Hypotheses and Newton’s Epistemic Triad
Kirsten Walsh writes…
Over the weekend, I participated in a conference on ‘Newton and his Reception’, at Ghent University. I presented a paper based on my idea that Newton is working with an ‘epistemic triad’. I had an excellent audience in Ghent, and received some very helpful feedback, but I’d like to hear what you think…
To begin, what is Newton’s ‘epistemic triad’?
In his published work, Newton often makes statements about his purported method in order to justify his scientific claims. In these methodological statements, he contrasts things that have strong epistemic credentials with things that lack those credentials. Consider, for example, these passages from his early papers on optics:
- For what I shall tell concerning them is not an Hypothesis but most rigid consequence, not conjectured by barely inferring ’tis thus because not otherwise or because it satisfies all Phænomena … but evinced by ye mediation of experiments concluding directly & wthout any suspicion of doubt. (6 February 1672)
- I shall not mingle conjectures with certainties… (6 February 1672)
- To determine by experiments these & such like Queries wch involve the propounded Theory seems the most proper & direct way to a conclusion. (3 April 1673)
What these passages tell us is that Newton is making a distinction between theories, which are certain and experimentally confirmed, hypotheses, which are uncertain and speculative, and queries, which are not certain, but provide the proper means to establish the certainty of theories. I call this three-way division Newton’s ‘epistemic triad’, and argue that this triad provides the framework for Newton’s methodology.
To support this argument, I defended the following three theses:
Endurance thesis. There are some general features of Newton’s methodology that don’t change. These are characterised by the framework of the epistemic triad.
Developmental thesis. There are some particular features of Newton’s methodology that change over time. These can be characterised as a development of the epistemic triad.
Contextual thesis. There are some particular features of Newton’s methodology that vary with respect to context (namely, mechanics versus optics). These can be characterised as an adaptation of the epistemic triad to particular contexts.
The developmental and contextual theses are not news to most Newton scholars. It is commonly accepted that Newton’s methodology changed in important ways over the course of his life, and that there are methodological differences between Principia and Opticks. The endurance thesis is more problematic, so I made a special effort to show that Newton’s use of hypotheses is more consistent than we think. I argued that:
- In Principia, Newton appears to be working with the same implicit definition of ‘hypothesis’ that he works with in his early optical papers; and
- Hypotheses perform similar methodological roles in all of Newton’s natural philosophical work.
I need to do some more work to properly explicate this methodological role. But, to state it very broadly, Newton temporarily assumes hypotheses, which act as ‘helping premises’ in his inferences from phenomena. The fact that a statement may appear in Newton’s writing as a hypothesis, and then reappear later in a query, rule of reasoning, or phenomenon, has convinced many Newton scholars that Newton is inconsistent in his use of hypotheses. Against this conviction, I argue that Newton applies the label ‘hypothesis’ to things that perform a particular function, rather than to a particular claim.
Hypotheses versus Queries in Newton’s Opticks
Kirsten Walsh writes…
A while ago I argued that the queries in Newton’s early optical papers are not hypotheses. Rather, they are empirical questions that may be resolved by experiment. In Newton’s Opticks, however, his queries become increasingly speculative – especially the famous ‘Query 31’. What should we make of this? Did Newton abandon his early distinction between hypotheses and queries?
In his early optical papers, Newton explains that “the proper Method for inquiring after the properties of things is to deduce them from Experiments”. Having obtained a theory in this way, one should proceed as follows:
- specify queries that suggest experiments that will test the theory; and
- carry out those experiments.
He tells us that hypotheses have a role in this procedure. They may be useful for: (a) suggesting further experiments, as the first step toward specifying queries; and (b) ‘illustrating’ the theory to assist understanding.
The queries in Newton’s Opticks have been much talked about, and often Newton has been accused of slipping hypotheses into his work under the guise of the more-respectable query. To examine this claim, I looked at the draft manuscripts* of Newton’s Opticks; in particular, “The fourth book concerning the nature of light & ye power of bodies to refract & reflect it” (Add. 3970, 337-8).
The draft begins, as many of the other books of Opticks begin, with a list of observations, followed by numbered propositions. However, it contains little in the way of argument and virtually no discussion of experimental evidence. Shapiro points out that this is because this is a draft of an outline or plan of a book; not a draft of the book itself. The propositions are things that Newton hoped to prove. For example:
- Prop. 1. The refracting power of bodies in vacuo is proportional to their specific gravities.
Prop. 2. The refracting power of two contiguous bodies is the difference of their refracting powers in vacuo.
