Workshop: Mathematics and methodology from Newton to Euler
University of Sydney
20 March, 2014
9:15-5:30
Program:
- 9.15 Katherine Dunlop (Texas): ‘Christian Wolff on Newtonianism and Exact Science’
- 10.45 Coffee
- 11.00 Peter Anstey (Sydney): ‘From scientific syllogisms to mathematical certainty’
- 12.30 Lunch
- 2.00 Kirsten Walsh (Otago): ‘Newton’s method’
- 3.30 Stephen Gaukroger (Sydney): ‘D’Alembert, Euler and mid-18th century rational mechanics: what mechanics does not tell us about the world’
- 5.00 Wind up
Location: Common Room 822, Level 8, Brennan MacCallum Building
Contact: Prof Peter Anstey
Phone: 61 2 9351 2477
Email: peter.anstey@sydney.edu.au
RSVP: Here
Observation and Experiment in the Opticks: A Baconian Interpretation
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.
Figure 1 (Opticks, book 2 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.
Halley’s Comet and Christmas Day
Kirsten Walsh writes…
Hello Readers!
Since this is our last post for the year, and the holidays are almost upon us, I thought I’d tell you a Christmas story:
On Christmas day in 1758, Johann Georg Palitzsch, a German farmer and amateur astronomer, became the first person to witness the return of, what would become known as, Halley’s comet.
Halley’s comet is the only short-period comet (i.e. comet that completes an orbit in under 200 years) that is visible with the naked eye. It has featured in astronomical reports since at least 240 BC. However, it wasn’t until 1705 that it was recognised as the same object. That year, the English astronomer Edmund Halley determined the periodicity of the comet, writing about it in his Synopsis Astronomia Cometicae. With the help of Newton’s theories of elliptical orbit, Halley had studied the data of the comets that had appeared in 1531, 1607 and 1682, and recognised that they all followed similar paths. He made a rough estimate that the comet would return in 1758.
Halley died in 1742, and so he never saw the return of the comet. But Palitzsch’s Christmas day observation confirmed his claim that, indeed, there was a comet, visible by the naked eye, that had period of approximately 76 years. It was the first time anything other than a planet had been shown to orbit the earth. In 1759, the French astronomer Nicolas Louis de Lacaille named the comet after Halley.
This prediction counts, not only as a confirmation of Halley’s theory, but also of Newtonian physics, and of the mathematico-experimental method more generally. It seems fitting that this confirmation happened on the 116th anniversary of Newton’s birth!*
We at Early Modern Experimental Philosophy wish you a happy holiday. We look forward to hearing from you in 2014!
*Actually, Newton was born in England on 25 December 1642, but Palitzsch saw Halley’s comet in Germany on 25 December 1758. Until 1752, England used the Julian (‘Old Style’) calendar, whereas Europe had adopted the Gregorian (‘New Style’) calendar much earlier. There is a 10-day difference between the two calendars, so Newton’s birthdate adjusts to 4 January 1643 on the Gregorian calendar. So while both events happened on Christmas day, they happened on different Christmas days. (Also, I hope you will forgive me for this picture, that I couldn’t resist posting!)
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.
Defining early modern experimental philosophy (3): Some clarifications
Alberto Vanzo writes…
This is the third post in a series on defining early modern philosophy. In my earlier posts (1, 2), I claimed that
[E] To endorse the method of (early modern) experimental philosophy is to believe that one should only firmly commit to those substantive claims and theories that are warranted by experiments and observations.
In this post, I will clarify three related points in order to address some misunderstandings concerning the nature and the usefulness of the notion of experimental philosophy. I will make three claims. First, experimental philosophers did not need to eschew any theories altogether. Second, this does not entail that even Descartes, Leibniz, or some Scholastics were experimental philosophers. Third, the difficulty in classifying certain authors as experimental philosophers is not as worrying as it is sometimes portrayed.
