Shapiro Newton's 'Experimental Philosophy

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newton’s “experimental philosophy” 185

NEWTON’S “EXPERIMENTAL PHILOSOPHY”

ALAN E. SHAPIRO*University of Minnesota

Abstract

Newton abjured using the term “experimental philosophy,” widely usedin Restoration England at the start of his career, until 1712 when he

added a passage to the General Scholium of the Principia that briefly expounded his anti-hypothetical methodology. Drafts for query 23 of thesecond edition of the Opticks (1706) (which became query 31 in the thirdedition), however, show that he had intended to introduce the term toexplain his methodology earlier. Newton introduced the term for polemi-cal purposes to defend his theory of gravity against the criticisms of Car-tesians and Leibnizians but, especially in the Principia, against Leibnizhimself. “Experimental philosophy” has little directly to do with experi-ment, but rather more broadly designates empirical science. Newton’smanuscripts provide insight into his use of “experimental philosophy”

and the formulation of his methodology, especially such key terms as“deduce,” “induction,” and “phenomena,” in the early eighteenth cen-tury.

Newton is deservedly renowned as an experimentalist, and theterm “experimental philosophy” has long been associated with hisname. It is, however, at least as closely associated with Restorationscience and the early Royal Society. When Newton was just begin-

ning his scientific studies the term was widely used and appearedin the titles of such works as Robert Boyle’s Some ConsiderationsTouching the Usefulness of Experimental Natural Philosophy (1663) andHenry Power’s Experimental Philosophy (1664). The apparent conti-nuity between Newton’s usage and that of the early Royal Society is, however, largely an illusion. Newton had consciously avoidedusing “experimental philosophy” until the beginning of the eight-eenth century,1 when he publicly introduced that venerable term

* A very early version of this paper was delivered at a program in honor of J.E “Ted” McGuire’s seventieth birthday at the University of Pittsburgh on January



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in the second edition of the Principia in 1713 in order to defendhis work, especially the theory of gravity, against the criticisms of Cartesians and Leibnizians but, above all, Leibniz himself. Whenconsidering Newton’s “experimental philosophy” we should not imagine pictures of air pumps, electrical machines, and the likethat abound in such a classic Newtonian work as J. T. Desaguliers’s A Course of Experimental Philosophy (1734). “Experimental philoso-phy” has little directly to with experimental science as we conceiveof it. Who now would consider the Principia to be an experimental work, although it admittedly contains some experiments? Ratherthe term more broadly designates empirical science.

In this paper I will examine what “experimental philosophy”meant for Newton as well as such other terms as “deduction fromthe phenomena” and “induction” that he used to define his new methodology and which have long puzzled scholars. My concern will be with his methodological pronouncements or his rhetoricrather than with his actual practice. The latter is at least as impor-tant as the former, but there is no necessary identity between ascientist’s methodological statements and his actual methodology,

so that they must each be studied. In the first part I will traceNewton’s use of “experimental philosophy” in his published andunpublished writings; then I will turn to determining the role that his dispute with Leibniz played in his adopting that term; and I willconclude by attempting to capture what the key methodologicalterms meant for Newton and describe how his methodological views changed since the beginning of his career.

Defining Newtonian Natural Philosophy

Newton’s first published use of “experimental philosophy” appearsin the widely quoted penultimate paragraph of the General Scho-lium that was added to the second edition of the Principia in 1713,in which he asserted that although he had not found the cause of gravity, he had nonetheless demonstrated that it exists. After de- voting the first three pages of the four-page General Scholium to

vortices and God, he turned to gravity. He enumerated the vari-




ous properties of gravity that he had discovered and did not hesi-tate to point out that it acts in proportion to the quantity of mat-ter in a body, or the volume, and not to the surface “as mechanicalcauses are wont to do.” He then declared:

I have not as yet been able to deduce from phenomena the reason for theseproperties of gravity, and I do not feign hypotheses. For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechani-cal, <have no place in experimental philosophy. In this philosophy, proposi-tions are deduced from the phenomena and are made general by induction.The impenetrability, mobility, and impetus of bodies, and the laws of mo-tion and the law of gravity have been found by this method.> And it is

enough that gravity really exists and acts according to the laws that we haveset forth and is sufficient to explain all the motions of the heavenly bodiesand of our sea.2

In a draft of the letter to Roger Cotes, the editor of the secondedition of the Principia , in which he forwarded to him the finalchanges and additions to the General Scholium—including thepassage with “experimental philosophy”—Newton made it quiteclear who the advocates of the Hypothetical Philosophy were:

Experimental Philosophy reduces Phaenomena to general Rules & looksupon the Rules to be general when they hold generally in Phaenomena....Hypothetical Philosophy consists in imaginary explications of things & im-aginary arguments for or against such explications, or against the argumentsof Experimental Philosophers founded upon Induction. The first sort of Philosophy is followed by me, the latter too much by Cartes, Leibnitz & someothers.3

It was not an accident that Newton publicly introduced the term“experimental philosophy” in the General Scholium in defense of

the Principia and the concept of gravity. Indeed, I claim that this was precisely why he introduced the term. All the other passages

2 Isaac Newton, The Principia: Mathematical Principles of Natural Philosophy, trans.I. Bernard Cohen and Anne Whitman, with the assistance of Julia Budenz (Ber-keley, 1999), 943. I have made one change in the translation; the phrase “In thisphilosophy” ( In hac Philosophia ) is rendered by Cohen and Whitman, “In thisexperimental philosophy.” The passage in angle brackets was a late change madeby Newton in a letter to Cotes (discussed below at note 37) that replaced “I donot follow.” For a full discussion of the drafts of the General Scholium see I.

Bernard Cohen, Introduction to Newton’s ‘Principia’ (Cambridge, Mass., 1971), 240-245. In fact, the first appearance of “experimental philosophy,” spatially if not temporally, was in the preceding paragraph—“to treat of God from phenomena



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where he introduced the “experimental philosophy” are in thecontext of defending his natural philosophy and his concept of theuniversal attraction of gravity against the criticisms of Cartesiansand Leibnizians. Query 31 of the Opticks in which Newton alsochose to expound his methodology, has little to do with optics andis primarily concerned with force and Newtonian natural philoso-phy.

We can immediately make some comments about Newton’s ideaof experimental philosophy. It is defined as a methodology withtwo essential elements: the distinction of experimental from hypo-thetical philosophy, or the exclusion of hypotheses from natural

philosophy; and the requirement that propositions in experimen-tal philosophy are “deduced from the phenomena and are madegeneral by induction.” Newton’s rejection of hypotheses is a con-stant element of his natural philosophy from his first publicationsthrough his last and was part of his quest for certainty. The letterthat Newton actually sent to Cotes on 28 March 1713 contains animportant clarification of what he meant by a hypothesis: “And the word Hypothesis is here used by me to signify only such a Propo-

sition as is not a Phaenomenon nor deduced from any Phaeno-mena but assumed or supposed wthout any experimental proof.”4

Newton is thus rejecting hypotheses that are totally imaginary, withno experimental support whatever. Hypotheses that have someexperimental support, but which is insufficient to render themdemonstrated scientific principles, are allowed provided they arekept distinct from these established principles, as in the queriesappended to the Opticks. Newton believed that the latter sort of

hypothesis was useful for suggesting new experiments and render-ing previously discovered properties and principles intelligible. If,however, they were mingled with established propositions or prin-ciples there would be no way to achieve certainty in science.5

By essentially equating “experimental philosophy” with naturalphilosophy, Newton has ruled out totally imaginary hypothesesfrom natural philosophy. While the negative aspect of Newton’s

4

Newton, Correspondence , 5: 397.5 For a full discussion of hypotheses in Newton’s natural philosophy see my Fits Passions and Paroxysms: Physics Method and Chemistry and Newton’s Theories of




“experimental philosophy” is quite clear, it is not at all evident from this passage how propositions are “deduced from the phe-nomena” and “made general by induction,” and I will explorethese problems in this paper. But let me now observe that New-ton’s statement that the “impenetrability, mobility, and impetus of bodies, and the laws of motion and the law of gravity have beenfound by this method” mixes three very different kinds of princi-ples—universal qualities of matter, the laws of motion, and a so-phisticated mathematical-physical theory. The heterogeneity of these examples should make us suspicious that there is one me-thod underlying their demonstration. It is, moreover, not even

clear what phenomena are. The choice of the term “phenomena” was a natural one for the Principia , for it had played a prominent role in Book III. At the beginning of that book, before he under-takes demonstrating universal gravitational attraction, he enu-merates six “Phaenomena,” which are observational results—forexample, Phenomenon 3, that the orbits of the five primary plan-ets encircle the sun—or sets of observed astronomical data—suchas Phenomenon 4 that gives the data supporting Kepler’s third law

for the five planets. But we will see that Newton had a much morecapacious concept of phenomena in mind.

