Kirsten Walsh writes…
Lately I have been examining Baconian interpretations of Newton’s Principia. First, I demonstrated that Newton’s Moon test resembles a Baconian crucial instance. And then, I demonstrated that Newton’s argument for universal gravitation resembles Bacon’s method of gradual induction. This drew our attention to some interesting features of Newton’s approach, bringing the Principia’s experimental aspects into sharper focus. But they also highlighted a worry: Newton’s methodology resembling Bacon’s isn’t enough to establish that Newton was influenced by Bacon. Bacon and Newton were gifted methodologists—they could have arrived independently at the same approach. One way to distinguish between convergence and influence is to see if there’s anything uniquely or distinctively Baconian in Newton’s use of crucial experiments and gradual induction. Another way would be if we could find some explicit references to Bacon in relation to these methodological tools. Alas, so far, my search in these areas has produced nothing.
In this post, I’ll consider an alternative way of understanding Baconianism in the Principia. I began this series by asking whether we should regard Newton’s methodology as an extension of the Baconian experimental method, or as something more unique. In answering, I have hunted for evidence that the Principia is Baconian insofar as Newton applied Baconian methodological tools in the Principia. But you might think that whether Newton was influenced by Bacon isn’t so relevant. Rather, what matters is how the Principia was received by Newton’s contemporaries. So in this post, I’ll examine Mary Domski’s argument that the Principia is part of the Baconian tradition because it was recognised, and responded to, as such by members of the Royal Society.
Domski begins by dispelling the idea that there was no place for mathematics in the Baconian experimental tradition. Historically, Bacon’s natural philosophical program, centred on observation, experiment and natural history, was taken as fundamentally incompatible with a mathematical approach to natural philosophy. And Bacon is often taken to be deeply distrustful of mathematics. Domski argues, however, that Bacon’s views on mathematics are both subtler and more positive. Indeed, although Bacon had misgivings about how mathematics could guide experimental practice, he gave it an important role in natural philosophy. In particular, mathematics can advance our knowledge of nature by revealing causal processes. However, he cautioned, it must be used appropriately. To avoid distorting the evidence gained via observation and experiment, one must first establish a solid foundation via natural history, and only then employ mathematical tools. In short, Bacon insisted that the mathematical treatment of nature must be grounded on, and informed by, the findings of natural history.
Domski’s second move is to argue that seventeenth-century Baconians such as Boyle, Sprat and Locke understood and accepted this mathematical aspect of Bacon’s methodology. Bacon’s influence in the seventeenth century was not limited to his method of natural history, and Baconian experimental philosophers didn’t dismiss speculative approaches outright. Rather, they emphasised that there was a proper order of investigation: metaphysical and mathematical speculation must be informed by observation and experiment. In other words, there is a place for speculative philosophy after the experimental stage has been completed.
Domski then examines the reception of Newton’s Principia by members of the Royal Society—focusing on Locke. For Locke, natural history was a necessary component of natural philosophy. And yet, Locke embraced the Principia as a successful application of mathematics to natural philosophy. Domski suggests that we read Locke’s Newton as a ‘speculative naturalist’ who employed mathematics in his search for natural causes. She writes:
[O]n Locke’s reading, Newton used a principle—the fundamental truth of universal gravitation—that was initially ‘drawn from matter’ and then, with evidence firmly in hand, he extended this principle to a wide store of phenomena. By staying mindful of the proper experimental and evidentiary roots of natural philosophy, Newton thus succeeded in producing the very sort of profit that Sprat and Boyle anticipated a proper ‘speculative’ method could generate (p. 165).
In short, Locke regarded Newton’s mathematical inference as the speculative step in the Baconian program. That is, building on a solid foundation of observation and experiment, Newton was employing mathematics to reveal forces and causes.
In summary, Domski makes a good case for viewing the mathematico-experimental method employed in the Principia as part of the seventeenth-century Baconian tradition. I have a few reservations with her argument. For one thing, ‘speculative naturalist’ is surely a term that neither Locke nor Newton would have been comfortable with. And for another thing, although Domski has provided reasons to view Newton’s mathematico-experimental method as related to, and a development of, the experimental philosophy of the Royal Society, I’m not convinced that this shows that they viewed the Principia as Baconian. That is to say, there’s a difference between being part of the experimental tradition founded by Bacon, and being Baconian. I’ll discuss these issues in my next post, and for now, I’ll conclude by discussing some important lessons that I think arise from Domski’s position.
