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Newton's "Experimental Philosophy"Author(s): Alan E. ShapiroSource: Early Science and Medicine, Vol. 9, No. 3, Newtonianism: Mathematical and'Experimental' (2004), pp. 185-217Published by: BRILLStable URL: http://www.jstor.org/stable/4130349 .Accessed: 12/07/2013 00:02

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NEWTON'S "EXPERIMENTAL PHILOSOPHY"'

ALAN E. SHAPIRO*University f Minnesota

Abstract

Newton abjured using the term "experimental philosophy," widely used

in Restoration England at the start of his career, until 1712 when headded a passage to the General Scholium of the Principia that brieflyexpounded 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

provideinsight 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 appeared

in the titles of such works as Robert Boyle's Some ConsiderationsTouching the Usefulness of Experimental Natural Philosophy (1663) and

Henry Power's Experimental Philosophy (1664). The apparent conti-

nuity between Newton's usage and that of the early Royal Societyis, however, largely an illusion. Newton had consciously avoided

using "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 January15, 2002. I dedicate the paper to Ted and wish him many more fruitful years. Ithank George Smith for useful discussions on Newton's method, and MordechaiFeingold for his comments.

1 The title of one of Newton's letters on his theory of light in the PhilosophicalTransactions contains "experimental philosophy," but the title is Henry Olden-

? Koninklijke Brill NV, Leiden, 2004Also available online - www.brill.nl

Early Science and Medicine 9, 3

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186 ALAN E. SHAPIRO

in the second edition of the Principia in 1713 in order to defend

his work, especially the theory of gravity, against the criticisms ofCartesians and Leibnizians but, above all, Leibniz himself. When

considering 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'sA 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 experimentalwork, although it admittedly contains some experiments? Rather

the 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 concernwill 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 and

unpublished writings; then I will turn to determining the role thathis 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 methodologicalviews 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 tovortices and God, he turned to gravity. He enumerated the vari-

burg's, the editor, not Newton's; "A Serie's of Quere's Propounded by Mr. IsaacNewton ... and Here Recommended to the Industry of the Lovers of Experimen-tal Philosophy, As They Were Generously Imparted to the Publisher in a Letterof the Said Mr. Newtons of July 8.1672," Philosophical Transactions 7, no. 85 (July1672), [5]004-5007



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NEWTON'S "EXPERIMENTAL PHILOSOPHY" 187

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 notdeduced from the phenomena must be called a hypothesis; and hypotheses,whether metaphysical or physical, or based on occult qualities, or mechani-cal, And it isenough 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 final

changes and additions to the General Scholium-including the

passage 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 ofthe 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 this

philosophy" (In hac Philosophia) is rendered by Cohen and Whitman, "In this

experimental philosophy." The passage in angle brackets was a late change made

by 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 phenomenais certainly a part of experimental Philosophy"-but Newton instructed Cotes tomake both changes in the same letter.

Newton to Cotes, 28 March 1713, Newton, The Correspondence f Isaac Newton,ed., H. W. Turnbull, J. F. Scott, A. Rupert Hall, and Laura Tilling, 7 vols. (Cam-bridge, 1959-77), 5: 398-399.



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188 ALAN E. SHAPIRO

where he introduced the "experimental philosophy" are in the

context 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 naturalphilosophy; and the requirement that propositions in experimen-tal philosophy are "deduced from the phenomena and are made

general 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 an

important clarification of what he meant by a hypothesis: "And theword 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."4Newton is thus rejecting hypotheses that are totally imaginary, withno experimental support whatever. Hypotheses that have some

experimental support, but which is insufficient to render themdemonstrated scientific principles, are allowed provided they are

kept 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 natural

philosophy, 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 ofColored Bodies and Fits of Easy Reflection (Cambridge, 1993), ch. 1.2. Since Newtonused one word for two distinct meanings of hypothesis, I there introduced adistinction between "imaginary hypotheses," which are excluded, and "experimen-tal hypotheses," which may be used provided they are kept distinct from es-tablished principles, 13.