Let me turn to Newton’s various invocations of “experimentalphilosophy” to uncover what he meant by the term. The first,though unpublished, use of the term “experimental philosophy”by Newton that I have found is in a draft of the paragraph inQuery 23 for the Latin translation of the Opticks in 1706 where hediscusses the method of analysis and synthesis. (This Query was

renumbered 31 in the second English edition of the Opticks.) Inthis longest of the queries Newton chose to expound his corpus-cular philosophy and defend his conception of natural philosophy:

The business of Experimental Philosophy is only to find out by experience& Observation <not how things were created but> what is the present frameof nature. This inquiry must proceed first by Analysis in arguing from effectsto causes & from compositions to ingredients. And when we have found <theprinciples> [the causes & ingredients] of things we may proceed by <Synthe-sis> [composition] from those Principles to explain the things. Of this me-

thod I gave instances in the two first books proceeding first by Resolution &then by composition.6



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Newton continued by explaining that the third book on diffraction was incomplete and that he had only begun the analysis and wasleaving the further development of that subject to others; a decla-ration that would be included in all subsequent versions of thispassage. The first sentence, with its rejection of cosmogonies likethat in Descartes’ Principles of Philosophy, shows that Newton com-posed this paragraph with Descartes in his sights. Even though henow chose to emphasize the empirical aspect of science with hisexperimental philosophy, it is revealing of the mathematical foun-dation of so much of his thought that he chose to explain themethod of the experimental philosophy by means of concepts

drawn from mathematics, the method of analysis and synthesis or,as it was also known, resolution and composition. Newton’s adop-tion of terminology from Greek mathematics also reflected hisgrowing admiration for things ancient, as part of the prisca sapientia tradition in which he had so solidly enlisted. From the 1690s New-ton was much concerned with ancient wisdom and even drafted ascholium to the Principia showing how the ancients had arrived at a theory of inverse-square gravitation.7

The methods of analysis and synthesis are invoked instead of “deduction from the phenomena” in the Principia , and rather thanusing the term “phenomena” here he uses “experience & Obser- vation,” which is less vague and more apt for the experimentalscience of optics. In later versions he would adopt “experiment” which is still more apt. Newton was confronted with the problemof briefly describing his method in the Principia and Opticks in lessthan a hundred words, and even with sufficiently general state-

ments he had difficulty in encompassing his method for the two works in a single statement. In practice the methods of the Prin- cipia and Opticks differed greatly, and Newton had to rely on very general descriptions to encompass the two. He would later try toalign the methodological statements in the two works. Another,

dicate phrases that he was considering deleting, and the first set are his. I will not indicate changes in the manuscripts that are of no significance for the argument

in this paper.7 See J. E. McGuire and P. M. Rattansi, “Newton and the ‘Pipes of Pan’,” Notesand Records of the Royal Society of London 21 (1966), 108-43; Paolo Casini, “Newton:




more significant difference between them is that in the Principia Newton talks about induction as an essential part of his method, whereas in the Opticks it is not at all mentioned.

Newton first chose to characterize his method by the terms“analysis and synthesis” (or resolution and composition) in 1703or 1704 for a projected preface of the first edition of the Opticks(which we will turn to later), before these terms got involved inthe priority dispute with Leibniz. At this time there were two mean-ings to the term “analysis”: a method of discovery utilized in math-ematics, logic, and natural philosophy; and symbolic, algebraicmethods of mathematics. The two meanings are not unrelated, for

ancient mathematical analysis as a method of discovery came to beassociated with the new algebra and mathematical methods. New-ton came to reject the latter, the modern analytic method, andfavored the geometrical.8 Modern analysis was intimately involvedin the dispute with Leibniz, because the Leibnizians accused New-ton of not having written the Principia in analytic form, but rathersynthetic, because he did not command analytic calculus beforeLeibniz. Newton had to engage in a lot of fancy footwork to get

around his use (or lack of use) of analysis in the Principia , whileclaiming that he had discovered it many years earlier.

He later explained his position on this in his review of the Com- mercium epistolicum and then in other, unpublished documents,

By the help of the new Analysis Mr. Newton found out most of the Proposi-tions in his Principia Philosophiae : but because the Ancients for making thingscertain admitted nothing into Geometry before it was demonstrated syntheti-cally, he demonstrated the Propositions synthetically, that the Systeme of the

8 The methods of analysis and synthesis have been much studied in the last thirty years. One of the major issues is understanding what ancient mathemati-cians understood by the terms, and another is that of determining the “direction”of analysis, i.e., whether it goes from the more to the less known or vice versa.Some noteworthy works on Newton and analysis and synthesis, including its usein mathematics, are Henry Guerlac, “Newton and the Method of Analysis,” in Dic- tionary of the History of Ideas, ed. Philip Wiener, 4 vols. (New York, 1973), 3: 378-91; Jaakko Hintikka and Unto Remes, The Method of Analysis: Its Geometrical Origin and its General Significance (Dordrecht, 1974); D. T. Whiteside in Newton, The Math-

ematical Papers of Isaac Newton, ed. D. T. Whiteside, 8 vols. (Cambridge, 1967-81),7: 185-199, 8: 442-459; I. Bernard Cohen, The Newtonian Revolution. With Illustra- tions of the Transformation of Scientific Ideas (Cambridge, 1980), 12-15, and 293, n.16;



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Heavens might be founded upon good Geometry. And this makes it now difficult for unskillful Men to see the Analysis by which those Propositions were found out.9

By the term “new analysis” Newton is referring to calculus, but inthe second sentence he slips into its other meaning, consideringanalysis as a method of discovery. I strongly suspect that Newtondid not introduce the term “method of analysis” in the Principia toavoid possible confusion with its technical, mathematical meaning, which by this time had become a sensitive word entwined in thecontroversy with Leibniz. This factor helps to explain why Newtonchose not to expound his new way of doing science in the General

Scholium using the methods of analysis and synthesis that he hadadopted for this purpose about a decade earlier and had already published in the Latin translation of the Opticks. A second factor,as I shall argue later, is that Newton did not at all intend to definehis method in the General Scholium until shortly before it went tothe printer. The “experimental philosophy,” “deduction from thephenomena,” and “induction” were added at the last minute spe-cifically to oppose Leibniz who, he felt, had provoked him.