Experiments and theories
As it should be clear from [E], one need not take on a fully a-theoretical attitude in order to endorse the method of experimental philosophy. The Proem of the Saggi di naturali esperienze, alongside other texts by experimental philosophers, states that the sole purpose of the Accademia del Cimento is “experimenting and narrating”, while eschewing any “hint of anything speculative”. Nevertheless, experimental philosophers were not required to completely avoid any theories. Those who endorse the method of experimental philosophy can consistently entertain theories, put them forward as hypotheses to be tested experimentally, reject theories that are incompatible with experimental evidence, tentatively or provisionally endorse the theories that they take to be more probable than their competitors, and even firmly endorse certain theories (such as corpuscularism), insofar they are warranted by experience. In the light of this, Boyle, Hooke, Locke and Newton can be said to have endorsed the method of experimental philosophy, even though they did not endorse the fully a-theoretical stance that is often associated with the movement.
Who wasn’t an experimental philosopher?
One may fear that, once we grant that experimental philosophers could be engaged in some forms of theorizing, the notion of experimental philosophy becomes too inclusive, so that Descartes, Leibniz, and even certain Aristotelians can be classed as experimental philosophers. This is not the case. The fact that an experimental philosopher can endorse theories and substantive natural-philosophical claims does not entail that there is no real distinction between those who endorsed and those who did not endorse the method of experimental philosophy.
Descartes and Leibniz too engaged in experiments. Leibniz even claimed to be “strongly in favour of the experimental philosophy”. However, insofar as Descartes thought that he had firmly established the highly speculative cosmogonical theories of the Principles of Philosophy, in spite of the scant empirical evidence with which he backed them up, he was hardly following the methodological prescription spelt out in [E]. As for Leibniz, although he stressed the importance of experience for natural philosophy, he also held that some basic propositions of natural philosophy (like the principle of uniformity of nature) could be established only a priori. This view is incompatible with [E], we should not take Leibniz to be an experimental philosopher even though he stressed the importance of experience.
Problems of classification
Although there is a real distinction between those who endorsed the method of experimental philosophy and those who did not, establishing whether an early modern author really was an experimental philosopher is sometimes difficult. There can be a disconnect between rhetoric and methodology, or methodology (understood in the etymological sense of method-talk) and actual, practised method.
Some philosophers called themselves experimental philosophers, or endorsed the rhetoric of the movement (e.g. using “hypothesis” and “speculation” as a term of abuse), but they thought they were entitled to endorse certain natural-philosophical claims a priori. Others claimed that they were following the method of experimental philosophy, but they endorsed theories that outstripped the empirical evidence. Leibniz, as we have seen, is an example of the disconnect between rhetoric and methodology. Another example is provided by those Jesuits, like Daniello Bartoli, who rehearsed the experimentalist rhetoric, but attempted to take the sting out of experimentalism and to combine it with some Aristotelian doctrines that were hardly warranted by experience. In other cases, there was a disconnect between methodology and actual method. An example is provided by the account of vision of the late seventeenth-century Italian natural philosopher Francesco Bianchini. Not only his rhetoric, but also his methodological pronouncements were in line with [E]. However, his account of vision was far more speculative than those pronouncements allowed.
The disconnect between rhetoric, methodology, and practised method determines a difficulty in establishing whether certain authors were experimental philosophers. This would be worrying if a primary aim of the study of early modern experimental philosophy were providing a handy classification of early modern authors. However, the point of studying early modern experimental philosophy is not pigeonholing early modern authors, but understanding their philosophical views and practices, even when the former were not in line with the latter. Finding these discrepancies should not be surprising. People sometimes fail to practice what they preach. Other times, they use a rhetoric that is at least partly out of step with their actual views. Early modern philosophers were no exception.
Cartesianism, experimentalism, and the experimental-speculative distinction
A guest post by Tammy Nyden and Mihnea Dobre.
Tammy Nyden and Mihnea Dobre write…
A while ago, we published an announcement on this blog of our forthcoming edited volume, Cartesian Empiricisms (Springer 2013). A claim in that post – that some Cartesians “seem to escape the ESD distinction” – has been questioned by Peter Anstey in another post. We thank him for the intervention and would like to push forward our claim and discuss it in more detail as this will reveal some of our concerns with the ESD (experimental-speculative distinction).
In his reply, Peter Anstey asked, “Did the Cartesians practise a form of experimental philosophy analogous to that of the Fellows of the early Royal Society?” We would argue that the question itself is problematic, as there are not two practices or worldviews to compare. There is variation among the Cartesians as well as among the fellows of early Royal Society. In order to gain a nuanced understanding of these historical actors, we suggest a rather different question: “What role did Cartesian philosophy play in the acceptance and spread of experimental practices in late seventeenth-century philosophy?” When we ask this question, we recognize the experiments of Robert Desgabets on blood transfusion, Henricus Regius on liquids, Burchard de Volder’s with air-pumps, etc., and consider how their work improved experimental technologies, influenced a theoretical reflection on the role of experiments and the senses in natural philosophy, and influenced institutional change that was favorable to experimental science.