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"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 ofbodies, 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 ofthese examples should make us suspicious that there is one me-

thod underlying their demonstration. It is, moreover, not evenclear what phenomena are. The choice of the term "phenomena"was a natural one for the Principia, for it had played a prominentrole 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-for

example, 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 in

Query 23 for the Latin translation of the Opticks n 1706 where hediscusses the method of analysis and synthesis. (This Query wasrenumbered 31 in the second English edition of the Opticks.) In

this 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 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 [the causes & ingredients] of things we may proceed by [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

6 Cambridge University Library, MS Add. 3970, f. 243r; since all manuscriptscited here are in this collection, I will henceforth cite only the manuscript num-ber. Angle brackets indicate Newton's additions and square brackets his deletionsunless otherwise indicated. Newton also used square brackets in his drafts to in-



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190 ALAN E. SHAPIRO

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 this

passage. 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 his

experimental philosophy, it is revealing of the mathematical foun-dation of so much of his thought that he chose to explain the

method of the experimental philosophy by means of conceptsdrawn 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 his

growing admiration for things ancient, as part of the prisca sapientiatradition 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 ata 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 than

using 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 n 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 verygeneral descriptions to encompass the two. He would later try to

align the methodological statements in the two works. Another,

dicate phrases that he was considering deleting, and the first set are his. I will notindicate changes in the manuscripts that are of no significance for the argumentin this paper.

7 See J. E. McGuire and P. M. Rattansi, "Newton and the 'Pipes of Pan'," Notes

and Records of the Royal Society of London 21 (1966), 108-43;Paolo

Casini,"Newton:

The Classical Scholia," History of Science 22 (1984), 1-58; and Volkmar Schiiller,"Newton's Scholia from David Gregory's Estate on the Propositions IV through IX,Book III of His Principia," in Between Leibniz, Newton, and Kant: Philosophy andScience in the Eighteenth Century, ed. Wolfgang Lefrvre, Boston Studies in the Phi-

losophy of Science, 220 (Dordrecht, 2001), 213-65.



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192 ALAN E. SHAPIRO

Heavens might be founded upon good Geometry. And this makes it now

difficult for unskillful Men to see the Analysis by which those Propositionswere found out.'

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 the

controversy with Leibniz. This factor helps to explain why Newton

chose not to expound his new way of doing science in the GeneralScholium using the methods of analysis and synthesis that he had

adopted for this purpose about a decade earlier and had alreadypublished 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 the

phenomena," 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 exceptfor 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 ofNature. This enquiry should proceed first by Analysis in arguing from effects tocauses & from compositions to their ingredients. And when we have found[the principles]

we may proceed by Synthesis from those 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 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 betweenNewton

and Leibniz (Cambridge, 1980). D. T. Whiteside observedin a footnote to this passage, that he has found "little to support" the truth ofNewton's claim; "on the contrary, it seems to us that, except for a number ofopening propositions in its second book, the Principia was in its greatest part 'in-vented' in the highly geometrical form in which it was 'composed' for the press";Newton, Mathematical Papers, 8: 599.



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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 thin

transparent plates, & those of feathers & tinctures are easily compounded.10

After acknowledging the incompleteness of the third book, he

explained that by pursuing this method our knowledge of God andmoral philosophy would be expanded."l

The most significant additions are the examples of analysis and

synthesis in Books I and II of the Opticks with the admission thatBook II "is not in so good a method," a rare display of candor and

admission of imperfection by Newton, so it is not surprising thathe 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 ofnatural 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 lightrevision 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 and

put it into the form that we know. While working on a revision ofthe part on the colors of thick plates (then in a separate book

together with diffraction) Newton devised his theory of fits ofeasy 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

10MS Add. 3970, f. 242v." Since this draft on the relation of natural philosophy to knowledge of God

differs 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 wecan expect from Phaenomena, Natural Philosophy will be perfected, & a goodfoundation will be laid for enlarging the bounds of Moral Philosophy. " (ibid.)