Firstly, we can identify divergences between Newton and the Baconian experimental philosophers. And these could be surprising. It’s not, in itself, his use mathematics and generalisations that makes Newton different—Domski has shown that even the hard-out Baconians could get on board with these features of the Principia. The differences are subtler. For example, as I’ve discussed in a previous post, Boyle, Sprat and Locke advocated a two-stage approach to natural philosophy, in which construction of natural histories precedes theory construction. But Newton appeared to reject this two-stage approach. Indeed, in the Principia, we find that Newton commences theory-building before his knowledge of the facts was complete.
Secondly, the account highlights the fact that early modern experimental philosophy was a work in progress. There was much variation in its practice, and room for improvement and evolution. Moreover, its modification and development was, to a large extent, the result of technological innovation and the scientific success of works like the Principia. Indeed, it was arguably the ability to recognise and incorporate such achievements that allowed experimental philosophy to become increasingly dominant, sophisticated and successful in the eighteenth century.
Thirdly, the account suggests that, already in the late-seventeenth century, the ESD framework was being employed to guide, and also to distort, the interpretation and uptake of natural philosophy. By embracing the Principia as their own, the early modern experimental philosophers intervened on and shaped its reception, and hence, the kind of influence the Principia had. This raises an interesting point about influence.
As I have already noted, it is difficult to establish a direct line of influence stretching from Bacon to Newton. But, by focusing on how Bacon’s program for natural philosophy was developed by figures such as Boyle, Sprat and Locke, we can identify a connection between Bacon’s natural philosophical program and Newton’s mathematico-experimental methodology. That is, we can distinguish between influence in terms of actual causal connections—Newton having read Bacon, for instance—and influence insofar as some aspect of Newton’s work is taken to be related to Bacon’s by contemporary (or near-contemporary) thinkers. Indeed, Newton could have been utterly ignorant of Bacon’s actual views on method, but the Principia might nonetheless deserve to be placed alongside Bacon’s work in the development of experimental philosophy. Sometimes what others take you to have done is more important than what you have actually done!
Kirsten Walsh writes…
Recently, I have been looking for clear cases of Baconianism in the Principia. In my last post, I offered Newton’s ‘moon test’ as an example of a Baconian crucial instance, ending with a concern about establishing influence between Bacon and Newton. Newton used his calculations of the accelerations of falling bodies to provide a crucial instance which allowed him to choose between two competing explanations. However, one might argue that this was simply a good approach to empirical support, and not uniquely Baconian. In this post, I’ll consider another possible Baconianism: Steffen Ducheyne’s argument that Newton’s argument for universal gravitation resembles Baconian induction.
Let’s begin with Baconian induction (this account is based on Ducheyne’s 2005 paper). Briefly, Bacon’s method of ampliative inference involved two broad stages. The first was a process of piecemeal generalisation. That is, in contrast to simple enumerative induction, shifting from the particular to the general in a single step, Bacon recommended moving from particulars to general conclusions via partial or mediate generalisations. Ducheyne refers to this process as ‘inductive gradualism’. The second stage was a process of testing and adjustment. That is, having reached a general conclusion, Bacon recommended deducing and testing its consequences, adjusting it accordingly.
Ducheyne argues that, in the Principia, Newton’s argument for universal gravitation proceeded according to Baconian induction. In the first stage, Newton’s argument proceeded step-by-step from the motion of the moon with respect to the Earth, the motions of the moons of Jupiter and Saturn with respect to Jupiter and Saturn, and the motions of the planets with respect to the Sun, to the forces producing those motions. He inferred that the planets and moons maintain their motions by an inverse square centripetal force, and concluded that this force is gravity—i.e. the force that causes an apple to fall to the ground. And, in a series of further steps (still part of the first stage), Newton established that, as the Sun exerts a gravitational pull on each of the planets, so the planets exert a gravitational pull on the Sun. Similarly, the moons exert a gravitational pull on their planets. And finally, the planets and moons exert a gravitational pull on each other. He concluded that every body attracts every other body with a force that is proportional to its mass and diminishes with the square of the distance between them: universal gravitation. Moving to the second stage, Newton took his most general conclusion—that gravity is universal—and examined its consequences. He demonstrated that the irregular motion of the Moon, the tides and the motion of comets can be deduced from his theory of universal gravitation.
Ducheyne notes that Newton didn’t attribute this method of inference to Bacon. Instead, he labelled the two stages ‘analysis’ and ‘synthesis’ respectively, and attributed them to the Ancients. However, Ducheyne argues that we should recognise this approach as Baconian in spirit and inspiration.