Returning to Newton’s drafts for query 23, we see that he revisedand expanded this passage. The first sentence is the same except for the deletion of “only.” He then continued by explaining themethods of analysis and synthesis:

The business of Experimental Philosophy is [only] to find out by experience& observation not how things were created but what is the present frame of Nature. This enquiry should proceed first by Analysis in arguing <fromthings more known to things less known & particularly> from effects tocauses & from compositions to their ingredients. And when we have found

[the principles] <out & established any new causes or ingredients of things> we may proceed by Synthesis from those <causes & ingredients as> Princi-ples to explain their effects & compositions. Of this Method I gave an in-stance in the first book of these Opticks, investigating first by Analysis theoriginal differences of the rays in respect of refrangibility reflexibility &colour & then from these <differences considered as> principles compound-ing explications of the colours made by Prisms, the colours of the Rainbow & those of natural bodies. Most of the second Book was written some years

9 [Newton], “ An Account of the Book Entituled Commercium epistolicum,” Philo-

sophical Transactions 29, no. 342 (January 1714/15),173-224, on 206; this is con- veniently reprinted as an appendix in A. Rupert Hall, Philosophers at War: The Quarrel between Newton and Leibniz (Cambridge, 1980). D. T. Whiteside observed




before the First & so is not in so good a method. However it proceeds by Analysis to discover the fits of easy reflexion & easy transmission of the rays,& from thence the explication of the colours of <bubbles & other> thintransparent plates, & those of feathers & tinctures are easily compounded.10

After acknowledging the incompleteness of the third book, heexplained that by pursuing this method our knowledge of God andmoral philosophy would be expanded.11

The most significant additions are the examples of analysis andsynthesis in Books I and II of the Opticks with the admission that Book II “is not in so good a method,” a rare display of candor andadmission of imperfection by Newton, so it is not surprising that

he dropped this concession from later drafts and never publishedit. Since Newton does not set out the precise nature of the meth-odological problems of Book II, I can offer only what I hope aresome well-founded conjectures as to its limitations. Its four partsdeal with the colors of thin plates (Parts I and II), the colors of natural bodies and the periodicity of light or its fits (Part III), andthe colors of thick plates (Part IV). To understand its lack of a“good method” it is crucial to understand the history of its compo-

sition.The first three parts through Part III, Proposition VIII are a light revision of a paper on the colors of thin plates and natural bodiesthat Newton sent to the Royal Society in 1675, where it was read tothe members but not published. Over a decade ago I demon-strated that Newton had completed the Opticks some time aroundthe fall of 1691, and that by February 1692 he had revised it andput it into the form that we know. While working on a revision of the part on the colors of thick plates (then in a separate booktogether with diffraction) Newton devised his theory of fits of easy reflection and transmission on the periodicity of light and at-tached this to the earlier propositions on the colors of bodies inPart III. He also removed the colors of thick plates from Book IIIand made it Part IV of Book II.12

10 MS Add. 3970, f. 242v.11

Since this draft on the relation of natural philosophy to knowledge of Goddiffers significantly from the published version, I include it here: “And by pursu-ing this method till we come to as clear & full a knowledge of the first cause as we



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Newton, quite properly, cites the theory of fits as part of theanalysis, but he never went back to revise the first three parts that had already been completed to incorporate his newly formulatedtheory of fits. Only in the fourth part, which he was in any caserevising did he add the theory of fits. The first part consists of twenty-four “observations” whose centerpiece is a description of the colors of thin plates produced by the air in the space betweentwo lenses (Newton’s rings). It contains some fundamental observations, such as that the colors in Newton’s rings repeat accordingto integral multiples of the thickness of the air gap, but there areno propositions at all, as there are in the first book of the Opticks

or the Principia . The second part consists of “Remarks upon theforegoing Observations” in which he explains the various phenom-ena by means of conclusions drawn from the observations (thesynthesis). In a series of propositions in Part III Newton demon-strates that the colors of natural bodies are produced by the mi-croscopic corpuscles of those bodies in exactly the same way as inmacroscopic thin plates of air. The demonstration is a deductiveargument with experimental and observational evidence, and in

arriving at a cause of the colors of bodies it is an analysis. Yet in itsdependence on the cause of the colors in thin plates it is a synthe-sis. Newton himself had problems deciding whether the colors of natural bodies are an analysis or a synthesis. In this draft he tellsus that the colors of bodies (“tinctures”) are a part of the synthesis(composition). If one considers the wording here to be ambigu-ous, an earlier draft was perfectly clear: “In the second Book Iproceeded by Analysis in searching out the fits of easy Reflexion &

easy transmission of the rays of light, & then from this Principlecompounded a further explication of the colours of natural bod-ies [& of the constitution of those bodies requisite for makingthose].”13 Yet by the next draft he made the colors of natural bod-ies part of the analysis, which is how it is expounded in the pub-lished edition: “In the two first Books of these Opticks I proceededby Analysis to discover & prove …the properties of bodies bothopake & pellucid on which their reflexions & colours depend.”14

Newton’s difficulty in trying to fit his theory of colored bodies intohis methodological scheme of analysis and synthesis shows thebl f l h d l i l Th fi




all cases. It also offers a warning to historians who work backwardsfrom such methodological statements in an attempt to interpret Newton’s scientific work.

A few years before he wrote this new query for the Latin trans-lation of the Opticks, Newton was already sufficiently concernedabout method and hypotheses that he planned to make a state-ment about them in a preface for the first edition. He is clearly worried about the hypothetical physics and starts by criticizing themultiplying of hypotheses without end. The examples that he givesin the opening paragraph, for instance, magnetic effluvia and light and color, show that he has Descartes and the Cartesians in mind.

“And,” he countered,

there is no other way of doing any thing with certainty then by drawingconclusions from experiments & phaenomena untill you come at generalPrinciples & then from those Principles giving an account of Nature. What-ever is certain in Philosophy is owing to this method & nothing can be done without it.15

In another draft of the preface in this same manuscript Newtonfirst introduced an account of the methods of analysis and synthe-

sis as the foundations of natural philosophy. One interesting as-pect of this account is that it shows that Newton recognized that physics or natural philosophy is in fact more complex and difficult than mathematics, for he has abandoned his earlier view on a sim-ple relation between the two.

As Mathematicians have two Methods of doing things which they call Com-position & Resolution & in all difficulties have recourse to their method of resolution before they compound so in explaining the Phaenomena of na-ture the like methods are to be used & he that expects success must resolve

before he compounds. For the explications of Phaenomena are Problemsmuch harder then those in Mathematicks. The method of Resolution con-sists in trying experiments & considering all the Phaenomena <of nature>relating to the subject in hand <& drawing conclusions from them> & exam-ining the truth of those conclusions by new experiments & drawing new conclusions (if it may be) from those experiments & so proceeding alter-nately from experiments to conclusions & from conclusions to experimentsuntill you come to the general properties of things, [& by experiments &phaenomena have established the truth of those properties]. Then assum-ing those properties as Principles of Philosopy you may by them explain thecauses of such Phaenomena as follow from them: which is the method of Composition. But if without deriving the properties of things from Phaeno-mena you feign Hypotheses & think by them to explain all nature you may



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make a plausible systeme of Philosophy for getting your self a name, but yoursysteme will be little better then a Romance.16

The introduction of the methods of analysis and synthesis (whichhe still calls resolution and composition), it is quite clear, wasclosely tied to Newton’s defense of his approach to science anddirected against the hypothetical philosophers. At this time,around 1704, Descartes was his greatest concern, but by the next decade it would be Leibniz.17

The description of analysis here—”proceeding alternately fromexperiments to conclusions” and “considering all the Phaenomenaof nature relating to the subject in hand”—is the most detailed

Newton provided of it and most aptly describes his method as heapplied it in optics, especially in the theory of color. Though New-ton did not mention induction in his optical work until the sec-ond English edition of the Opticks in 1717, this is also probably theprocedure that he had in mind for rendering principles “generalby induction” in an experimental science and would later refer toas the “consent of phenomena.”