Because Cartesians took various aspects of Descartes’ system and merged it with various aspects of experimentalism, there is not one ‘Cartesian’ use of experiment, but several. For example, both Regius and de Volder promoted experiment, but Regius rejects Descartes’ theory of innate ideas while de Volder defends it. Many Cartesians came to reject hyperbolic doubt, some defended vortex theory, some did not. Cartesian Empiricisms is not a complete inventory of such views expressed by Descartes’ followers. Rather our goal was to encourage the discussion of the above-mentioned question and to reveal some aspects that have been unfortunately neglected so far by both historians of philosophy and science.
Readers of this blog are familiar with the objection that traditional historiography of science was built on the Rationalist-Empiricist distinction (RED). A consequence is the exclusion of so-called “rationalists” from the histories of science, particularly history of the use, development and acceptance of experiment. This is problematic because recent research (e.g., Ariew, Lennon and Easton, Easton, Schmaltz, Cook, Nyden, Dobre, etc.) shows that many so-called rationalists were deeply involved in the practice and spread of the acceptance of experiment in natural philosophy. Cartesian Empiricisms gives further emphasis to this issue, as it examines several philosophers who identified as committed Cartesians who were deeply involved in experiment. According to historiographies that divide the period into two mutually exclusive epistemologies or methodologies these philosophers either do not exist (i.e., they are overlooked by histories of philosophy and science) or are seen as “not really Cartesian” or “not really experimentalist,” as it would be needed by that particular narrative. Thus, we do share the concern of the authors of this blog, that such binaries as RED force us to fit philosophers into categories that they would not themselves recognize and causes us to misrepresent seventeenth-century natural philosophy. Moreover, we acknowledge that this blog importantly shows the anachronism of the RED, a way of viewing the period that is constructed later by what may be called Kantian propaganda. However, we would like to raise now some of our concerns with the distinction promoted by this blog, the experimental-speculative distinction (ESD) and explain why some Cartesians would escape the ESD. Our worries cover two important aspects of the ESD: the label “speculative” and the actor-category problem.
(1) In a very recent post, Peter Anstey argued that eighteenth-century Newtonians pointed out Cartesian vortex theory as a prime representative of speculative philosophy (our emphasis). We caution against letting eighteenth-century Newtonian propaganda color a historical interpretation of seventeenth-century natural philosophy. Voltaire, d’Alembert and others took great pains to contrast Newtonianism from Cartesianism as two mutually exclusive worldviews who battled it out, with Newton’s natural philosophy as the victor. But the reality is that after Descartes’ death (1650) and before the victory of Newtonianism in the middle of the eighteenth century, followers of both Descartes and Newton had more in common than we are led to believe. More importantly, both “camps” had more diversity than we were ready to accept in the traditional histories. Cartesian Empiricisms draws attention to that diversity within Cartesianism. Perhaps the one thing Cartesians discussed in the chapters of this volume do have in common is that they do both experimental and speculative philosophy, as these two categories are sometimes defined on this blog. But this last claim leads to our second concern with the ESD.
(2) A reader of this blog will find that when ESD is compared to RED, the first advantage highlighted over the latter is that “the ESD distinction provided the actual historical terms of reference that many philosophers and natural philosophers used from the 1660s until late into the 18th century.” While there is no doubt that many early modern philosophers were using this language (i.e., “experimental” and “speculative”) in their writings, it is equally true that such language is not in use by the Cartesians. If one would be very strict with picking up “the actual historical terms of reference,” one will see another pair of terms keep mentioned by various Cartesians, “experience” and “reason.” Of course, one can read this pair as another form of the ESD, but that would be an interpretation, and a problematic one at that. Both the Cartesians and the so-called “experimentalists” were trying to determine the proper relationship between reason and experience and when one looks at their attempts, it becomes even more difficult to draw a clear line between speculative philosophers and experimentalist philosophers.