The draft contains a section entitled ‘The conclusion’, which contains five ‘hypotheses’. I am interested in ‘Hypothesis 2’:
- As all the great motions in the world depend upon a certain kind of force (wch in this earth we call gravity) whereby great bodies attract one another at great distances: so all the little motions in ye world depend upon certain kinds of forces whereby minute bodies attract or dispell one another at little distances.
- How the great bodies of ye earth Sun moon & Planets gravitate towards one another what are ye laws of & quantities of their gravitating forces at all distance from them & how all ye motions of those bodies are regulated by those their gravities I shewed in my Mathematical Principles of Philosophy to the satisfaction of my readers: And if Nature be most simple & fully consonant to her self she observes the same method in regulating the motions of smaller bodies wch she doth in regulating those of the greater… The truth of this Hypothesis I assert not because I cannot prove it. But I think it very probable because a great part of the phaenomena of nature do easily flow from it wch seem otherways inexplicable…
I. Bernard Cohen describes this as “a ‘whale’ of an hypothesis” – and he’s right! When Newton started writing out this statement, he intended for it to be ‘Proposition 18’. But at some point, he has scratched out ‘Prop 18’, and re-branded it as ‘Hypoth 2’. There is no real semantic difference between a proposition and a hypothesis, but, for Newton, there is an epistemic difference. Propositions are things that he is able to assert as true. Hypotheses are things that he is unable to assert, because he does not have the evidence. Newton clearly hoped to assert Proposition 18. But as he started to explicate it, he must have realised that he couldn’t prove it. Thus, he re-labelled it as a hypothesis.
When Newton abandoned the fourth book, and restructured the rest of his Opticks, this ‘Hypothesis 2’ appears to have been re-worked to become ‘Query 31’ in Opticks, 2nd edition (1717):
- Have not the small Particles of Bodies certain Powers, Virtues, or Forces, by which they act at a distance, not only upon the Rays of Light for reflecting, refracting, and inflecting them, but also upon one another for producing a great Part of the Phaenomena of Nature? For it’s well known, that Bodies act one upon another by the Attractions of Gravity, Magnetism, and Electricity; and these Instances shew the Tenor and Course of Nature, and make it not improbable but that there may be more attractive Powers than these. For Nature is very consonant and conformable to her self…
Here, there is an obvious semantic shift between hypothesis and query: the query is stated as a question. Some scholars have argued that this is the only difference between hypotheses and queries: in the Opticks, queries are simply Newton’s way of getting around his self-imposed ban on hypotheses. I claim that there is more to the shift than this. Newton is using the semantic structure of the query to explore a possible future research program. The epistemic difference between the query and the hypothesis is similar to the epistemic difference between Popper’s falsifiable and unfalsifiable theories. The former is testable-in-principle, whereas the latter is not; and testability is a necessary condition of something becoming well-tested.
There is a difference between Newton’s early queries and his later queries: the former are part of the process of justification; but the latter are part of the process of discovery. In a previous post I noted that:
- While Newton’s [early] method of queries is experimental, it does not appear to be strictly Baconian. For the Baconian-experimental philosopher, queries serve “to provoke and stimulate further inquiry”. Thus, for the Baconian-experimental philosopher, queries are part of the process of discovery. However, for Newton, queries serve to test the theory and to answer criticisms. Thus, they are part of the process of justification.
The queries in Newton’s later work seem closer to the Baconian tradition that inspired him.
That the themes of Hypothesis 2 and Query 31 appear in Rule 3 of Principia, raises questions about the status of Newton’s ‘Rules of Philosophising’ and how we should interpret the re-branding of ‘hypotheses’ as ‘rules’ in later editions of Principia. I’d love to hear what you think!
* Recently, Cambridge University put Newton’s papers online, making it possible for those of us who live ‘down under’ to examine copies of many of Newton’s manuscripts!
Hypotheses and Newton’s Rings
Kirsten Walsh writes…
In Ian Lawson’s recent post, he mentioned Hooke’s work on colours in thin films. In this post, I’ll look at how Newton used his hypotheses on light to build on Hooke’s work in some interesting and important ways.
In his optical work of the early 1670s, while Newton prefers theories to hypotheses, he thinks that hypotheses are acceptable, even useful, for two purposes:
- To ‘illustrate’ (i.e. provide an intuitively plausible explanation of) the theory; and
- To ‘suggest’ experiments.
However, he insists that hypotheses should always be removed from the final version of the theory. Recall Newton’s claim from his 1672 paper: “I shall not mingle conjectures with certainties”.
