Leibniz: An Experimental Philosopher?
Alberto Vanzo writes…
In an essay that he published anonymously, Newton used the distinction between experimental and speculative philosophy to attack Leibniz. Newton wrote: “The Philosophy which Mr. Newton in his Principles and Optiques has pursued is Experimental.” Newton went on claiming that Leibniz, instead, “is taken up with Hypotheses, and propounds them, not to be examined by experiments, but to be believed without Examination.”
Leibniz did not accept being classed as a speculative armchair philosopher. He retorted: “I am strongly in favour of the experimental philosophy, but M. Newton is departing very far from it”.
In this post, I will discuss what Leibniz’s professed sympathy for experimental philosophy amounts to. Was Newton right in depicting him as a foe of experimental philosophy?
To answer this question, let us consider four typical features of early modern experimental philosophers:
- self-descriptions: experimental philosophers typically called themselves such. At the very least, they professed their sympathy towards experimental philosophy.
- friends and foes: experimental philosophers saw themselves as part of a tradition whose “patriarch” was Bacon and whose sworn enemy was Cartesian natural philosophy.
- method:experimental philosophers put forward a two-stage model of natural philosophical inquiry: first, collect data by means of experiments and observations; second, build theories on the basis of them. In general, experimental philosophers emphasized the a posteriori origins of our knowledge of nature and they were wary of a priori reasonings.
- rhetoric: in the jargon of experimental philosophers, the terms “experiments” and “observations” are good, “hypotheses” and “speculations” are bad. They were often described as fictions, romances, or castles in the air.
Did Leibniz have the four typical features of experimental philosophers?
First, he declared his sympathy for experimental philosophy in passage quoted at the beginning of this post.
Second, Leibniz had the same friends and foes of experimental philosophers. He praised Bacon for ably introducing “the art of experimenting”. Speaking of Robert Boyle’s air pump experiments, he called him “the highest of men”. He also criticized Descartes in the same terms as British philosophers:
- if Descartes had relied less on his imaginary hypotheses and had been more attached to experience, I believe that his physics would have been worth following […] (Letter to C. Philipp, 1679)
Third, the natural-philosophical method of the mature Leibniz displays many affinities with the method of experimental philosophers. To know nature, a “catalogue of experiments is to be compiled” [source]. We must write Baconian natural histories. Then we should “infer a maximum from experience before giving ourselves a freer way to hypotheses” (letter to P.A. Michelotti, 1715). This sounds like the two-stage method that experimental philosophers advocated: first, collect data; second, theorize on the basis of the data.
Fourth, Leibniz embraces the rhetoric of experimental philosophers, but only in part. He places great importance on experiments and observations. However, he does not criticize hypotheses, speculations, or demonstrative reasonings from first principles as such. This is because demonstrative, a priori reasonings play an important role in Leibniz’s natural philosophy.
Leibniz thinks that we can prove some general truths about the natural world a priori: for instance, the non-existence of atoms and the law of equality of cause and effect. More importantly, a priori reasonings are necessary to justify our inductive practices.
When experimental natural philosophers make inductions, they presuppose the truth of certain principles, like the principle of the uniformity of nature: “if the cause is the same or similar in all cases, the effect will be the same or similar in all”. Why should we take this and similar principles to be true? Leibniz notes:
- [I]f these helping propositions, too, were derived from induction, they would need new helping propositions, and so on to infinity, and moral certainty would never be attained. [source]
There is the danger of an infinite regress. Leibniz avoided it by claiming that the assumption of the uniformity of nature is warranted by a priori arguments. These prove that the world God created obeys to simple and uniform natural laws.
In conclusion, Leibniz really was, as he wrote, “strongly in favour of the experimental philosophy”. However, he aimed to combine it with a set of a priori, speculative reasonings. These enable us to prove some truths on the constitution of the natural world and justify our inductive practices. Leibniz’s reflections are best seen not as examples of experimental or speculative natural philosophy, but as eclectic attempts to combine the best features of both approaches. In his own words, Leibniz intended “to unite in a happy wedding theoreticians and observers so as to improve on incomplete and particular elements of knowledge” (Grundriss eines Bedenckens […], 1669-1670).
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.