But let me return yet again to Query 23 and the “experimental

philosophy.” In the version that he actually published in the 1706Latin translation Newton eliminated the phrase “experimentalphilosophy” and substituted the more traditional “natural philoso-phy,” showing that experimental philosophy was simply Newton’s variety of natural philosophy. Why he chose not to introduce hisnew “experimental philosophy” at this time is not clear to me:

As in Mathematicks so in Natural Philosophy the investigation of difficult things by the method of Analysis ought ever to precede the method of Com-

position. This Analysis consists in [arguing] <making experiments & observations & in arguing by them> from compositions to ingredients & frommotions to the forces producing them & in general from [Phaenomena]<effects> to their causes & from particular causes to more general ones, tillthe Argument end in the most general: The Synthesis consists in assumingthe causes discovered & established, as Principles; & by them explaining thePhaenomena proceeding from them, & proving the explanations. In the twofirst Books of these Opticks I proceeded by Analysis to discover & prove theoriginal differences of the rays of light in respect of refrangibility reflexibility

16

MS Add. 3970, f. 480v; the square brackets are Newton’s.17 Newton had in fact introduced the concept of the methods of analysis andsynthesis in his preface to the first edition of the Principia although without us-




& colour & their alternate fits of easy reflexion & easy transmission & theproperties of bodies both opake & pellucid on which their reflexions & col-ours depend: & these discoveries being proved may be assumed as Principlesin the method of Composition for explaining the phaenomena arising fromthem: an instance of which Method I gave in the end of the first Book.18

We can note some small changes from the preceding version.Book II is now seen as exemplifying the method of analysis andsynthesis without restriction, and Newton is trying to bring in the Principia by introducing “arguing …from motions to the forcesproducing them” as an example of composition or synthesis.19

Only in the second English edition of 1717 (that is, in the edi-tion with which we are all familiar) did Newton restore the term“experimental philosophy” and introduce the method of induc-tion:

This Analysis consists in making Experiments and Observations, <and indrawing general Conclusions from them by Induction, and admitting of noObjections against the Conclusions, but such as are taken from Experiments,or other certain Truths. For Hypotheses are not to be regarded in experi-mental Philosophy. And although the arguing from Experiments and Obser- vations by Induction be no Demonstration of general Conclusions; yet it isthe best way of arguing which the Nature of Things admits of, and may be

looked upon as so much the stronger, by how much the Induction is moregeneral. And if no Exception occur from Phaenomena, the Conclusion may be pronounced generally. But if at any time afterwards any Exception shalloccur from Experiments, it may then begin to be pronounced with suchExceptions as occur.>20

In a draft for the Principia from about the same time he makes it clear that by a “more general induction”, he means a greater num-ber of experiments or phenomena.21 Newton’s acknowledgement of the limitations of empirical investigations and induction are asignificant admission. He is no longer even hinting at the infalli-bility of his method as he had over forty years earlier. This state-

18 MS Add. 3970, f. 286r. This is Newton’s English version of this paragraphthat served as the basis for Clarke’s translation into Latin, which differs somewhat from Newton’s text; Newton, Optice: Sive de reflexionibus, refractionibus, inflexionibus& coloribus lucis libri tres, trans. Samuel Clarke (London, 1706), 347-8.

19 This is an allusion to his claim in the Preface to the Principia ; see note 17above.

20

Newton, Opticks: Or, a Treatise of the Reflections, Refractions, Inflections and Col- ours of Light. Based on the Fourth Edition London, 1730 (New York, 1952), 404. Thepassage in angle brackets was added in the English edition. The remainder of this



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ment is almost the same as the fourth rule of philosophizing that he added to the third edition of the Principia in 1726.22

With this addition to query 31 Newton has managed, at least verbally, to bring together the two descriptions of his method,analysis and synthesis in the Opticks and deduction from the phe-nomena and induction in the Principia . Both, to be sure, stress that the starting point of experimental philosophy is phenomena, but they otherwise differ in how they approach the description of hismethod. That in the General Scholium is more epistemological instressing the source of knowledge and its generalization by induc-tion. The description in the Opticks is more methodological in

explaining how to proceed in science, namely, by analysis to un-cover elements or causes and then by synthesis to explain thecauses of other phenomena. The examples that Newton no doubt had in mind were deducing forces from motions in mechanics andthe decomposition of light into the spectral colors.

An earlier draft of this paragraph for the second English editionof the Opticks sheds more light on Newton’s concept of phenom-ena, an essential component of his experimental philosophy. Im-

mediately after declaring “For Hypotheses are not to be regardedin Experimental Philosophy,” he added

Nor are we here to regard Metaphysical Principles unless so far as they arefounded upon experience. For all Metaphysicks not founded upon experi-ence is Hypothetical: And so far as Metaphysical Propositions are foundedupon experience they are a part of experimental Philosophy. Even that cel-ebrated Proposition Ego cogito ergo sum is known to us by experience. Weknow that we think by an inward sensation of or thoughts. And thereforefrom that Proposition we cannot conclude that any thing more is true then what we deduce from experience. And even in proving a Deity all a[r]gu-ments not taken from Phaenomena are little better then dreams.23

Newton is unhesitatingly declaring that metaphysics that is basedon experience or phenomena is a part of experimental philoso-phy. He justifies this inclusion by his definition of experience,

22 Rule 4 stated, “In experimental philosophy, propositions gathered fromphenomena by induction should be considered either exactly or very nearly truenotwithstanding any contrary hypotheses, until yet other phenomena make such

propositions either more exact or liable to exceptions. This rule should be fol-lowed so that arguments based on induction may not be nullified by hypotheses”(Newton, Principia , 796). The only possible difference between the two statements





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Definition I

Phenomena I call whatever can be perceived, either things external whichbecome known by the five senses, or things internal which we contemplate

in our minds by thinking. As fire is hot and water is wet, gold is heavy, andthe sun is luminous, I am and I think. All these are sensible things and canbe called phenomena in a wide sense; but those things are <properly called>phenomena which can be seen, but I understand the word in a wider sense.27

Newton is clearly aware that his concept of phenomenon is not theproper, ordinary one and that he has broadened it. It is not clearto me why he was contemplating introducing such a broad con-cept of phenomena during this two or three year period. He ap-parently thought better of it, for it does not appear in the revisedqueries of the 1717 edition of the Opticks or the third edition of the Principia in 1726. To have published it would only have invitedmore controversy, of which he already had a surfeit.

In another draft Newton presents a number of examples of what he considered to be imaginary or hypothetical phenomena, some-thing he never publicly identified:

Definition II

[The quintessence is different from the four elements, and is subject to noneof the senses nor is it numbered among phenomena. The prime matter which is neither a thing, nor possessed of quality, nor a thing which can bemeasured, is not a phenomenon. The solid orbits in which the planets in-here are not phenomena. The subtle matter in which the planets float, andbodies move without resistance is not a phenomenon. And what are not phenomena, and subject to none of the senses, have no place in experimen-tal philosophy.28

These imaginary hypotheses clearly differ from the sort of hypoth-eses that Newton pursued in the queries of the Opticks, such aslight corpuscles, short-range forces, and atoms, for which he hadsome experimental evidence but insufficient to make them dem-onstrated principles.