In December 1675, Newton wrote his paper, “An hypothesis explaining the Properties of Light”. Here, he published his hypotheses on the nature of light for the first time. To summarise them briefly:
- There is an ‘aethereal medium’;
- Aether vibrates, carrying sounds, smells and light;
- Aether penetrates and passes through the pores of solid substances;
- Light is neither the aether itself, nor the vibrations, but a substance that is propagated from ‘lucid’ bodies and travels through the aether;
- Light warms the aether and the aether refracts the light; and
- The rays (or bodies) of which light consists differ from one another physically.
In this paper, Newton claims that he is only discussing these hypotheses for the purposes of ‘illuminating’ his theory. Moreover, he does not assert that these hypotheses are true, and emphatically does not use them to support his theory. For example, when he discusses hypothesis (4), Newton is careful not to push too forcefully for any particular account of light. He says one might suppose light to be “an aggregate of various peripatetic qualities”, or “unimaginably small and swift” corpuscles of various sizes, or “any other corporeal emanation or impulse or motion of any other medium diffused through the body of the aether”:
- Onely whatever Light be, I would suppose, it consists of Successive rayes differing from one another in contingent circumstances, as bignes, forme or vigour… And further I would suppose it divers from the vibrations of the aether.
In this paper, there is a notable emphasis on experiment. For example, when Newton discusses hypothesis (1), he gives an account of a new electrical experiment which seems to support his claim. And when he discusses hypothesis (3), he discusses the implications for Boyle’s tadpole experiments. But the most important experiments in this paper are his investigations on the colours that appear between two glass surfaces.
Alan Shapiro notes that Newton began these investigations while he was reading Hooke’s Micrographia. But his experiments and mathematical descriptions quickly developed into something well beyond the scope of Hooke’s investigations. Hooke described the colours that appear when two thin sheets of glass are placed one on top of the other. When he made the thin film of air between the two sheets thicker or thinner by pressing the two sheets together with greater or lesser force, the colours changed. He observed that different colours appeared at different thicknesses, but he was unable to quantify this observation as he was unable to measure accurately the thickness of the film at any given point. Newton had the idea of placing a convex lens on top of a flat sheet of glass. This enabled him to easily calculate the thickness of the film of air, and the colours appeared as a set of concentric coloured circles centred at the point of contact between the two surfaces. These concentric circles are now known as ‘Newton’s Rings’.
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Opticks, Book 2, Figure 3
Next Newton considered his hypotheses. According to hypothesis (2) the vibrations of the aether vary in size, according to hypothesis (3) aether passes through the pores of solid substances, and according to hypothesis (6) rays of different colours will cause aethereal vibrations of different sizes. If these hypotheses were correct, he argued, then light of a particular colour would be reflected either when the length of the vibration, or some multiple of the length of the vibration, matched the thickness of the film, and transmitted otherwise. So he predicted that:
- if the Glasses in this posture be looked upon, there ought to appear at A [the centre], the contact of the Glasses, a black spott, & about that many concentric circles of light & darknesse, the squares of whose semidiameters are to sense in arithmetical progression.
Newton’s “Hypothesis” paper provides a good example of his method of hypotheses. He remains carefully detached from his own hypothesis, using it only to ‘illustrate’ his theory and to suggest further experiments. Newton was also careful to keep his hypotheses well separate from his theory; the paper ends with a series of ‘Observations’ that contain no reference to his hypotheses at all!
The Aims of Newton’s Natural Philosophy
Kirsten Walsh writes…
In a previous post I discussed the aim of absolute certainty in Newton’s early optical papers. I argued that this aim provides the link between Newton’s mathematical and experimental methods. This quest for certainty is an enduring feature of Newton’s natural philosophy, leading to a modest natural philosophical agenda. For example, in the General Scholium to the Principia (1713), Newton writes:
- “I have not as yet been able to discover the reason for these properties of gravity from phenomena, and I do not feign hypotheses … And it is enough that gravity really exists and acts according to the laws that we have set forth and is sufficient to explain all the motions of the heavenly bodies and of our sea.”
But is this really enough, for Newton? Apparently it’s not. In the very next paragraph, Newton begins to speculate on the “subtle spirit” that permeates bodies and might be operative in various phenomena. It looks like he is proposing a causal explanation of universal gravitation. However, these speculations end before they really begin, when Newton concludes that “there is not a sufficient number of experiments to determine and demonstrate accurately the laws governing the actions of this spirit.”
This is the final line of Principia. And, for such a controversial book, this is a rather inauspicious ending. But I think we can glean something about the aims of Newton’s natural philosophy from this.