Thomas Reid and the dangers of introspection
Juan Gomez writes…
In the upcoming symposium we are hosting here at the University of Otago, I will be giving a paper on the features of the experimental method in moral philosophy (you can read the abstract). One of the salient features of this method was the use of introspection as a tool to access the nature and powers of the human mind. In fact, some Scottish moral philosophers acknowledge introspection as the only way we can get to know the nature of our mind. George Turnbull and David Fordyce were proponents of such claims, as well as Thomas Reid. The latter, in the Introduction to his Inquiry into the Human Mind (1764) draws an analogy with anatomy where he tells us that, in the same way we gain knowledge of the body by dissecting and observing it, we must perform an ‘anatomy of the mind’ to “discover its powers and principles.” The problem is that unlike the anatomist who has multiple bodies to observe, the anatomist of the mind can only look into his own mind:
- It is his own mind only that he can examine with any degree of accuracy and distinctness. This is the only subject he can look into.
Reid notices that this is not good for our experimental inquiry into the human mind, since a general law or rule cannot be deduced from just one subject:
- So that, if a philosopher could delineate to us, distinctly and methodically, all the operations of the thinking principle within him, which no man was ever able to do, this would be only the anatomy of one particular subject; which would be both deficient and erroneous, if applied to human nature in general.
But this obstacle doesn’t persuade Reid to give up introspection (Reid uses the term ‘reflection’) since it is “the only instrument by which we can discern the powers of the mind.” What we have to do is be very careful:
- It must therefore require great caution, and great application of mind, for a man that is grown up in all the prejudices of education, fashion, and philosophy, to unravel his notions and opinions, till he find out the simple and original principles of his constitution… This may be truly called an analysis of the human faculties; and, till this is performed, it is in vain we expect any just system of the original powers and laws of our constitution, and an explication from them to the various phaenomena of human nature.
Scottish moral philosophers were faced with this dilemma. On one hand, in order to access the nature of the human mind, they had to rely on a tool that could only examine and observe one particular mind, making the generalization of the principles discovered impossible; on the other hand, introspection was the only way to access the human mind, since by observing others we cannot gain any knowledge of what goes on in their minds, at least not accurately. The solution, consistent with the spirit of the experimental method, was to focus only on what we can experience and observe, and follow this evidence only as far as it can take us. Therefore as Reid points out, we are to use reflection with
- caution and humility, to avoid error and delusion. The labyrinth may be too intricate, and the thread too fine, to be traced through all its windings; but, if we stop where we can trace it no farther, and secure the ground we have gained, there is no harm done; a quicker eye may in time trace it farther.
These comments by Reid show that even when the problems of relying on introspection were explicitly recognized, the Scottish moral philosophers still used it as their way to access the nature of the human mind. Since introspection was considered to be the only reliable way into the workings of the human mind, they had to be very careful with the use they made of it. This caution was achieved by following the methodology of the experimental method, where they could only go as far as their observations would take them, and their conclusions had to be confirmed by the particular experience of many. But such limits to the conclusions drawn from introspection cast doubt on the status of the exercise of reflection: could introspection really be considered ‘experimental,’ or was the justification given by the moral philosophers (Reid in particular) just a rhetorical device? This is a problem that requires a lot more space than a blog post, but if you have any particular thoughts and comments I am looking forward to receiving and discussing them with you.
Paintings as Experiments in Natural and Moral Philosophy
Juan Gomez writes…
About a month ago I published a post on George Turnbull’s Treatise on ancient Painting. There I briefly commented that Turnbull thought that paintings could work as proper samples or experiments for natural and moral philosophy (understood as the ‘science of man’). I want to expand on this issue in this post.
Engraving by Camillo Paderni, first edition of Turnbull's 'Treatise'
The whole of Turnbull’s Treatise, as he comments at the beginning of chapter seven, is designed to show the usefulness of the imitative arts for philosophy and education in general. After a recollection of the thoughts of the ancient philosophers on these arts, Turnbull dedicates the last two chapters of the book to sketch the reasons for incorporating the arts in the Liberal education program. This is where paintings can serve as samples or experiments.
To understand the role of paintings, it is necessary to point out a general characteristic of Turnbull’s philosophy. He believed that human beings were made to contemplate and to imitate nature, and their happiness was mainly achieved through these two activities. If we take a look and examine all our faculties and powers, we will see that we are perfectly constituted for the study of nature. We acquire knowledge through the observation of nature, and the desire to imitate it leads us to perform experiments that will enhance our understanding of it.