This strikes me as a plausible account, and it illuminates some interesting features of Newton’s approach. For one thing, it helps us to make sense of ‘Rule 4’:
In experimental philosophy, propositions gathered from phenomena by induction should be considered either exactly or very nearly true notwithstanding any contrary hypotheses, until yet other phenomena make such propositions either more exact or liable to exceptions.
Newton’s claim that, in the absence of counter-instances, we should take propositions inferred via induction to be true seems naïve when interpreted in terms of simple enumerative induction. However, given Newton’s ‘inductive gradualism’, Rule 4 looks less epistemically reckless.
Moreover, commentators have often been tempted to interpret this rule as an expression of the hypothetico-deductive method, in which the epistemic status of Newton’s theory is sensitive to new evidence. Previously, I have argued that, when we consider how this rule is employed, we find that it’s not the epistemic status of the theory, but its scope, that should be updated. Ducheyne’s Baconian interpretation supports this position—and perhaps offers some precedent for it.
Ducheyne’s suggestion also encourages us to re-interpret other aspects of Newton’s argument for universal gravitation in a Baconian light. Consider, for example, the ‘phenomena’. Previously, I have noted that these are not simple observations but observed regularities, generalised by reference to theory. They provide the explananda for Newton’s theory. In Baconian terms, we might regard the phenomena as the results of a process of experientia literata—they represent the ‘experimental facts’ to be explained. This, I think, ought to be grist for Ducheyne’s mill.
Interpreting Newton’s argument for universal gravity in terms of Baconian induction brings the experimental aspects of the Principia into sharper focus. These aspects have often been overlooked for two broad reasons. The first is that the mathematical aspects of the Principia have distracted people from the empirical focus of book 3. I plan to examine this point in more detail in my next post. The second is that the Baconian method of natural history has largely been reduced to a caricature, which has made it difficult to recognise it when it’s being used. Dana Jalobeanu and others have challenged the idea that a completed Baconian natural history is basically a large storehouse of facts. Bacon’s Latin natural histories are complex reports containing, not only observations, but also descriptions of experiments, advice and observations on the method of experimentation, provisional explanations, questions, and epistemological discussions. We don’t find such detailed observation reports in the Principia, but we do find some of the features of Baconian natural histories.
So, Ducheyne’s interpretation of Newton’s argument for universal gravitation in terms of Bacon’s gradualist inductive method proves both fruitful and insightful. However, recall that, in my last post, I worried that the resemblance of Newton’s methodology to Bacon’s isn’t enough to establish that Newton was influenced by Bacon’s methodology. If Bacon was just describing a good, general, epistemic method, couldn’t Newton have simply come up with it himself? He was, after all, an exceptional scientist who gave careful thought to his own methodology. Is Ducheyne’s discussion sufficient to establish influence? What do you think?
Kirsten Walsh writes…
In the General Scholium, which concluded later editions of Principia, Newton described the work as ‘experimental philosophy’:
In this experimental philosophy, propositions are deduced from phenomena and are made general by induction. The impenetrability, mobility, and impetus of bodies, and the laws of motion and the law of gravity have been found by this method.
On this blog, I have argued that we should take this statement at face value. In support, I have emphasised similarities between Newton’s work in optics and mechanics. For example, I have considered the kind of evidence provided in each work, arguing that both the Principia’s ‘phenomena’ and the Opticks’s ‘experiments’ are idealisations based on observation, and that they perform the same function: isolating explananda. I have also emphasised Newton’s preoccupation in the Principia with establishing his principles empirically. Finally, I have suggested that this concern with experimental philosophy, in combination with his use of mathematics, made Newton’s method unique.
In my last blog post, I wondered if we should regard Newton’s methodology as an extension of the Baconian experimental method, or as something more unique. I have written many blog posts discussing the Baconian aspects of Newton’s optical work (for example, here, here and here), but the Baconian aspects of the Principia are less well-established. I can identify at least three possible candidates for Baconianism in the Principia. The first, suggested by Daniel Schwartz in recent conversation, is that book 3 contains what might be interpreted as Baconian ‘crucial instances’. The second, discussed by Steffen Ducheyne, is that Newton’s argument for universal gravitation resembles Bacon’s method of induction. The third, discussed by Mary Domski, is that the mathematical method employed in the Principia should be viewed as part of the seventeenth-century Baconian tradition. In this post, I’ll focus on Schwartz’s suggestion—the possibility there is a crucial instance in book 3 of the Principia—I’ll address the rest in future posts.