To begin, we need to distinguish between what Newton wants to achieve, and what he thinks he can achieve. Newton wants to give a complete, true theory of the world – including an account of the motions of the planets, the cause of gravity, and even God’s relation to the natural world. But, in the trade-off between completeness and truth, Newton sides with truth. For, as he writes in an unpublished Preface to Principia (mid-1710s), “still it is better to add something to our knowledge day by day than to fill up men’s minds in advance with the preconceptions of hypotheses.”
Newton’s modesty and restraint should not be misinterpreted as lack of epistemic ambition. The surest way to achieve absolute certainty would be to keep his domain of inquiry as narrow as possible. But Newton doesn’t do this. Instead, he pushes at the boundaries of what can be known with certainty. This is demonstrated by his use of Baconian Induction to make increasingly general claims about gravity. Newton ambitiously generalises from pendulums, to terrestrial bodies, to all bodies. In an unpublished Preface to Principia, he writes:
- “But it has also been shown in the Principia that the precession of the equinoxes and the ebb and flow of the sea and the unequal motions of the moon and the orbits of comets and the perturbation of the orbit of Saturn by its gravity toward Jupiter follow from the same principles and what follows from these principles plainly agrees with the phenomena.”
So what do those final two paragraphs of the General Scholium tell us about the aims of Newton’s natural philosophy? I. Bernard Cohen says that the General Scholium is similar to the discussions that are found in scientific papers today: Newton is discussing the implications of his results and suggesting areas of further research. On this reading, Newton is saying that there are two jobs ahead:
- To give a causal explanation of gravity; and
- To apply the theory of gravity to other phenomena in order to solve other problems.
Importantly, Newton thinks that we can begin on (2) without waiting to complete (1). This is why Newton says it is enough that he has established that gravity exists and acts according to certain laws.
Related Posts: Newton on Certainty, Newton’s 4th Rule for Natural Philosophy.
Newton and the Case of the Missing Calculus
Kirsten Walsh writes…
The case of the missing calculus is well-known. Newton (co-)invented calculus in the late 1660s, and he wrote Principia in the late 1680s. It would be natural to expect that Newton used the calculus in Principia. But it seems that he didn’t. Instead, Newton wrote Principia in the style of Euclid’s Elements, that is, using Classical Greek geometry. This is surprising indeed, given the powerful new tool he had at his disposal. What should we make of this?
Almost thirty years after the publication of Principia, Newton explained that he had used algebraic calculus to discover the propositions of Principia, but used classical geometry to demonstrate them:
- “By the help of the new Analysis [i.e. algebraic calculus] Mr. Newton found out most of the Propositions in his Principia Philosophiae: but because the Ancients for making things certain admitted nothing into Geometry before it was demonstrated synthetically, he demonstrated the Propositions synthetically, that the System of the Heavens might be founded upon good Geometry. And this makes it now difficult for unskilful men to see the Analysis by which those Propositions were found out.”
But Newton was lying. Scholars have found no evidence that he wrote or developed Principia in any other way than the published form. Moreover, few, if any, of the propositions in Principia can even be presented in the form of algebraic calculus.
This raises two questions:
- Why did Newton lie?
- Why did Newton eschew modern algebraic calculus in favour of classical geometry?
These questions have been discussed by numerous scholars including A. Rupert Hall and I. Bernard Cohen. The answer to (1) can be found in Newton’s priority dispute with Leibniz. The answer to (2) was summarised neatly by Thony Christie last year:
- “Put simply Newton had serious doubts about the reliability of the new analytical mathematics and that is why he didn’t use it for his magnum opus.”
But what caused these doubts?
In 1714, Newton wrote that the algebraic calculus is “arithmetic applied to geometrical matters… Its operations are complicated and excessively susceptible to errors, and can be understood by the learned in algebra alone”. Whereas geometry “may be appreciated by the great majority and thus most impress the mind with [its] clarity”. One might wonder why Newton bothered to invent algebraic calculus at all!
Well it seems that Newton wasn’t always so anti-algebra, nor was he always so interested in classical geometry. In fact, as an undergraduate, Newton didn’t read the ancients. Rather, he read a few modern summaries of the ancient texts, building his own mathematics on the algebraic work of mathematicians such as Descartes, Wallis and Barrow.
Newton seems to have become interested in classical geometry in the late 1670s, after re-reading Descartes’ La Géométrie. La Géométrie was an attempt to unite algebra and geometry – Descartes aimed to show how symbolic algebra could be applied to the study of plane curves. Guiccardini writes:
- “[Descartes’] tract could be read as a deliberate proof of the superiority of the new analytical method, uniting symbolic algebra and geometry, over the purely geometrical ones of the ancients.”