Contra Leibniz

Let us now turn to Leibniz as Newton’s immediate target in the

methodological statement in the General Scholium and Newton’s27 J E McGuire “Body and Void and Newton’s De mundi systemate: Some New




reason for adding it. Leibniz publicly, but mildly, criticized New-ton’s ideas about attraction in his Essais de Theodicée (1710), but it is not clear when Newton saw this.29 What certainly did catch hisattention was a letter that Leibniz wrote to Nicolas Hartsoeker inFebruary 1711 criticizing his physical theories. This letter, together with Hartsoeker’s response, had been published on the Continent,but when Newton saw the translation published in the Memoirs of Literature in the issue of 5 May 1712 it incensed him. He prepareda letter to the editor in reply but did not submit it. Newton couldhave written his letter to the editor any time after 5 May 1712, but I argue that it is very likely that he did not come upon Leibniz’s

“very extraordinary letter” until shortly after 18 March 1713, whenCotes called his attention to it. 30 This is just ten days before he sent his final changes to the General Scholium to Cotes on 28 March1713. These changes (which are indicated by angle brackets in thequotation at note 2) include the addition of the phrase with theterm “experimental philosophy” and the following two sentencesthat define that philosophy and give examples of what has beenfound by that method. The editors of Newton’s Correspondence ob-

served that Newton’s draft anticipates his methodological com-ments in the General Scholium.31 In fact, I believe that it parallelsthe General Scholium because the General Scholium had already been composed and sent to Cotes on 2 March; and that it wasLeibniz’s letter to Hartsoeker that prompted Newton to resurrect the term “experimental philosophy,” which he had tentatively usedin the Latin translation of the Opticks before deciding to remain with the more traditional “natural philosophy.” As we shall see,

Leibniz’s remarks are also responsible for the concluding sectionon natural philosophy in Newton’s review of the Commercium epistolicum in 1715.

29 Newton knew of the Theodicée by the time he wrote his review of the Com- mercium epistolicum in 1715, because he mentions it in a draft, MS Add. 3968, f.25r.

30 Cotes wrote Newton that in his planned preface to the Principia he intendedto respond to various criticisms of it, “ As that it deserts Mechanical causes, is built

upon Miracles & recurrs to Occult qualitys. That you may not think it unneces-sary to answer such Objections You may be pleased to consult a Weekly papercall’d Memoirs of Literature In ye 18th Number published May 5th 1712 You



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In his letter to Hartsoeker Leibniz did not mention Newton by name, but he charged that the concept of gravity with action at adistance demanded a continual miracle unlike a rational, mechani-cal explanation by means of the aether. He conceded that in a way every thing is a miracle, but he distinguished between rationalmiracles, as when “a Planet [is] kept in its Orb by the Matter, which constantly drives it towards the Sun,” and supernatural mira-cles, “or rather between a reasonable Explication, and a Fictioninvented to support an ill-grounded Opinion. Such is the Methodof those who say … that all Bodies attract one another by a Law of Nature, which God made in the Beginning of Things.” He then

identified Newton’s concept of gravity, which “is performed with-out any Mechanism, by a simple primitive Quality, or by a Law of God” as an “unreasonable occult Quality, and so very occult, that ‘tis impossible it should ever be clear….” 32

Leibniz then turned to a primary or universal quality, hardness:“If any one … pretends that Hardness proceeds from any otherCause than Mechanism, and if he has recourse to a primitive Hard-ness, as the Assertors of Atoms do, he recurs to a Quality that is so

occult, that it can never be made clear….”33 This too was an attackon Newton through the device of responding to Hartsoeker, whoas an atomist held that hardness was an original property of atoms.Leibniz was undoubtedly referring to a passage in Query 23 in which Newton suggested that, “All these things being consider’d,it seems probable to me, that God in the Beginning form’d Matterin solid, massy, hard, impenetrable, moveable Particles, of suchSizes and Figures, and with such other Properties, and in such

Proportion to Space, as most conduced to the End for which heform’d them.”34 Although Newton is only offering it as a probableconjecture that God created atoms with these properties, in thethird rule of philosophizing in the second edition of the Principia (which Leibniz saw only after his letter to Hartsoeker) he estab-lishes these properties as universal properties of all matter. Theonly issue of conjecture for Newton was whether God created theparticles, not whether they existed.

32 “Philosophical Letters Written by M Leibniz and M Hartsoeker ” Memoirs of




In his draft reply Newton argued, much as he did in the Gen-eral Scholium, that the existence of gravity has “been proved by mathematical demonstrations grounded upon experiments & the

phaenomena of nature: & Mr Leibnitz himself cannot deny that they have been proved.” But Newton’s further remarks show what really rankled him, “Because they do not explain gravity by a me-chanical hypothesis, he charges them wth making it a supernatu-ral thing, a miracle & a fiction invented to support an ill groundedopinion.”35 Newton also replied to Leibniz’s demand that hardnessrequires a mechanical cause by expanding it to include all theuniversal qualities,

So then gravity & hardness must go for unreasonable occult qualitys unlessthey can be explained mechanically. And why may not the same be said of the vis inertiae & the extension the duration & mobility of bodies, & yet noman ever attempted to explain these qualities mechanically, or took themfor miracles or supernatural things or fictions or occult qualities. They arethe natural real reasonable manifest qualities of all bodies seated in them by the will of God from the beginning of the creation & perfectly uncapable of being explained mechanically, & so may be the hardness of primitive parti-cles of bodies.36

I will examine Newton’s argument for the existence of universalqualities later, but we should note that he has attempted to shift the issue to less problematic qualities such as inertia and exten-sion, and then rather tentatively argues that hardness also “may be” a universal quality. One reason that Newton may not have sent this letter is the assertion, with no qualification as to its conjecturalnature, that God created the universal properties.

Newton’s draft letter to the editor does not contain the term“experimental philosophy.” Leibniz’s accusation that his concept

of gravity was “a fiction invented to support an ill grounded opin-ion” must have stung Newton deeply, for if he had one methodo-logical principle from his first publication forty years earlier to hislast, it was the exclusion of hypotheses from natural philosophy. If I am correct that Newton drafted this letter after the General Scho-lium was initially sent to Cotes, then it would easily explain his lateadditions to the General Scholium a few days later. The “experi-mental philosophy” allowed him to try to turn the tables on Leib-

niz and reply that far from his proposing fictions it was Leibniz who was advocating a hypothetical philosophy. On 28 March New-



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and hypotheses, whether metaphysical or physical, or based on occult quali-ties, or mechanical, <have no place in experimental philosophy. In thisphilosophy, propositions are deduced from the phenomena and are madegeneral by induction. The impenetrability, mobility, and impetus of bodies,and the laws of motion and the law of gravity have been found by this me-thod.>37

The addition excludes hypotheses, like Leibniz’s, from natural orrather “experimental philosophy,” whereas in the earlier versionhe had simply declared that he does not follow them. The intro-duction of universal qualities in the final sentence also respondsto Leibniz’s charge in his letter to Hartsoeker.

The Commercium epistolicum was the report that was issued by the

Royal Society in 1712 to adjudicate the calculus priority disputebetween Newton and Leibniz. As if it were not sufficient for New-ton as President of the Royal Society to have appointed the com-mittee and then to have anonymously written the report, he alsoanonymously reviewed it in the Philosophical Transactions in Janu-ary 1715. Most of this long review is devoted to mathematics, but at the conclusion he turns to the many issues of natural philoso-phy that divide him from Leibniz. Newton wields his “experimen-

tal philosophy” in a strictly polemical context to contrast Leibniz’shypothetical philosophy with his own experimental one:

The Philosophy which Mr. Newton in his Principles and Optiques has pursuedis Experimental; and it is not the Business of Experimental Philosophy toteach the Causes of things any further than they can be proved by Experi-ments. We are not to fill this Philosophy with Opinions which cannot beproved by Phaenomena. In this Philosophy Hypotheses have no place, un-less as Conjectures or Questions proposed to be examined by Experiments.38

For a page and a half he proceeded to cite the numerous passages where he conceded that he did not know the cause of gravity. Inexasperation he lamented: “And after all this, one would wonderthat Mr. Newton should be reflected upon for not explaining theCauses of Gravity and other Attractions by Hypotheses; as if it werea Crime to content himself with Certainties and let Uncertaintiesalone.”39 In conclusion he further contrasted their philosophiesand continued to use the resurrected “experimental philosophy”as a powerful resource to ridicule Leibniz:

It must be allowed that these two Gentlemen differ very much in Philoso-phy The one proceeds upon the Evidence arising from Experiments and




Phaenomena, and stops where such Evidence is wanting; the other is takenup with Hypotheses, and propounds them, not to be examined by Experi-ments, but to be believed without Examination. The one for want of Experi-ments to decide the Question, doth not affirm whether the Cause of Gravity be Mechanical or not Mechanical: the other that it is a perpetual Miracle if it be not Mechanical. The one (by way of Enquiry) attributes it to the Powerof the Creator that the least Particles of Matter are hard: the other attributesthe Hardness of Matter to conspiring Motions, and calls it a perpetual Mira-cle if the Cause of this Hardness be other than Mechanical.… And must Experimental Philosophy be exploded as miraculous and absurd , because it asserts nothing more than can be proved by Experiments, and we cannot yet prove by Experiments that all the Phaenomena in Nature can be solved by meer Mechanical Causes? Certainly these things deserve to be better consid-ered. 40

Many drafts of Newton’s review survive. In these he vents his spleenagainst Leibniz, and I cannot resist including one passage in whichhe flaunts his experimental prowess to further ridicule Leibniz:“And must Experimental Philosophy be rendred uncertain by fill-ing it with <Opinions> [Hypotheses] not yet proved by any experi-ment? If Mr Leibnitz never found but a new experiment in all hislife for proving anything; If M. Newton has by so great multitudeof new Experiments discovered & proved many things about light

& colours & setled a new Theory thereof never to be shaken.”41

This is the only passage that I have found in which Newton appealsto actual experiments when invoking his “experimental philoso-phy.”

Newton’s rejection of Leibniz’s demand for mechanical expla-nations of gravity and hardness shows he had shifted the meaningof the experimental philosophy from the one it had acquired inthe Restoration. According to Charles Webster, the terms “me-

chanical” and “experimental philosophy” were synonymous, as inthe writings of Boyle and Hooke.42 Hooke in the preface to his Micrographia , for example, spoke of “the real, the mechanical, theexperimental Philosophy.”43 The experimental philosophy—as itsname declares—was always associated with experiment and observation. It was no doubt because of its association with empiricism,experiment and observation, that Newton chose experimental phi-losophy.

40 Ibid., 224.41 MS Add 3968 f 586v



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A few years before Newton first used “experimental philosophy” William Whiston, who had assumed Newton’s duties as LucasianProfessor at the University of Cambridge when Newton left forLondon, had used the term in defending Thomas Burnet’s Sacred Theory of the Earth as well as his own New Theory of the Earth against John Keill’s criticism. “We are not now in a Cartesian Vortex ,” he wrote, “where fancy and contrivance can introduce and hinder any effect at pleasure: But we are in Mechanical and ExperimentalPhilosophy, which is an inflexible thing, and not at all subject toour inclinations.”44 Whiston is still equating the mechanical andexperimental philosophies, but he is now using both as anti-hypo-

thetical terms, which represents a new twist on these old terms. Although Newton owned this pamphlet, we cannot assume that Whiston influenced Newton’s choice of the term, or vice versa,since there is no evidence on the point.45

The meaning of the mechanical philosophy was more complexand varied than that of “experimental philosophy.” It contained anumber of distinct, interrelated elements, including the following:the world and its components behave like a machine; or, more

strongly, the world can be described solely by the mathematicallaws of mechanics; all causation is by contact action so that imma-terial, spiritual agents are banished; matter is composed of invis-ible corpuscles; and hypotheses about the properties and motionsof these invisible corpuscles may be formulated to explain visibleeffects.46 Different natural philosophers adopted various combina-tions of these elements, but Descartes, perhaps the archetypalmechanical philosopher, adopted all of them. On the Continent,

under the influence of Descartes, there was widespread acceptanceof the demand for mechanical explanations by corpuscles andcontact action. Since these explanations involved invisible motionsof invisible corpuscles, they necessarily involved hypothetical expla-nations. The demand for mathematization was not as widespread,but we may note that the two most eminent neo-Cartesians on the

44 William Whiston, A Vindication of the New Theory of the Earth from the Exceptionsof Mr. Keill and Others (London, 1698), 22; this was reissued in 1700 as A Second

Defence of the New Theory of the Earth from the Exceptions of Mr. John Keill, and it con-tains the identical passage. Whiston’s work is in reply to Keill’s An Examination of Dr Burnet’s Theory of the Earth Together with Some Remarks on Mr Whiston’s New




Continent, Huygens and Leibniz, were as strongly committed to it as Newton. In England there was a reluctance to accept that allphenomena could be explained solely by matter in motion andcontact action, and various active principles were considered.47

Mathematization also was not widely seen as an essential aspect of the mechanical philosophy. Although the mechanical philosophy was formulated early in the seventeenth century, the term was in-troduced by Boyle in 1661. Despite the differences between Car-tesians and atomists, compared with Aristotelians, Boyle explained,“both parties agree in deducing all the Phaenomena of Naturefrom Matter and local Motion,” so that they may be considered

“one Philosophy. Which because it explicates things by Corpuscles,or minute Bodies, may (not very unfitly) be call’d Corpuscular …I sometimes also term it the Mechanical Hypothesis or Philoso-phy.”48 Boyle was perhaps the leading English exponent of themechanical philosophy, and he had reservations about extrememechanization and mathematization. In his formative years New-ton thoroughly studied all the available works of Descartes andBoyle.

From the beginning of his career Newton operated within theframework of the mechanical philosophy, but he never adheredstrictly to all of its elements, except for the corpuscular nature of matter and the goal of mathematization.49 Insofar as I can deter-mine, he does not appear to have used the term “mechanical phi-losophy” in the seventeenth century (and perhaps never at all), but rather more restricted terms like “mechanical hypotheses” or “me-chanical causes.”50 His use of the term “mechanical” rather than

47 John Henry, “ Occult Qualities and the Experimental Philosophy: ActivePrinciples in Pre-Newtonian Matter Theory,” History of Science 24 (1986), 335-81.

48 Robert Boyle, “Some Specimens of an Attempt to Make Chymical Experi-ments Useful to Illustrate the Notions of the Corpuscular Philosophy,” in The Works of Robert Boyle, ed. Michael Hunter and Edward B. Davis, 14 vols. (London/Brookfield, Vt., 1999), 2: 87.

49 See, for example, J. E. McGuire and Martin Tamny, Certain Philosophical Questions: Newton’s Trinity Notebook (Cambridge, 1983), 323-4; Shapiro, Fits, Pas- sions, and Paroxysms, 73-7; and Gabbey, “ Newton, Active Powers, and the Mechani-cal Philosophy.”

50 For “mechanical hypotheses” see Newton’s letter to Oldenburg for Hooke, June 11, 1672, Newton, Correspondence , 1: 174; and his letter to Huygens on 3 April1673 264 I d ft f hi l t H k N t f d t th “m h i ll



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“mechanical philosophy” reflects his lack of commitment to that philosophy, as well as his rejection of speculative systems of scien-tific thought. Newton was not a systematic philosopher, and whenhe announced his new “experimental philosophy” he defined it methodologically and not as a natural philosophy. To be sure, af-ter the Principia and the introduction of the concept of force, which he hoped would be the new foundation for natural phi-losophy, he had moved far from the mechanical philosophy.The meaning of “mechanics” and “mechanical” would as a conse-quence change. A mechanical explanation of gravity had been theholy grail of the mechanical philosophy, and serious mechanical

philosophers—including Newton himself—attempted to explain it by contact action of aetherial particles. Afterward, the Principia , asNewton explained to Leibniz, largely ruled that out.