To begin, what is a ‘crucial instance’? For Bacon, crucial instances (instantiae crucis) were a subset of ‘instances with special powers’ (ISPs). When constructing a Baconian natural history, ISPs were experiments, procedures, and instruments that were held to be particularly informative or illuminative of aspects of the inquiry. These served a variety of purposes. Some functioned as ‘core experiments’, introduced at the very beginning of a natural history, and serving as the basis for further experiments. Others played a role later in the process. This included experiments that were supposed to be especially representative of a certain class of experiments, tools and experimental procedures that provided interesting investigative shortcuts, and model examples that came close to providing theoretical generalisations.
Crucial instances are part of a subset of ISPs that were supposed to aid the intellect by “warning against false forms or causes”. When two possible explanations seemed equally good, then the crucial instance was employed to decide between them. To this end, it performed two functions: the negative function was to eliminate all possible explanations except the correct one; the positive function was to affirm the correct explanation.
According to Claudia Dumitru, Bacon’s crucial instances have a clear structure:
- Specify the explanandum;
- Consider the competing explanations (these are assumed to exhaust the possibilities);
- Derive a consequence from one explanation that is incompatible with the other explanation(s);
- Test that consequence.
Are there any arguments in the Principia that look like crucial instances? I think there’s at least one: Newton’s famous ‘Moon test’. Let’s have a look at it.
In proposition 4 book 3, Newton used his Moon test to establish that “The moon gravitates toward the earth and by the force of gravity is always drawn back from rectilinear motion and kept in its orbit”. Here, Newton argued that the inverse-square centripetal force, keeping the moon in orbit around the Earth, is the same force that, say, makes an apple fall to the ground, namely, gravity. I think we can tease out the features of a Baconian crucial instance from Newton’s reasoning here.
Firstly, there is an explanandum: what kind of force keeps the Moon in its orbit and prevents it from flying off into space? Secondly, two possible explanations are provided: the force is either (a) the same force that that acts on terrestrial objects, namely, gravity; or (b) a different force. Thirdly, we have a consequence of (a) that is incompatible with (b): if the moon were deprived of rectilinear motion, and allowed to fall towards Earth, it would begin falling at the rate of 15 1/12 Paris feet in the space of one minute, accelerating so that at the Earth’s surface it would fall 15 1/12 Paris feet in a second. Finally, we see a test of that consequence: the calculations based on the size and motion of the Moon, and its distance from the Earth. The results are taken to support (a) and refute (b).
I have three concluding remarks to make.
Firstly, interpreting the Moon test as a crucial instance involves ‘rational reconstruction’. In the text, Newton starts by calculating the rate at which the Moon would fall, and shows that this supports proposition 4. But I think my reading of this as a crucial instance is supported by Newton’s concluding remarks:
For if gravity were different from this force, then bodies making for the earth by both forces acting together would descend twice as fast, and in the space of one second would by falling describe 301/6 Paris feet, entirely contrary to experience.
Here, Newton described the Moon test as a crucial instance: he used an observation to choose between two competing explanations of the explanandum.
Secondly, when looking for crucial instances in the Principia, it might be tempting to start with the phenomena, listed at the beginning of book 3. Elsewhere, I have argued that these resemble Newton’s experiments in the Opticks, which function as instances with special powers. But the label ‘crucial instance’ describes the function, not the content, of an empirical claim. And so, to see if they provide crucial instances, we need to consider how the phenomena are used. In fact, I think they do provide crucial instances for Newton’s rejection of Cartesian vortex theory in favour of universal gravitation, found at the end of book 2. But again, this requires rational reconstruction.
Finally, there is the issue of historical influence. I have shown that Newton employed the Moon test to decide between two competing explanations, and that this argument resembles one of Bacon’s crucial instances. However, one might think that this was simply a good approach to empirical support, and that Newton was using his common-sense. So perhaps we shouldn’t take this to indicate (direct or indirect) influence. And so I have a question for our readers: was this style of reasoning uniquely Baconian?
Kirsten Walsh writes…
Recently, Zvi Biener and Eric Schliesser’s long-awaited volume, Newton and Empiricism, appeared on the shelves. The book is an excellent collection of papers, which makes a significant new contribution to the field. Today I want to focus on one aspect of this volume: the decision to frame the collection in terms of empiricism rather than experimental philosophy.