Nature is also the source for the work of the artist:
- The Artist derives all his Ideas from Nature, and does not make Laws and Connexions agreeably to which he works in order to produce certain Effects, but conforms himself to such as he finds to be necessarily and unchangeably established in Nature. (Treatise on Ancient Painting, p. 137)
From this it follows that the paintings of an artist should represent (imitate) nature as it is in reality, following all its laws. With this in mind Turnbull goes on to tell us that paintings in fact serve as samples or experiments for natural and moral philosophy:
- Philosophy is rightly divided into natural and moral; and in like manner, Pictures are of two Sorts, natural and moral: The former belong to natural, and the other to moral Philosophy. For if we reflect upon the End and Use of Samples or Experiments in Philosophy, it will immediately appear that Pictures are such, or that they must have the same Effect. What are Landscapes and Views of Nature, but Samples of Nature’s visible Beauties, and for that Reason Samples and Experiments in natural Philosophy? And moral Pictures, or such as represent parts of human Life, Men Manners, Affections, and Characters; are they not Samples of moral Nature, or of the Laws and Connexions of the moral World, and therefore Samples or Experiments in moral Philosophy? (Treatise, p. 145)
Since the paintings are supposed to represent nature, it is impossible to appreciate them without comparing them to the original (reality). In this sense paintings will provide us with a proper sample of nature that will enhance our knowledge of it. Turnbull’s theory relies on the artist making exact ‘copies’ of nature, and only then can they serve as proper samples. In the case of natural pictures, he allows two sorts of ‘copies’: either exact representations of nature (like a photograph), or imaginary scenes, as long as they conform to the Laws of Nature. If they are not in these categories, then they shouldn’t be taken as proper samples for the study of nature, and in Turnbull’s case, not even as good works of art. Those works of art that do not imitate nature do not give us the pleasure derived from those that do.
Turnbull prescribes a parallel form of realism for moral paintings. These pictures should depict human nature as it really is, and through them we can gain knowledge of our actions and characters:
- Moral Pictures, as well as moral Poems, are indeed Mirrours in which we may view our inward Features and Complexions, our Tempers and Dispositions, and the various Workings of our Affections. ‘Tis true, the Painter only represents outward Features, Gestures, Airs, and Attitudes; but do not these, by an universal Language, mark the different Affections and Dispositions of the Mind? (Treatise, p. 147)
As long as the sole purpose of the arts is to imitate nature, and all the works follow the laws of nature (even in cases of imaginary scenes), Turnbull can count them as having the same effect ‘real’ samples and experiments have.
Galileo and Experimental Philosophy
Greg Dawes writes…
In a recent conference paper I have argued that in some key respects Galileo’s natural philosophy anticipates the experimental philosophy of the later seventeenth century. I am not claiming that Galileo uses the term “experimental philosophy.” Nor do I claim that he makes any distinction comparable to that between experimental and speculative natural philosophy. His Italian followers in the Accademia del Cimento would later do so, but he does not. Nonetheless, the way in which Galileo undertakes natural philosophy displays at least two of the features that Peter Anstey and his collaborators have argued are characteristic of experimental philosophy.
Galileo's sketch of a device to demonstrate the power of a vacuum.
The first of these has to do with the role of experiment. Much of the twentieth-century debate centred on whether Galileo actually performed the experiments about which he writes. But the more important question has to do with the role of experiments in Galileo’s thought. Like his Aristotelian predecessors, Galileo seeks to construct a demonstrative natural philosophy: one in which the conclusions follow with certainty from the premises. But unlike the Aristotelian, he relies on geometrical proofs. Like any mathematical proofs, these can be elaborated in an a priori fashion, without any reference to experience. But whether a particular proof applies to the world of experience – or, better still, whether it accurately describes the structure of the world – can only be ascertained experimentally. It is experiment which tells us which geometrical proof is to be used, even if the geometrical proof itself can be developed independently of experience. (I am relying here on the work of Martha Féher, Peter Machamer, and others.)
Perhaps more importantly, Stephen Gaukroger has argued that experimentation shaped the very way in which Galileo’s physical theories are framed and formulated. Alexander Koyré and others have argued that the laws of Galilean physics are “abstract” laws which refer to an ideal reality. It is true, of course, that in setting aside “impediments” (impedimenti), such as the resistance of the air, Galileo’s proofs do not refer to the world of everyday experience. But it is unhelpful to think of them as an idealisations of, or abstractions from, experienced reality. There is an experienced reality to which they conform. It may not be that of everyday experience, but it is that of carefully controlled physical experiments. It follows that in Galileo’s work, the task of natural philosophy is being rethought. It is no longer the study of reality as revealed to everyday observation; it is the study of that reality revealed in experimental situations.