Newton was very critical of Descartes’ text, writing comments such as “error” and “I hardly approve” in the margins. He even drafted a paper entitled ‘Errors in Descartes’ Geometry’. To find support for his position, Newton began to read the ancient texts, including Pappus.
Newton wrote:
- “To be sure, [the ancients’] method is more elegant by far than the Cartesian one. For [Descartes] achieved the result by an algebraic calculus which, when transposed into words (following the practice of the Ancients in their writings), would prove to be so tedious and entangled as to provoke nausea, nor might it be understood. But they accomplished it by certain simple propositions, judging that nothing written in a different style was worthy to be read, and in consequence concealing the analysis by which they found their constructions.”
Newton was neither the first, nor the only, philosopher to equate algebra and geometry with the ancient methods of analysis and synthesis respectively. But he was the first to reject modern algebraic calculus in favour of ancient geometry. (If only because he was the first to invent it!) Does Newton’s rejection of algebraic calculus stem from his anti-Cartesian stance? What if Newton had never re-read Descartes’ Géométrie? Could his priority dispute with Leibniz have been avoided?
Newton’s Method in Three Minutes
Kirsten Walsh writes…
Last week I competed in the Otago University Three-Minute Thesis Competition. I had to explain my PhD thesis in no longer than three minutes. It was challenging indeed, in such a short length of time, to describe my research, communicate its significance and impart my enthusiasm for it – while pitching it at the level of an intelligent non-expert. Fortunately, I had great material to work with. There are so many interesting stories about Newton! Unfortunately, it’s often difficult to figure out which stories are true.
I opted to begin with the ‘approximately true’ story of Newton’s anni mirabilis, or miraculous years. The general thrust of the story is true, even if some of the particulars are false: the plague years mark a significant turning point in Newton’s scientific work. As Whiteside pointed out over forty years ago, we may
- “salute this first creative outburst – whether or not contained in one single marvelous year – of a man who twenty years afterwards was to construct a scientific Weltanschauung which is, in its essentials, still ours.”
So, with apologies to those of you with ‘historically sensitive’ ears, here is my script for the three-minute thesis competition:
It’s 1665. Cambridge has been struck by Plague, and Newton has been sent home from University. Summer is stretching out before him. Nice! What will he do on his extended summer holiday? Well, he did what I imagine most Scarifies* do on their summer holidays: he invented calculus, discovered the composition of light, and (after watching an apple fall from a tree) conceived the laws of universal gravitation… Okay, so perhaps Newton wasn’t quite your typical undergraduate student. The story about the apple is controversial, but everyone agrees about the discoveries. Scholars have called those years the ‘years of miracles’.
Why were they ‘miraculous’? Well, these were revolutionary discoveries – and there were so many of them. They provided the basic material for Newton’s Principia, and his Opticks. Enough material for a lifetime of publications! And real publications. Not just those ‘puff pieces’ that fill our journals nowadays. All in just 2 years!
Furthermore, these discoveries seemed to come out of nowhere. Newton was able to invent, discover and conceive things no one else could, because seemingly he had invented an entirely new scientific method. He had come up with a whole new way of mathematising physics, and claimed to have achieved mathematical certainty! Philosophers and scientists tried to emulate his method. But no one was as successful as Newton. Whatever Newton was doing, he was doing it right. But what was he doing?
This is the central question of my PhD, and it’s a question that dominates discussions of scientific method even now, 300 years later. But scholars still barely understand what Newton’s method was. Did Newton really think his scientific theories were as certain as mathematical proofs? Why did he think his theory of gravity was true, when he couldn’t even say for certain what gravity is? And, at the centre of it all, the question that’s been keeping me up at nights (as it has kept up generations of Newton-scholars before me): what did Newton mean when he wrote that enigmatic sentence at the end of Principia: ‘Hypotheses non fingo’; ‘I do not feign hypotheses’?
I do not feign hypotheses. What an odd thing to say. What does it even mean? ‘I haven’t invented these hypotheses’? ‘I didn’t prove them’? This sentence lies at the heart of my thesis. Unlike other Newton scholars, I think it describes a crucial aspect of Newton’s method. What it tells us is that Newton made a distinction. On the one hand, theories: mathematical, certain, experimentally confirmed. On the other hand, hypotheses: non-mathematical, uncertain, non-experimental, and speculative. This distinction is a crucial feature of Newton’s spectacularly successful scientific method. And I think it’s this distinction that explains Newton’s years of miracles.