Our concern is the possible danger of transforming ESD into a new RED. Experimental and speculative may be useful adjectives to describe aspects of a particular philosophy or particular commitments of a philosopher (especially when the two terms are clearly stated in one’s writings). However, they are not useful for dividing philosophers or their natural philosophies, particularly when they are not already conceived as falling within the “experimental philosophy” camp, as is the case for Cartesians at the end of the seventeenth century.
Newton’s ‘Phenomena’ continued…
Kirsten Walsh writes…
In my last post, I considered the phenomena in book 3 of Newton’s Principia. Newton’s decision to label these propositions ‘phenomena’ is puzzling, as they do not seem to fit any standard definition of the term. In this post, I’ll consider Bogen & Woodward’s (1988) distinction between data, phenomena and theories, and suggest that it sheds light both on Newton’s use of ‘phenomena’ and on the connection between his methodology in Opticks and Principia.
Bogen & Woodward (B&W) have argued for a 3-level picture of scientific theories in which:
- ‘Data’ are records produced by measurement and experiment that serve as evidence or features of phenomena. E.g. bubble chamber photographs, and patterns of discharge in electronic particle detectors.
- ‘Phenomena’ are features of the world that in principle could recur under different contexts or conditions. E.g. weak neutral currents, and the decay of a proton.
- ‘Theories’ are explanations of the phenomena.
B&W argue that theories explain phenomena, but not data. Data usually reflect many causal influences besides the explanatory target, while phenomena typically reflect single, or small, manageable numbers of causal influences. For example, General Relativity explains the phenomenon of bending light, but doesn’t explain the workings of the cameras, optical telescopes, etc. that causally influence the data.
Can we characterise Newton’s phenomena in terms of these three levels of theory? Let’s consider phenomenon 1:
- “The circumjovial planets, by radii drawn to the centre of Jupiter, describe areas proportional to the times, and their periodic times – the fixed stars being at rest – are as the 3/2 powers of their distances from that centre.”
In his discussion of this phenomenon Newton explained, “This is established from astronomical observations.” He provided the following table:
These observations are not data in the ‘pure’ sense that B&W discuss. Rather, they are generalisations: average distances and calculated periods of orbit. Moreover, the bottom row contains the average distances calculated from the period and the Harmonic rule (that the periods are as the 3/2 power of the semidiameters of their orbits). These calculations illustrate the ‘fit’ between the expected distance and the observed distance. Nevertheless, they provide a good example of how we might get from a set of data to a phenomenon. So perhaps we can think of them as ‘data’ in a methodological sense: they are records from which phenomenal patterns can be drawn.
I have another reason for considering these calculations ‘data’ in B&W’s sense of the term. In his discussion of phenomenon 1, Newton indicated that these calculations reflect a number of causal influences besides gravity. For instance, he explained that the length of the telescope affected the measurement of Jupiter’s diameter, because
- “the light of Jupiter is somewhat dilated by its nonuniform refrangibility, and this dilation has a smaller ratio to the diameter of Jupiter in longer and more perfect telescopes than in shorter and less perfect ones.”
This is a nice illustration of B&W’s notion of the shift from data to phenomena. By attending to his theory about telescopes, Newton was able to manipulate the data to control for distortion.
Now let’s consider the role of phenomenon 1 in Principia. Phenomenon 1 is employed (in conjunction with proposition 2 or 3, book 1, and corollary 6 to proposition 4, book 1) to support proposition 1, theorem 1, book 3:
- “The forces by which the circumjovial planets are continually drawn away from rectilinear motions and are maintained in their respective orbits are directed to the centre of Jupiter and are inversely as the squares of the distances of their places from that centre.”
This theorem doesn’t contain any information about the sizes or positions of the satellites of Jupiter, or about the workings of telescopes. So, while it explains the phenomenon, it gives no direct explanation of the data. This suggests that, in the Principia, data and phenomena are methodologically distinct.
B&W’s distinction between ‘data’ and ‘phenomena’ reveals two methodological features of Newton’s phenomena:
Firstly, Newton’s phenomena are explananda, but not appearances. Traditionally, ‘phenomenon’ seems to have been synonymous with both ‘appearance’ and ‘explanandum’. For example, the ancient Greeks were concerned to construct a system that explained and preserved the motions of the celestial bodies as they appeared to terrestrial observers. 2000 years later, Galileo and Cardinal Bellarmine argued over which system, heliocentric or geocentric, provided a better fit and explanation of these appearances. This suggests that, traditionally, there was no real difference between phenomena and data. For Newton, however, these come apart. The six phenomena of Principia describe the motions of celestial bodies, but not as they appear to terrestrial observers. In this sense, they are not appearances, but they do require an explanation.