The second way in which Galileo’s natural philosophy anticipates the later experimental philosophy is in its comparative lack of interest in the mechanisms thought to underlie phenomena. It is not that Galileo was a positivist in our modern sense. There are passages in which he engages in speculation regarding matter theory and on these occasions he favours a corpuscularian view. But such speculations are, as Salviati says in the Two New Sciences, a mere “digression.” Galileo does not consider that his new science requires them. Indeed his work on motion is almost entirely a kinematics – as he freely admits, it says nothing about the causes of motion – but Galileo does not consider it any less significant as a result.
Galileo's solution of the "rota Aristotelis" paradox, demonstrating that a body could be composed of an infinite number of unquantifiable atoms.
This should not be interpreted as a general lack of interest in causation, as Stillman Drake suggests. Galileo shares the ancient desire cognoscere rerum causas (to know the causes of things). But the causal properties Galileo seeks are different from those sought by his predecessors. His causes are the mathematically describable properties of the objects whose behaviour is being explained, properties that no Aristotelian would regard as essential. (Even his atoms are more akin to mathematical points than physical objects.) It is, once again, experimentation that allows us to pick up which of those mathematically describable properties are generally operative and therefore the proper subject of a science. It is this move that allows Galileo, as it would later allow Newton, to be content with a causal account that remains on the level of phenomena, rather than speculating about a realm inaccessible to observation.
In an early dialogue, Galileo has two rustics (contadini) speculating about the new star of 1605. One of them advises his companion to listen to the mathematicians rather than the philosophers, for they can measure the sky the way he himself can measure a field. It doesn’t matter of what material the heavens are made. “If the sky were made of polenta,” he says, “couldn’t they still see it alright?” This is surely something new in the history of natural philosophy.
Postscript:
While I would still defend the individual claims contained here, my continued study of Galileo has made me increasingly cautious about the usefulness of a distinction between experimental and speculative natural philosophy. It is certainly the case that many late seventeenth-century thinkers made such a distinction, but is it a useful one for us to make? I’m not confident that it is.
Experiment certainly played an important role in Galileo’s work, although precisely what that role was continues to be contested. And it is true that Galileo has little interest in speculating about the underlying structure of the world: even if, as he writes, the sky were made of polenta, the mathematicians could still measure it. The problem is that the classical, mathematical tradition out of which he comes — that of astronomy, statics, optics, and (after Galileo) the study of local motion — cannot be helpfully characterized as either experimental or speculative. It certainly uses experiment, but it also reasons a priori, in ways that seem independent of experience.
So perhaps it would be better to have a threefold classification of early modern scientific traditions. (A classification of this kind is suggested by Casper Hakfoort in the last chapter of his Optics in the Age of Euler.) A first tradition would be that of matter theory, which is inevitably speculative insofar as it deals with matters not accessible to direct observation. (This is the realm of Newton’s “hypotheses.”) Corpuscularian proposals would fall into this category, as would Descartes’s vortex theory. A second tradition would be that of experimental natural philosophy, which regarded the results of experiment as themselves significant forms of knowledge, whether or not they could be connected with an underlying theory of the nature of matter. Finally, there is the mathematical tradition that Galileo transformed, so successfully, by producing a mathematical account of local motion.
Individual natural philosophers could engage in all three kinds of activities, but will differ according to the emphasis they place on one or other of them. So although Galileo certainly engaged in experiments, his emphasis was on the kind of reasoning characteristic of the mathematical tradition. It is this form of reasoning, I have come to believe, that cannot be easily fitted into the experimental-speculative scheme.
Newton’s ‘Crucial Experiment’
Kirsten Walsh writes…
In his first optical paper, Newton claims that he has performed an Experimentum Crucis, which proves that refrangibility is an original property of the light, not an effect of the prism:
- …the true cause of the length of that Image was detected to be no other, then that Light consists of Rays differently refrangible, which, without any respect to a difference in their incidence, were, according to their degrees of refrangibility, transmitted towards divers parts of the wall.
This experiment and its role in Newton’s theory of colours raises some questions that I’m not really sure how to answer. I hope you can help me.
Firstly, let’s have a closer look at this Experimentum Crucis:
Newton's Experimentum Crucis
White light travels from the Sun (S), through the first aperture (F), through the first prism (ABC), where it is refracted for the first time, producing an image on the first board (DE). A small amount of light passes through the second aperture (G), producing an image on the second board (de). A small amount of light passes through the third aperture (g), through the prism (abc), where it is refracted for the second time, producing an image on the screen (MN). Newton “took the first Prisme in [his] hand, and turned it to and fro slowly about its Axis”, so that different parts of the refracted image could pass through the apertures to the second prism. He took careful note of where each image appeared on the board MN.