When at the beginning of the eighteenth century Newton wassearching for a name to defend and define his natural philosophy,especially that of the Principia , he would have naturally been drawnto “experimental philosophy” because of its association with anempirical approach to science. But Newton’s “experimental phi-

losophy” was no longer equivalent to the mechanical philosophy,as it had been forty years earlier. Newton rejected the hypotheti-cal explanations of the mechanical philosophy and the require-ment for contact action. His use of “experimental philosophy”against Leibniz’s demand for a mechanical explanation of gravity shows just how much the term had changed.

That the “experimental philosophy” could serve as a useful wea-pon against Cartesians and Leibnizian mechanists becomes further

evident from Cotes’ preface to the second edition of the Principia ,in which he presented and defended Newtonian natural philoso-phy. Newton played no direct role in the composition of the pref-ace other than providing some general guidelines to Cotes, but Cotes knew Newton’s mind and had carefully studied his methodo-logical statements in the queries and General Scholium. He beginsthe preface by dividing natural philosophers into three groups.First, there are those, in particular, Aristotelians, who endow

things with occult qualities. The second group are the mechanicalphilosophers who opposed the first, but, Cotes tells us, they haved if d ff l i “d ” b i i i i i ibl i l





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it when he claims that all matter is heavy (or that every part of matter at-tracts every other part), which is certainly not proved by experiment…53

Newton wrote draft after draft in reply to Leibniz and would not grant any justification for admitting hypotheses into natural phi-losophy. It will suffice to quote just one of his draft replies, forNewton’s views were unalterable on this point:

He commends experimental Philosophy, but adds that when experimentsare wanting, it is allowed to imagin Hypotheses & expect till new experi-ments shall determin which of them are true & upon this account he thinkshis philosophy may be justified. But he should consider that Hypotheses arenothing more then imaginations, conjectures, & suspicions & ougt not to bepropounded as Truths or Opinions nor admitted into Philosophy as such

until they are verified & established by experiments. And if you consider hisPhilosophy you will find that it consists generally in such Hypotheses as cannever be established by experiments: Such as are That God is intelligentiasupramundana …54

The response that Newton actually sent to Conti on 26 February 1716 was surprisingly restrained in light of the drafts: “He preferrsHypotheses to Arguments of Induction drawn from experiments,accuses me of opinions wch are not mine, & instead of proposing

Questions to be examined by Experiments before they are admit-ted into Philosophy he proposes Hypotheses to be admitted &beleived before they are examined.”55 Leibniz replied briefly toNewton’s charge, and Newton did not even address this point inhis final response to Leibniz, which was devoted solely to math-ematics. Further debate on the role of hypotheses was apparently judged to be fruitless.56

The Meaning of ‘Experimental Philosophy’

We are now in a position to clarify what Newton meant by hisenigmatic statement in the General Scholium that “in this experi-

53 Newton, Correspondence , 6: 252; the phrases in italics are in Latin, while thebody of the letter is in French.

54 Alexandre Koyré and I. Bernard Cohen, “Newton & the Leibniz-ClarkeCorrespondence with Notes on Newton, Conti, & Des Maizeaux,” Archives inter-

nationales d’histoire des sciences 15 (1962), 63-126, on 114; some other interestingdrafts can be found on 73 and 109-110.

55 Newton Correspondence 6: 285-6





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from the method of others, vizt by deducing things mathematically fromprinciples derived from Phaenomena by Induction. These Principles are the3 laws of motion. And these Laws in being deduced from Phaenomena by Induction & backt with reason & the three general Rules of philosophizingare distinguished from Hypotheses & considered as Axioms. Upon these arefrounded [sic] all the Propositions in the first & second Book. And thesePropositions are in the third Book applied to the motions of ye heavenly bodies.59

Here he more fully describes the structure of Books I and II as heconceives of it and explains in greater detail that the propositions(“things”) are mathematically deduced from principles that are inturn derived from phenomena by induction. He even specifies the

principles as the Laws of Motion and also adds that he had to apply further reasoning. There is no question of deducing propositionsdirectly from the phenomena. He gave a similar account in hisdraft letter to the editor of the Memoirs of Literature which, I haveargued, was probably composed shortly before the General Scho-lium. After briefly describing the properties of gravity that he hadderived, he states that, “These things have been proved by math-ematical demonstrations grounded upon experiments & the phae-

nomena of nature.”60

Now he uses “grounded upon” rather than“deduced from.”Later in his draft to Cotes on 28 March Newton further clarified

his position on what he means by induction: “Experimental phi-losophy argues only from phaenomena, draws general conclusionsfrom the consent of phaenomena, & looks upon the conclusion asgeneral when ye consent is general without exception, tho thegenerality cannot be demonstrated a priori.”61 We should note that he now “argues” from phenomena. And rather than appealing toinduction, he more specifically explains that it is by “the consent of phaenomena” that conclusions are rendered general. By this hepresumably means that the more phenomena that agree with orcan be explained by the conclusion (property, principle, proposi-tion, etc.) the more general it will be. Newton expressed a similaridea about ten years earlier in his draft preface for the Opticks when he first set forth his methods of analysis (resolution) andsynthesis. He explained that,

The method of Resolution consists in trying experiments & considering allthe Phaenomena of nature relating to the subject in hand & drawing con-




clusions from them & examining the truth of those conclusions by new ex-periments & drawing new conclusions (if it may be) from those experiments& so proceeding alternately from experiments to conclusions & from conclu-sions to experiments untill you come to the general properties of things…62

Here we are told that “all the Phaenomena of nature relating tothe subject in hand” are to be considered and we are to proceed“alternately from experiments to conclusions.” While this doesaptly describe his optical investigations, it also applies to the Prin- cipia . We again see that Newton has something more in mind by “Phaenomena” than simply experiments or astronomical observations, but rather ordinary occurrences of nature and the arts,

such as planets moving in their orbits, spinning hoops, and thechanging colors of foliage.63 Experiments and observations may be“Phaenomena,” but the category is not limited to them.

After defining the experimental philosophy in the GeneralScholium in which “propositions are deduced from the phenom-ena and are made general by induction,” Newton gave some ex-amples, “The impenetrability, mobility, and impetus of bodies, andthe laws of motion and the law of gravity have been found by thismethod.”64 This list is so heterogeneous that it is apparent that hehad to be using “induction” and “deduction from the phenomena”in a general way. It is also apparent that “proposition” here doesnot simply mean a statement in a formal theory, but encompassesproperties or qualities of bodies, principles, and a sophisticatedmathematical theory. The laws of gravity are demonstrated in BookIII from a set of precise astronomical data on the motions of theplanets and satellites and from the mathematical propositions inBook I establishing the properties of orbital motion. Newton’s

argument is so complex that contemporary philosophers of sci-ence cannot agree on the method that Newton used to deduceuniversal gravity. Whatever it is, it is very different from the “induc-tion” by which he deduces the Laws of Motion. For instance, heestablishes the first Law, the law of inertia—”Every body perseveresin its state of being at rest or of moving uniformly straight forward,except insofar as it is compelled to change its state by forces im-pressed”—by the following argument:

62 This passage was cited in full at note 16.63 For the spinning hoop and planetary orbits see the passage quoted at note



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Projectiles persevere in their motions, except insofar as they are retarded by the resistance of the air and are impelled downward by the force of gravity. A spinning hoop, which has parts that by their cohesion continually draw one another back from rectilinear motions, does not cease to rotate, except insofar as it is retarded by the air. And larger bodies—planets and comets—preserve for a longer time both their progressive and their circular motions, which take place in spaces having less resistance.65