Secondly, this reveals a continuity in Newton’s methodology. The point of Newton’s articulation of ‘phenomena’ in Principia is the same as his experiments in Opticks. Both identify and isolate a pattern or regularity. 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.
These considerations are admittedly speculative, so I’m keen to hear what our readers think. Does this look like a good way of characterising Newton’s phenomena?
Newton’s ‘Phenomena’
Kirsten Walsh writes…
On this blog, I have often argued that Newton’s Principia should be characterised as a work of experimental philosophy (for example, here, here and here). To support this argument, I have tended to emphasise similarities between Newton’s work in optics and mechanics. Recently, however, I have noted that some aspects of Newton’s methodology varied according to context. For example, in the Opticks, Newton employed ‘experiments’, but in the Principia, he employed ‘phenomena’. Given that experimental philosophy emphasises observation- and experiment-based knowledge, it is important for my project that I understand Newton’s use of phenomena, and its relationship to observation. In this post, I’ll discuss the phenomena in Principia, and in my next, I’ll discuss the relationship between phenomena and experiments in more detail.
Firstly, let’s consider the origin of the phenomena of Principia. In the first edition of Principia (1687), book 3 contained nine hypotheses. But in the second edition (1713), Newton re-structured book 3 so that it contained only two hypotheses. Five of the old hypotheses were re-labelled ‘phenomena’, and he added one more (phenomenon 2), to bring the total to six:
Phenomenon 1: The circumjovial planets, by radii drawn to the centre of Jupiter, describe areas proportional to the times, and their periodic times – the fixed stars being at rest – are as the 3/2 powers of their distances from that centre.
Phenomenon 2: The circumsaturnian planets, by radii drawn to the centre of Saturn, describe areas proportional to the times, and their periodic times – the fixed stars being at rest – are as the 3/2 powers of their distances from that centre.
Phenomenon 3: The orbits of the five primary planets – Mercury, Venus, Mars, Jupiter, and Saturn – encircle the sun.
Phenomenon 4: The periodic times of the five primary planets and of either the sun about the earth or the earth about the sun – the fixed stars being at rest – are as the 3/2 powers of their mean distances from the sun.
Phenomenon 5: The primary planets, by radii drawn to the earth, describe areas in no way proportional to the times but, by radii drawn to the sun, traverse areas proportional to the times.
Phenomenon 6: The moon, by a radius drawn to the centre of the earth, describes areas proportional to the times.
There are several things to notice about these phenomena. Firstly, they are distinct from data, in that they describe general patterns of motion, rather than measurements of the positions of planetary bodies at particular times. So, while the phenomena are detected and supported by astronomical observations, they are not observed or perceived directly.
Secondly, they are distinct from noumena (or the nature or essence of things), in that they are facts inferred from the observable, measurable properties of the world. They describe the motions, sizes and locations of bodies, but not the substance or causes of these properties of bodies.
Thirdly, they describe relative motions of bodies. That is, in each case, the orbit is described around a fixed point. For example, phenomenon 1 describes the motions of the satellites of Jupiter around Jupiter, which is taken as a stationary body for the purposes of this proposition. In phenomena 4 and 5, the motion of Jupiter is described around the sun, which is taken as stationary.
Fourthly, these phenomena do not prioritise the observer. Rather, each motion is described from the ideal standpoint of the centre of the relevant system: the satellites of Jupiter and Saturn are described from the standpoints of Jupiter and Saturn respectively, the primary planets are described from the standpoint of the sun, and the moon is described from the standpoint of the Earth. And because Newton doesn’t prioritise the observer, effects such the phases and retrograde motions of the planets are not phenomena but only evidence of phenomena.
The re-labelling of these propositions as ‘phenomena’ is somewhat puzzling. The term ‘phenomenon’ has a variety of uses, such as:*
- A particular (kind of) fact, occurrence, or change, which is perceived or observed, the cause or explanation of which is in question;
- An immediate object of sensation or perception (often as distinguished from a real thing or substance); or
- An exceptional or unaccountable thing, fact or occurrence.
