upon pure Contemplation, may make indeed an Admirable Fabrick, but the Materials are such as can promise no lasting one.

(The Young-Students-Library, London, 1692, vi–vii)

And yet the two passages are six decades apart. Why did it take so long for the French to take up experimental philosophy? Why is it, for example, that the first chair in experimental philosophy in England was the Cambridge Plumian Chair in Experimental Philosophy and Astronomy founded in 1708 and first held by Roger Cotes, whereas the first chair of experimental philosophy in France was held by Abbé Nollet who was appointed as Professeur Royal de Physique Expérimentale au College de Navarre in 1753?

Any light that our readers can shed on these questions would be most welcome.