The idea of anni mirabiles seems closely-related to the notion of a scientific revolution, which has been much discussed since Kuhn published The Structure of Scientific Revolutions in 1962. Philosophers of science disagree philosophically over the importance of revolutions to science, and historically over the occurrence of any genuine scientific revolutions. However, it is interesting to note that historians have recognised several anni mirabiles in the history of science. For example, 1543, the year that Vesalius published De Humani Corporis Fabrica and Copernicus published De Revolutionibus Orbium Coelestium. And 1905, the year that Einstein published his three ground-breaking papers in the Annalen der Physik. What role have these anni mirabiles played in the history of science? What do they tell us about scientific progress? Norwood R Hanson once said:
- “It is possible both to be driven by intuition and at the same time to reason carefully. Most scientific discoveries, indeed, result from just such an intertwining of headwork and guesswork.”
What do you think?
*Otago Undergraduate Students
Experimental Philosophy: Old and New
Over the last few months, we have been working with Dr Donald Kerr, the Special Collections Librarian at the University of Otago, to prepare a rare book exhibition on the history of experimental philosophy. We have brought together classic works of the past and cutting-edge books of the present, to illustrate the theme of experimental philosophy as it was understood and practised 350 years ago and as it is understood today.
- Our exhibition, ‘Experimental Philosophy: Old and New’, was launched a few weeks ago, to coincide with the annual conference of the Australasian Association of Philosophy (AAP). It will run until 23 September 2011, so if you are coming to Dunedin, be sure to stop by and see it.
The poster for our exhibition
For those who cannot come to Dunedin, we are thrilled to announce the launch of the online version of our exhibition. Notable items on display include a second edition of Isaac Newton’s Philosophiae Naturalis Principia Mathematica (1713), Francis Bacon’s Of the Advancement Learning (1640), poet Abraham Cowley’s ‘A Proposition for the Advancement of Experimental Philosophy’ (1668), and an exciting new discovery* concerning the philosopher David Hume!
A couple of months ago, I requested your help: we needed an image for our exhibition poster. We received some excellent feedback – so thank you everyone! We eventually settled on a modified version of the frontispiece to 1640 translation of Bacon’s ‘De Augmentis Scientiarum’.
We hope you enjoy our exhibition!
* On Monday Peter Anstey will tell us all about this new discovery regarding Hume.
Newton’s 4th Rule for Natural Philosophy
Kirsten Walsh writes…
In book three of the 3rd edition of Principia, Newton added a fourth rule for the study of natural philosophy:
- 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.
- This rule should be followed so that arguments based on induction be not be nullified by hypotheses.
Arguably this is the most important of Newton’s four rules, and it certainly sparked a lot of discussion at our departmental seminar last week. Let us see what insights we can glean from it.
Rule 4 breaks down neatly into three parts. I shall address each part in turn.
1. Propositions (acquired from the phenomena by induction) should be regarded as true or very nearly true.
While the term ‘phenomenon’ usually refers to a single occurrence or fact, Newton uses the term to refer to a generalisation from observed physical properties. For example, Phenomenon 1, Book 3:
- The circumjovial planets [or satellites of Jupiter], 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.
- This is established from astronomical observations…
Newton uses the term ‘proposition’ in a mathematical sense to mean a formal statement of a theorem or an operation to be completed. Thus, he further identifies propositions as either theorems or problems. Propositions are distinguished from axioms in that propositions are not self-evident. Rather, they are deduced from phenomena (with the help of definitions and axioms) and are demonstrated by experiment. For example, Proposition 1, Theorem 1, Book 3:
- The forces by which the circumjovial planets [or satellites of Jupiter] 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.
- The first part of the proposition is evident from phen. 1 and from prop. 2 or prop. 3 of book 1, and the second part from phen. 1 and from corol. 6 to prop. 4 of book 1.
Newton appears to be using ‘induction’ in a very loose sense to mean any kind of argument that goes beyond what is stated in the premises. As I noted above, his phenomena are generalisations from a limited number of observed cases, so his natural philosophical reasoning is inductive from the bottom up. Newton recognises that this necessary inductive step introduces the same uncertainty that accompanies any inductive generalisation: the possibility that there is a refuting instance that hasn’t been observed yet.
Despite this necessary uncertainty, in the absence of refuting instances, Newton tells us to regard these propositions as true or very nearly true. It is important to note that he is not telling us that these propositions are true, simply that we should act as though they are. Newton is simply saying that if our best theory fits the available data, then we should regard it as true until proven otherwise.