But, as we’ve seen, Newton’s ‘phenomena’ don’t properly fit any of these definitions. Can any reader shed light on what Newton really meant by the term?
* Definitions (a) and (c) feature in both C18th and C21st dictionaries, but in the C21st, definition (b) has become more prominent, particularly in philosophy.
UPDATE: I have written a follow-up post.
René Réaumur and Charles Dufay on Experimental Natural Philosophy
A guest post by Michael Bycroft, a PhD Student at Cambridge.
Michael Bycroft writes…
René Réaumur
In a recent post Peter Anstey asked: “When did the French embrace experimental philosophy?” In this post I want to do two things. One is to draw attention to two Frenchmen who practised experimental natural philosophy (ENP) well before Jean-Antoine Nollet began teaching this method in the mid-late 1730s. These men were René Réaumur and Charles Dufay. My other task is to try to explain why these men, who did so much to practice ENP, did so little to explicitly define or defend their practice.
René Réaumur (1683-1757) was arguably the most active and influential member of the Académie des Sciences in the first half of the eighteenth century. Nowadays he is known for his research on insects, steel-making, and thermometry, but his interests were truly encyclopaedic. Charles Dufay (1698-1739) is known to historians of physics as a student of electricity, but his research interests were nearly as broad as those of Réaumur, his patron and collaborator.
There is no doubt that these two men practiced ENP. It is true that they were Cartesians, in the sense that their chief theoretical resources were vortices and subtle fluids. But they wore their theory lightly, and they saw themselves primarily as experimenters rather than as system-builders. This pair was at least as committed to ENP, and in some cases more so, than their French colleague Nollet or their English counterparts Francis Hauksbee the Elder and John Desaguliers.
Yet it is hard to find clear, succinct, accessible endorsements of the key tenets of ENP in the writings of Dufay and Réaumur. Such endorsements do exist, but they are invariably buried in the middle of one or other of the many papers they published in the Académie’s journal, the Mémoires de l’Académie Royale des Sciences. Here is an example from one of Réaumur’s first papers, on the growth of shells, published in the 1709 volume of the Mémoires:
- But conjectures such as these [ie. the ones Réaumur had just advanced in the first part his paper] are not enough in true natural philosophy. Experiments performed on the matters at hand are the only sound basis for our reasoning…It is to experiments that I shall turn to decide whether I have correctly described the manner in which nature behaves, or whether [instead] everything I have said is merely a trick of the imagination.
- Mais de pareilles conjectures ne suffisent point en bonne Physique. Les seules expériences faites sur les choses dont il est question, y doivent servir de bases à nos raisonnemens. … C’est aux experiences que je vais rapporter à faire voir, si j’ai véritablement décrit la maniere dont la Nature agit, ou si l’on doit regarder tout ce qu’on vient d’avancer comme un simple jeu d’imagination.
Charles Dufay
This statement is clearly in the spirit of ENP, and similar statements can be found elsewhere in Réaumur’s papers, and in Dufay’s. But they are fleeting asides rather than stand-alone manifestos. Why were these men so reticent?
An important part of the answer is that the stand-alone manifestos of Nollet, Hauksbee and Desaguliers appear in the prefaces of their natural philosophy textbooks, and Dufay and Réaumur did not write textbooks. They did not need to. They were independently wealthy, drew sizeable pensions from the Academy, and were well-rewarded by the state for their research on French industries such as steel and textiles.
Perhaps it is also relevant that Bernard le Bovier de Fontenelle, the Perpetual Secretary of the Academy, did much to define and defend the Academy’s activities on behalf of its members.
Another factor may be that Dufay and Réaumur were more concerned to defend the application of natural philosophy to industry (against skeptical artisans and ministers) than they were to defend the application of experiment to natural philosophy (against speculative philosophers). At any rate, the former concern dominated the preface to Réaumur’s first book, L’art de convertir le fer en acier (1722).
Finally, as we have seen, Dufay and Réaumur dispensed methodological advice in the course of the papers they published in the Academy. Perhaps they considered this the best forum for expressing their views on ENP, even though this choice makes their views harder for the historian to identify than if they had written textbooks or dictionary entries instead.