Over the last four years, we have provided many arguments for the superiority of the ESD over the RED. An important line of argument has been to show that ‘experimental philosophy’ and ‘speculative philosophy’ were the key terms of reference used by the actors themselves, and that they characterised their own work in terms of this division. For example, I have argued here, here, here and here that Newton is best understood as an experimental philosopher.
In their introduction, Biener and Schliesser explain their decision. They acknowledge the ‘Otago School’, and argue that, while in general there may be some good reasons to prefer the ESD to the RED, they see various problems with labelling Newton an ‘experimental philosopher’. Their concerns amount to the following: labelling Newton an ‘experimental philosopher’ obscures the idiosyncrasies of his approach to natural philosophy. They argue, firstly, that the label belies the significant influence of non-experimental philosophers on Newton’s methodology, for example those who influenced his mathematical focus. Secondly, that the label unhelpfully groups Newton with Boyle and Locke, when many features of his work support a different grouping. For example, Newton’s mathematical-system building suggests that his work should be grouped with Descartes’. Thirdly, they argue that the fact that Newton did not employ the label himself until after the publication of the first edition of the Principia suggests that he did not fully identify with the label.
These are important issues about the ESD and Newton’s place in it. So today I want to reflect on the broad problem of Newton’s idiosyncratic position. I argue that Newton’s divergence from Baconian tradition of the Royal Society is best seen as a development of experimental philosophy.
On this blog, I have sketched many features of Newton’s natural philosophical methodology. I have argued that, if we look at Newton from within the framework of the ESD, he can be neatly and easily identified as an experimental philosopher. His use of queries, his cautious approach to hypotheses, and his many methodological statements decrying the construction of metaphysical systems, suggest that this is a label that Newton would have been comfortable with. However, there is an important caveat to note: while Newton was clearly influenced by the Baconian experimental tradition, he did not consider himself a Baconian experimental philosopher.
In the earliest statements of his mathematico-experimental approach, Newton set up his position in opposition to the Baconian experimental philosophers. In these passages, one feature of Newton’s methodology stands out in explicit rejection of the Baconian method: his claims to certainty. This feature, in itself, is not very significant – many experimental philosophers believed that, in the end, natural philosophy would be a form of scientia, i.e. a system of knowledge demonstrated from certain axioms. Indeed, Bacon shared this ideal of certainty. He thought that his method of induction could get around the problems usually associated with ampliative inference and deliver knowledge of the essences of things. Thus, Bacon’s method of natural history was ultimately supposed to provide the axioms on which scientia could be founded. The challenge, which everyone agreed on, was to discover those axioms on which the system would be built.
Newton and the Baconians seem to diverge on their responses to this challenge. Baconian experimental philosophers recommended that one should have all the facts before formulating generalisations or theories. In contrast, Newton thought that a few, or even just one, well-constructed experiment might be enough – provided you used it in the right way. This shows that Newton took a different view of the role of evidence in natural philosophy. This divergence amounts to three key differences between Newton and the Baconian experimental philosophers:
- Where the Baconian experimental philosophers advocated a two-stage model, in which construction of natural histories preceded theory construction, Newton appeared to reject this two-stage approach. Newton commenced theory-building before his knowledge of the facts was complete.
- Related to (1), the Baconian experimental philosophers conceived of phenomena as immediate facts, acquired via observation, and hence pre-theoretic. In contrast, Newton’s phenomena were generalised regularities, acquired via mediation between observation and theory.
- For the Baconian experimental philosophers, queries were used to give direction and define the scope of the inquiry. But Newton’s queries were more focussed on individual experiments.
There is strong textual evidence that the ESD was operative in Newton’s early natural philosophical work. We have good reason to suppose that Newton regarded his natural philosophical pursuits as experimental philosophy. This becomes clearer in Newton’s later work. For instance, in the General Scholium to the Principia (1713), Newton explicitly described his work as ‘experimental philosophy’ – indeed, Peter Anstey has noted that Roger Cotes also recognised this feature of Newton’s work. We also have good reason to suppose that, in important ways, Newton saw his work as aligned with the Royal Society and, by extension, with the Baconian movement. But Newton was also a mathematician, and he saw a role for mathematical reasoning in experimental philosophy. In many ways, it was this mathematical approach that led to his divergence from the Baconian experimental philosophy.