Newton finds that each time a particular ray passes through a prism it refracts to precisely the same degree. For example, light that refracts to 50 degrees at the first prism refracts to 50 degrees at the second prism as well. Newton argues that this shows that refrangibility is an original and constant property of light.
Newton’s Experimentum Crucis was heavily criticised by his contemporaries. Hooke, for example, argued that this experiment is not a crucial experiment, because it does not prove that colour is an original property of light. Hooke believes that light becomes coloured as it passes through the prism, and Newton’s experiment does not convince him otherwise.
While colour is conspicuously absent from Newton’s discussion of this experiment, this line of criticism is extremely common. For example, Newton’s contemporaries, Hooke, Huygens and Pardies, and more recently, writers such as Sabra and Bechler have all made criticisms along these lines. As I have previously discussed, Newton used mathematics and measurement in order to achieve absolute certainty. So it is no accident that Newton only discusses refrangibility and not colour in this experiment.
Newton concludes that white light is composed of rays of every colour in equal amounts, but he argues for this in two steps:
1) Light is a “Heterogeneous mixture of differently refrangible Rays”; and
2) There is a one-to-one correspondence between refrangibility and colour.
So, while the Experimentum Crucis only supports step (1), it is often mistaken as an argument for Newton’s conclusion. Newton takes a great deal of care to establish (1) experimentally, but he seems to take little care at all to establish (2), and hence, the conclusion. In his first optical paper he simply asserts it as proposition 2; in his reply to Huygens he asserts it as a note to his definitions.
This raises two questions. Why did Newton take so little care over step (2)? How did Newton’s main opponents miss this lack of care?
Newton on Certainty
Kirsten Walsh writes…
A few weeks ago, I said that in Newton’s early optical papers:
- Newton claims that his doctrine of colours is a theory, not a hypothesis, for three reasons:
1. It is certainly true, because it is supported by (or deduced from) experiment;
2. It concerns the physical properties of light, rather than the nature of light; and
3. It has testable consequences.
From this set of criteria, we can see that early-Newton’s strong anti-hypothetical stance is closely related to his goal of generating theories that are certainly true. Students from Florida have pointed out that Newton’s criterion of certainty seems to set the bar quite high. Indeed it does. So today I will explain early-Newton’s goal of absolute certainty and why he thought it was achievable.
For Newton, absolute certainty is closely related to mathematics – he wants to achieve certainty in the science of colours by making it mathematical. In his first letter to the Royal Society, he says:
- A naturalist would scearce expect to see ye science of those become mathematicall, & yet I dare affirm that there is as much certainty in it as in any other part of Opticks. 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 (the Philosophers universall Topick,) but evinced by ye mediation of experiments concluding directly & without any suspicion of doubt.
In a letter to Hooke, Newton says, ideally the science of colours will be “Mathematicall & as certain as any part of Optiques”. However, absolute certainty is difficult to achieve because the science of colours
- depend[s] as well on Physicall Principles as on Mathematicall Demonstrations: And the absolute certainty of a Science cannot exceed the certainty of its Principles.
Thus, Newton thinks that absolute certainty is also closely related to experiment. It is no accident that, in his first paper, Newton attempts to establish the physical principles of colour experimentally by focussing on refrangibility rather than colour of light. It would have been difficult to measure precisely changes in colour, but Newton was able precisely to measure degrees of refraction and lengths of refracted images. He hardly even mentions colour until he believes he has established that white light is a mixture of differently refrangible rays. When he is ready to reveal his theory of colour, he does so by first asserting that there is a one-to-one correspondence between refrangibility and colour of light rays. Newton claims that he has established the physical principles of colour with absolute certainty.
When he reveals his theory of colour, he does so in a quasi-mathematical style. In a letter to Oldenburg, Newton says:
- I drew up a series of such Expts on designe to reduce ye Theory of colours to Propositions & prove each Proposition from one or more of those Expts by the assistance of common notions set down in the form of Definitions & Axioms in imitation of the Method by which Mathematicians are wont to prove their doctrines.
This quasi-mathematical ‘proof’ of his theory of colours is set out in his reply to Huygens.
To summarise, Newton’s mathematical method and his experimental method are linked by his notion of absolute certainty. Newton claims his theory of colours is certainly true, because (1) his physical principles are established experimentally and are certainty true, and (2) he can use these physical principles as the basis of his mathematical proof. That a lengthy and sometimes heated debate followed Newton’s original paper, shows that his opponents weren’t as convinced by his careful demonstration as he was.
