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?
Observation, experiment and intervention in Newton’s Opticks
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.
Opticks, part I, figure 12.
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.