2. Hypotheses cannot refute or alter those propositions.
In a previous post I argued that, in his early optical papers, Newton was working with a clear distinction between theory and hypothesis. In Principia Newton is working with a similar distinction between propositions and hypotheses. Propositions make claims about observable, measurable physical properties, whereas hypotheses make claims about unobservable, unmeasurable causes or natures of things. Thus, propositions are on epistemically surer footing than hypotheses, because they are grounded on what we can directly experience. When faced with a disagreement between a hypothesis and a proposition, we should modify the hypothesis to fit the proposition, and not vice versa. Newton explains this idea in a letter to Cotes:
- But to admitt of such Hypotheses in opposition to rational Propositions founded upon Phaenomena by Induction is to destroy all arguments taken from Phaenomena by Induction & all Principles founded upon such arguments.
3. New phenomena may refute those propositions by contradicting them, or alter those propositions by making them more precise.
This final point highlights the a posteriori justification of Newton’s theories. In Principia, two methods of testing can be seen. The first involves straightforward prediction-testing. The second is a more sophisticated method, which involves accounting for discrepancies between ideal and actual motions by a series of steps that increase the complexity of the model.
In short, Rule 4 tells us to prioritise propositions over hypotheses, and experiment over speculation. These are familiar and enduring themes in Newton’s work, which reflect his commitment to experimental philosophy. Rule 4 echoes the remarks made by Newton in a letter to Oldenburg almost 54 years earlier, when he wrote:
- …I could wish all objections were suspended, taken from Hypotheses or any other Heads then these two; Of showing the insufficiency of experiments to determin these Queries or prove any other parts of my Theory, by assigning the flaws & defects in my Conclusions drawn from them; Or of producing other Experiments wch directly contradict me…
Images of Experimental Philosophy (and a request for help!)
Kirsten Walsh writes…
Over the last few weeks, we have been organizing a rare book exhibition* on the history of experimental philosophy. It has been a privilege to handle dozens of antique books such as a 2nd edition of Newton’s Principia, Bacon’s Opuscula and Kepler’s Epitome. One of the striking features of early modern books is their ornate frontispieces and detailed illustrations. They give the impression that publishers spent a lot of money to acquire and print these images. This got us thinking about what images really capture the spirit of the experimental philosophy. So this week, we thought we’d do a special post on images of experimental philosophy.
One of my favourite images is Wright’s 1768 ‘An Experiment on a Bird in the Air Pump’. It combines several aspects of the 18th century scientific pursuit: the experimenter as a ‘show man’, natural philosophy as ‘family entertainment’, and Boyle’s air pump centre stage. If you want to see some of the experiments that Wright’s subjects might have seen, have a look at the video on air pressure over at Discovering Science.
Wright (1768), 'An Experiment on a Bird in the Air Pump'
Another wonderful image is Stradanus’ (1580), ‘Lapis Polaris Magnes’, also known as ‘The Philosopher in his Chamber Studying a Lodestone’.
- “the scholar in his study is surrounded by the new instruments of navigation, drafting, and surveying. An armillary sphere, a compass, an octant, several books, and other measuring tools sit on the table at left. In the left foreground, a lodestone floats on a raft of wood in a wine cooler. The model galleon suspended from the ceiling contrasts to the single-masted, oared Mediterranean vessel that can be seen through the window. The juxtaposition of instruments and books on the scholar’s desk indicates the coming together of the hitherto generally separate traditions of practice and theory. Out of their union, the new experimental philosophy emerged.” (From Experience and Experiment in Early Modern Europe.)
Stradanus (1580), ‘Lapis Polaris Magnes’
Another gallon is represented in the frontispice of Bacon’s De augmentis. It has passed through the Pillars of Hercules, venturing into the unknown and increasing our knowledge. The line beneath the ship explains: “Many shall pass through and learning shall be increased” (“Multi pertransibunt & augebitur scientia”). How shall learning be increased? By overcoming a series of oppositions: between reason and experience (the motto at the top reads “Reason and Experience have been allied together”); between the visible world and the intelligible world (the two globes at the top); between science and philosophy (the two terms at the bottom of the pillars); and even between Oxford and Cambridge (“Oxonium” and “Cantabrigia”)!
Bacon (1640), 'De Augmentis Scientiarum'
The frontispiece to Voltaire’s (1738) Elemens is not a good representation of the experimental philosophy, but it is a lovely illustration. Voltaire sits at his desk, translating Newton’s Principia. Heavenly light seems to come from Newton himself, representing his divine inspiration. The light is reflected downwards to illuminate Voltaire’s work by Voltaire’s lover and muse Émilie du Châtelet (but it was really she who translated Principia and helped Voltaire to make sense of the work).