Newton is not really presenting evidence, but examples or phe-nomena that this law could explain. Certainly, no one before the1630s saw any of these phenomena as exhibiting the law of inertia,and well after that date it was still not apparent how that law ap-plied to the motion of the planets. In the Scholium to the Laws of

Motion he states, “The principles I have set forth are accepted by mathematicians and confirmed by experiments of many kinds,”and then he presents various experiments and arguments to sup-port the Laws. Thus, confirmation plays a role in Newton’s “deduc-tions.” In the Corollaries to the Laws of Motion he presents stillmore arguments and experiments. The method adopted agreesrather well with his descriptions in his draft letter to Cotes that theLaws were “deduced from Phaenomena by Induction & backt with

reason & the three general Rules of philosophizing,” and also “theconsent of phaenomena.”66

To establish the universal qualities of bodies Newton invokes histhird rule of philosophizing, “Those qualities of bodies that can-not be intended and remitted and that belong to all bodies on which experiments can be made should be taken as qualities of allbodies universally.” With this rule Newton is trying to justify theapplication of what has come to be called “transdiction” or “trans-duction,” a method by which the laws and properties of observablemacroscopic bodies are extended to the imperceptible, micro-scopic parts of bodies. Newton’s justification for this rule is that “the qualities of bodies can be known only through experiments;and therefore qualities that square with experiments universally are to be regarded as universal qualities.”67 A straightforward ex-ample of this is Newton’s argument for extension, which, because

65 Newton, Principia , 416.66

Ibid., 424. The letter to Cotes is cited at notes 59 and 61.67 Newton, Principia , Bk. III, 795. On transduction or transdiction see the pio-neering work of Maurice Mandelbaum, Philosophy, Science and Sense Perception:




it is found in all sensible bodies, is ascribed to all bodies univer-sally. Similar arguments apply to other qualities, including impen-etrability, mobility, and impetus that Newton cites in the General

Scholium as examples of the experimental philosophy.68 Newtonis appealing to the most basic sense experiences to justify the ex-istence of these universal qualities. After examining the three ex-amples Newton gave of his method, it is difficult to see a singlemethod of induction or deduction at work. It is equally difficult tocomprehend how one could expect Newton to have given a com-prehensive account of his method in all his work in 30 or 40 words. What these examples have in common, as Newton claims, is that

they are all based on phenomena in some way or other. Above all,none of them appealed to imaginary causes or hypotheses, whichNewton so decried. Thus, by the phrase “deduction from the phe-nomena” Newton meant only to set forth the general idea that hisconclusions were grounded on or argued from phenomena.

In trying to understand what Newton means by “deduction fromthe phenomena” and “induction” I have appealed to various draftsand unpublished documents, and it is reasonable to ask whether

these illuminate the words that he did choose to publish. In thiscase I believe that the answer is certainly yes, for none of themcontradict or conflict with his published ideas, but rather seem toexpress the same ideas in different words and thus serve to illumi-nate them.

Newton’s “experimental philosophy,” it can be safely concluded, was introduced to counter objections to his theory of gravity and way of doing science and to differentiate it from what Newtonconsidered to be “hypothetical philosophy.” If he first consideredadopting it to counter the Cartesians, when he finally published it in 1713 it was clearly directed even more against Leibniz and theLeibnizians, with whom he was now at war. He did not, however,have to choose the phrase “experimental philosophy,” which hehad abjured using throughout the seventeenth century. Why didhe use that phrase? I believe that he adopted it primarily becauseit was already coined and was ready to hand, and its empirical

68 Newton’s arguments for hardness and impenetrability are not, as ErnanMcMullin has warned us, unproblematic extensions of arguing from universal



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force contrasted nicely with speculative or hypothetical philoso-phies. Moreover, after a long and productive career, Newton, I amsure, recognized that the program that he espoused in his youth

of establishing a more certain science founded on mathematics was unrealistic and that experiment, or rather phenomena, must serve as both the foundation of any new science and a fundamen-tal limiting factor.

At the beginning of his career Newton’s statements on methodstressed the mathematical nature of his science and assigned ex-periment a subsidiary role. In this period he tended to be con-cerned with the certainty of his science. For example, in his Optical Lectures

in 1670, he announced his new experimental theory of color withthe declaration that:

the generation of colors includes so much geometry, and the understand-ing of colors is supported by so much evidence, that for their sake I can thusattempt to extend the bounds of mathematics somewhat, just as astronomy,geography, navigation, optics, and mechanics are truly considered math-ematical sciences even if they deal with physical things…. Thus althoughcolors may belong to physics, the science of them must nevertheless be con-sidered mathematical, insofar as they are treated by mathematical reason-ing.69

While in the heading to this passage Newton avows that “thesepropositions are to be treated not hypothetically and probably, but by experiments or demonstratively,” in the passage itself he speaksonly about mathematics and not experiment, except for a vaguereference to “evidence.”

When Newton first published a brief account of his theory of color and refraction in Philosophical Transactions in 1672, he

again associated his new theory with mathematics and made strongclaims for its certainty:

A naturalist would scearce expect to see ye science of those [i.e., colours]become mathematicall, & yet I dare affirm that there is as much certainty init as in any other part of Opticks. For what I shall tell concerning them isnot an Hypothesis but most rigid consequence, not conjectured by barely inferring ‘tis thus because not otherwise or because it satisfies all phaeno-mena (the Philosophers universall Topick,) but evinced by ye mediation of experiments concluding directly & wthout any suspicion of doubt.70

A notable feature of this claim, besides the extreme confidence inhis results, is that Newton seems to see experiments as essentially




transparent, yielding their meaning with no interpretation, “con-cluding directly & wthout any suspicion of doubt.”71 We shouldalso note Newton’s rejection of hypotheses, perhaps his most sus-

tained methodological principle, already appeared in his first pub-lication.

A few months later in a draft of a paper on Newton’s rings hemade the strongest claims for the certainty of his theory—”in-fallibly true & genuine”—and continued to emphasize its mathe-matical nature. After presenting a physical explanation of theappearance of Newton’s rings when viewed through a prism, heasserted,

For confirmation of all this I need alledg no more then that it is mathemati-cally demonstrable from my former Principles. But yet I shall add that they which please to take the paines may by the testimony of their senses be as-sured that these explications are not Hypotheticall but infallibly true & genu-ine.72

At this time for Newton confirmation is by mathematical demon-stration and secondarily—only if you think it is worth the bother—by experiment. He clearly believed that a mathematical deductive

approach would lead to great certainty and that experiment couldprovide the requisite certain foundations for such a science, but until the eighteenth century he did not assign experiment a pri-mary place in his methodology.

Despite Newton’s late conversion to experimental philosophy, Ihave no doubt that he remained committed to the effectivenessand necessity of mathematics in natural philosophy. In 1687 hechose to entitle his book the Mathematical Principles of Natural Phi- losophy to distinguish it from Descartes’ Principles of Philosophy. When preparing the subsequent editions in 1713 and 1725, henever considered retitling the work to the Principles of Experimental Philosophy or the Mathematical Principles of Experimental Philosophy.

71 Six months later, on 6 July 1672, Newton in a letter to Oldenburg Newtonreiterated this claim in slightly different words; Newton, Correspondence , 1: 209.

72 “Observations,” MS Add. 3970, f. 525r; see also f. 510v for the unchanged version from 1675, which was read to the Royal Society and subsequently pub-lished in Thomas Birch, ed., The History of the Royal Society of London, for Improving

of Natural Knowledge, from Its First Rise , 4 vols. (London: 1756-1757; facsimile rpt.:Brussels, 1968), 3: 293; and reprinted in Newton, Isaac Newton’s Papers and Letterson Natural Philosophy and Related Document ed. I. Bernard Cohen (Cambridge,



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Shapiro Newton's 'Experimental Philosophy