Biener and Schliesser are right to draw attention to the ways in which Newton’s position diverged from the experimental tradition of the Royal Society. However, they fail to recognise that Newton’s position diverged in a way that should be viewed as a development of this tradition. Indeed, the ‘Newtonian experimental philosophy’ eventually replaced the experimental philosophy of Boyle, Hooke and the other early members of the Royal Society. The label ’empiricism’ has no such historical relevance. But, more on this another time…
Kirsten Walsh writes…
In my last post, I considered the experimental support Newton offers for his laws of motion. In the scholium to the laws, Newton argues that his laws of motion are certainly true. However, in support he only cites a handful of experiments and the agreement of other mathematicians. I suggested that the experiments discussed do support his laws, but only in limited cases. This justifies their application in Newton’s mathematical theory, but does not justify Newton’s claims to certainty. In this post, I will speculate that the laws of motion were in fact better established than Newton’s discussion suggests. I introduce the notion ‘epistemic amplification’ – suggesting that Newton’s laws gain epistemic status by virtue of their relationship to the propositions they entail. That is, by reasoning mathematically from axioms to theorems, the axioms obtained higher epistemic status, and so the reasoning process effectively amplified the epistemic status of the axioms.
I am not arguing that epistemic amplification captures Newton’s thinking. In fact, Newton explicitly stated that epistemic gain was not possible. For him, the best one could achieve was avoiding epistemic loss. (I have discussed Newton’s aims of certainty and avoiding epistemic loss here and here.) I suggest that, objectively speaking, the epistemic status of Newton’s laws increases over the course of the Principia.
- The specification of the laws as the axioms of a mathematical system; and
- The justification of laws as first principles in natural philosophy.
Let’s consider the first project. In addition to the support of mathematicians and the experiments that Newton cites, it is plausible that the epistemic status of the laws increases by virtue of their success in the mathematical system: in particular, by entailing Keplerian motion. Kepler’s rules and Newton’s laws of motion have independent evidence: as we have seen, Newton’s laws are weakly established by localised experiments and the ‘agreement of mathematicians’; Kepler’s rules are established by observed planetary motion and were widely accepted by astronomers prior to the Principia. Newton’s laws entail Kepler’s rules, which boosts Newton’s justification for his laws. Moreover, Newton’s laws provide additional support for Kepler’s rules, by telling us about the forces required to produce such motions. The likelihood of the two theories is coupled: evidence for one carries over to the other. So Newton’s laws also boost the justification for Kepler’s rules. Thus, Newton achieves epistemic gain: the epistemic status of the laws, qua mathematical axioms, has increased by virtue of their relationship to Kepler’s rules.
Now let’s consider the second project – the application of the laws to natural philosophy. Again, the discussion in the scholium justifies their use, but not their certainty. I now suggest that these laws, as physical principles, gain epistemic status through confirmation of Newton’s theory. This occurs in book 3, when Newton explicitly applies his mathematical theory to natural phenomena. As I have previously discussed, the phenomena (i.e. the motions of the planets and their moons) are employed as premises in Newton’s argument for universal gravitation. However, the phenomena also support the application of the mathematical theory to the physical world: they show that the planets and their moons move in ways that approximate Keplerian motion. As we saw above, the laws of motion entail Kepler’s rules. So, since the phenomena support Kepler’s rules, they also support the laws of motion. So this is a straightforward case of theory-confirmation.
There is also scope for theory-testing in book 1. Each time Newton introduces a new factor (e.g. an extra body, or a resisting medium), the mathematical theory is tested. For instance, the contrasting versions of the harmonic rule in one-body and two-body model systems provides a test: it allows the phenomena to empirically decide between two theories, one involving singly-directed central forces, the other involving mutually-interactive central forces. Similarly, the contrasting two-body and three-body mathematical systems provide a test: they allow the phenomena to select between a theory involving pair-wise interactions and a theory involving universal mutual interaction. Moreover, in the final section of book 2, Newton shows that, unlike his theory, Cartesian vortex theory does not predict Keplerian motion. Thus, the phenomena seem to support his theory, and by extension the laws of motion, and to refute the theory of vortices. Again, the laws seem to gain support by virtue of their relationship to the propositions they entail.
To summarise, Newton claims that his laws are certainly true, but the support he gives is insufficient. Here, I have sketched an account in which Newton’s laws gain epistemic status by virtue of their relationship to the propositions they entail. ‘Epistemic amplification’ is certainly not something which Newton himself would have had truck with, but the term does seem to capture the support actually acquired by Newton’s laws in the Principia. What do you think?
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.
University of Sydney
20 March, 2014
- 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
Contact: Prof Peter Anstey
Phone: 61 2 9351 2477
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.