This is not to say that Dufay and Réaumur had no connections with earlier and later textbook writers on ENP in France. On the contrary. They both learned much of their physics from Jacques Rohault’s Traité de physique, and in their turn they taught Nollet much of what he knew about experimentation (Nollet assisted both Dufay and Réaumur in their laboratories in the early 1730s). These connections reinforce the broader lesson of this post, which is that the leading practitioners of ENP were not always its most explicit promoters.
Defining Early Modern Experimental Philosophy (2)
Alberto Vanzo writes…
In my last post, I raised the question as to whether there is any methodological view that was shared by all or most early modern experimental philosophers. To paraphrase Bas Van Fraassen, is there any statement E+ such that
- To endorse the method of (early modern) experimental philosophy = to believe that E+ (the experimentalists’ methodical dogma)?
As those of you who have followed this blog for a while will know, early modern experimental natural philosophers claimed that we should reject hypotheses and speculations (that is, roughly, natural-philosophical claims and theories) and rely instead on experiments and observations. In this post, I will discuss whether this claim, suitably understood, is the experimentalists’ methodical dogma. What does their rejection of hypotheses amount to?
The statement that we should reject hypotheses does not mean that we should avoid learning natural-philosophical claims and theories. On the contrary, according to Robert Hooke, learning hypotheses is beneficial because it helps us to devise new explanations and raise questions:
- the Mind will be somewhat more ready at guessing at the Solution of many Phenomena almost at first Sight, and thereby be much more prompt at making Queries, and at tracing the Subtilty of Nature, and in discovering and searching into the true Reason of things […]
Experimental philosophers also allow us to entertain claims and theories for the sake of testing them. Robert Boyle states in a letter to Oldenburg that natural histories should include “Circumstances” such that their “tryal or Observation” is “necessary or sufficient to prove or to invalidate this or that particular Hypothesis or Conjecture”.
Boyle’s statement makes clear that he allows for the acceptance of a natural-philosophical claims that are proven by “tryal [experiment] or Observation”. The claims in question must be those that are expressed by substantive or – in Kantian terms – synthetic a posteriori statements. Experiments and observations cannot prove analytic a priori statements. These are hardly the kind of statements that concerned experimental philosophers. Assuming that the analytic/synthetic distinction is tenable, accepting analytic a priori statements as true seems to be a harmless move anyway.
In the light of this, we may be tempted to paraphrase the rejection of hypotheses as follows:
- [A] Only commit to those substantive (as opposed to analytic) claims and theories that are warranted by experiments or observations.
[A] is in line with experimental philosophers’ rejection of arguments from authority, epitomized by the motto of the Royal Society: “nullius in verba“, which can be loosely translated as “take no man’s word for it”. [A] entails the rejection not only of arguments from authority, but also any kind of a priori arguments for substantive natural-philosophical claims – for instance, the arguments that Descartes used in the Principles of Philosophy to establish that material objects are made up of corpuscles. [A] has the welcome effect of classifying Descartes where, in my view, he belongs: outside of the movement of experimental philosophy, even though he too gathered natural-philosophical observations and performed some experiments.
However, [A] is inconsistent with the fact that many experimental philosophers were committed to substantive claims, like the corpuscularian and mechanist hypotheses, that were hardly warranted by the then extant empirical evidence. Boyle or Montanari did not seem to be concerned to provide detailed empirical arguments for corpuscularism or mechanism. However, they did not regard their acceptance of these views as being inconsistent with their commitment to experimentalism.
In view of this, I suggest replacing [A] with [B]:
- [B] Only firmly commit to those substantive claims and theories that are warranted by experiments and observations
and claiming that experimental philosophers like Boyle and Montanari did not firmly commit to corpuscularism and mechanism. They only weakly, tentatively, provisionally commit to these views, even though they were confident that future discoveries would dispel any doubt on their truth.
Is it correct to say that experimental philosophers’ commitments to mechanism and corpuscularism was typically weak, provisional, tentative? Are there other claims on the natural world that experimental philosophers firmly endorsed, even though the then available empirical evidence did not warrant them? Can a clear distinction between weak, provisional, tentative and strong, definitive, firm commitments be drawn, and if so, how? If you have any suggestions on how these questions should be answered, please let me know in the comments or get in touch. Answering these questions is important to establish if my suggestion that [B] represents a suitable candidate for the experimentalists’ methodical dogma is persuasive.