Voltaire (1738), 'Elemens de la philosophie de Neuton'
West’s (1816) painting depicts Benjamin Franklin’s famous (or infamous) kite experiment. In 1752, Franklin flew a kite in a storm to demonstrate that lightning is a form of electricity. He almost electrocuted himself!
- “As soon as any of the thunder clouds come over the kite, the pointed wire will draw the electric fire from them, and the kite, with all the twine, will be electrified, and the loose filaments of the twine, will stand out every way, and be attracted by an approaching finger. And when the rain has wetted the kite and twine, so that it can conduct the electric fire freely, you will find it stream out plentifully from the key on the approach of your knuckle. At this key the phial may be charged: and from electric fire thus obtained, spirits may be kindled, and all the other electric experiments be performed, which are usually done by the help of a rubbed glass globe or tube, and thereby the sameness of the electric matter with that of lightning completely demonstrated.” (Written by Benjamin Franklin to Peter Collinson, October 19, 1752.)
You can read more about Franklin’s work on electricity at Skulls in the Stars.
West (1816), 'Benjamin Franklin Drawing Electricity from the Sky'
Many of the books we looked at contain beautiful illustrations of instruments and experiments. These nicely capture the experimental natural philosophy.
Adams (1787), 'Essays on the Microscope'
Boyle (1744), 'The Works of the Honourable Robert Boyle in five volumes'
Hooke (1665), 'Micrographia'
Swanenburgh (1616) 'Comfortable Bones, the Skeletons of Adam and Eve'
But we claim that experimental philosophy went beyond natural philosophy. Are there any images that capture its wider application?
Finally, I couldn’t resist adding the burning arm chair, which has special significance for our team: it is at once both a nice image of the shift from speculative to experimental philosophy, and a nod to the local ‘scarfie’ (Otago undergraduate) population of Dunedin. A favourite pastime for scarfies, here in Dunedin, is to burn couches outside their houses!
Burning the proverbial 'Philosopher's Armchair'
We’re looking for an image for our exhibition poster, and we’d like your help. Have you seen an image that captures the spirit of early modern experimental philosophy? We’d love to hear from you. (We’re giving away a one-year subscription to our blog for the reader who provides the best image!)
*The exhibition will be at the Special Collections, Central Library, University of Otago in Dunedin. It will open in early July at the annual conference of the Australasian Association of Philosophy (AAP). So don’t forget to have a look at it, if you are coming to Dunedin in July. For those who cannot come, don’t miss the online version of the exhibition. We’ll be sure to let you know as soon as it is available.
Keith Hutchison on ‘De Gravitatione’ and Newton’s Mathematical Method
Keith Hutchison writes…
The core of Kirsten Walsh’s paper is a defence of her proposal that Newton’s De Gravitatione was composed after the publication of the new theory of colours (in 1672-3). Kirsten compares the methodology of the optical writings with that of De Grav. and notes that despite the similarity there are significant differences. Yet the methodology of De Grav. is effectively identical to that of the Principia, so is plausibly interpreted as the one preferred by Newton. So Newton would have displayed this methodology in the optical writings, Kirsten concludes, had De Grav. already been composed.
Isaac Newton, 1642-1727
Though I am (tentatively) happy with Kirsten’s observation that it is uncontroversial to see Newton’s Principia as deploying the methodology of De Grav., part of the reason for this is surely the fact that the discussion of methodology in De Grav. is so brief, and hardly exemplified in the actual science that Newton so fleetingly displays in his text. The little that we find in De Grav. does indeed seem concordant with much that happens in the Principia, but it is easy – too easy – to find agreement between a pair of texts if one of them is vague enough. Given that the identity between the two methodologies is so important to Kirsten’s case, she needs to find some way of sharpening this step of the argument.
She could, for instance, identify far more thoroughly the small differences between the methodology of the optical writings and that of De Grav. If each of these differences could be consistently found in the Principia as well, Kirsten would have a much better case, as long as there were not something about the optical investigations that required the alternative approach. Kirsten notes indeed, that Cohen has suggested that the Principia is primarily a mathematical investigation, but the optical work is overwhelmingly experimental. Cohen seems to be significantly wrong here, for investigations of the context of Newton’s treatment of chromatic aberration show that Newton originally dreamt of creating a mathematical science of colours – until he found that refraction was puzzlingly idiosyncratic, and so unlike the extremely orderly gravitational interaction that provided much of the mathematics of the Principia. But it remains true that the optical work is saturated with experiment, and it could be this that allows an earlier (?) De Grav. to seem more like the Principia.