12 Shapiro, Fits, Passions, and Paroxysms, ch. 4.1.



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194 ALAN E. SHAPIRO

Newton, quite properly, cites the theory of fits as part of the

analysis, but he never went back to revise the first three parts thathad already been completed to incorporate his newly formulated

theory of fits. Only in the fourth part, which he was in any case

revising did he add the theory of fits. The first part consists of

twenty-four "observations" whose centerpiece is a description ofthe colors of thin plates produced by the air in the space betweentwo lenses (Newton's rings). It contains some fundamental obser-vations, such as that the colors in Newton's rings repeat accordingto integral multiples of the thickness of the air gap, but there are

no propositions at all, as there are in the first book of the Opticksor the Principia. The second part consists of "Remarks upon the

foregoing 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 in

macroscopic thin plates of air. The demonstration is a deductive

argument 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 ofnatural 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 I

proceeded 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]."'" 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."14Newton's difficulty in trying to fit his theory of colored bodies intohis methodological scheme of analysis and synthesis shows theproblem of general methodological statements: They may not fit

13 MS Add. 3970, f. 244r.14 Ibid., f. 286r



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all cases. It also offers a warning to historians who work backwards

from such methodological statements in an attempt to interpretNewton'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 clearlyworried about the hypothetical physics and starts by criticizing the

multiplying of hypotheses without end. The examples that he givesin the opening paragraph, for instance, magnetic effluvia and lightand 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 donewithout 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 difficultthan 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 ofresolution before they compound so in explaining the Phaenomena of na-ture the like methods are to be used & he that expects success must resolvebefore 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 relating to the subject in hand & exam-ining the truth of those conclusions by new experiments & drawing newconclusions (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 ofComposition. But if without deriving the properties of things from Phaeno-mena you feign Hypotheses & think by them to explain all nature you may

15 Ibid., f 479r. J. E. McGuire discovered and identified this manuscript; "New-ton's 'Principles of Philosophy': An Intended Preface for the 1704 Opticks and aRelated Draft Fragment," British Journal for the History of Science 5 (1970), 178-86.



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196 ALAN E. SHAPIRO

make a plausible systeme of Philosophy for getting your self a name, but your

systeme will be little better then a Romance.16The introduction of the methods of analysis and synthesis (whichhe still calls resolution and composition), it is quite clear, was

closely 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 nextdecade it would be Leibniz.17

The description of analysis here-"proceeding alternately from

experiments to conclusions" and "considering all the Phaenomena

of nature relating to the subject in hand"-is the most detailedNewton provided of it and most aptly describes his method as he

applied 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 n 1717, this is also probably the

procedure 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 "experimentalphilosophy." 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'svariety 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 difficultthings by the method of Analysis ought ever to precede the method of Com-position. This Analysis consists in [arguing] from compositions to ingredients & frommotions to the forces producing them & in general from [Phaenomena] 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 and

synthesis in his preface to the first edition of the Principia, although without us-ing those terms. In a famous programmatic statement on the search for forces asthe foundation of natural philosophy, he wrote that "the basic problem of phi-losophy seems to be to discover the forces of nature from the phenomena ofmotions and then to demonstrate the other phenomena from these forces"; New-ton, Principia, 382.



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& colour & their alternate fits of easy reflexion & easy transmission & the

properties 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 and

synthesis without restriction, and Newton is trying to bring in the

Principia by introducing "arguing ...from motions to the forces

producing them" as an example of composition or synthesis.'9

Onlyin the second

Englishedition 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, 20

In a draft for the Principia from about the same time he makes itclear that by a "more general induction", he means a greater num-ber of experiments or phenomena.2" Newton's acknowledgementof the limitations of empirical investigations and induction are a

significantadmission. He is no

longereven

hintingat 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 somewhatfrom 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. The

passage in angle brackets was added in the English edition. The remainder of thisparagraph was largely unchanged from the Latin edition.

21 In a draft preface for the Principia, which Whiteside dates to 1716-18, New-ton wrote that for "an argument by induction... the more numerous the experi-ments or phenomena from which it is deduced the stronger it proves to be";Newton, Mathematical Papers, 8: 452, n. 34, my translation.



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198 ALAN E. SHAPIRO

ment is almost the same as the fourth rule of philosophizing that

he added to the third edition of the Principia in 1726.22With 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 thatthe 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 in

stressing the source of knowledge and its generalization by induc-

tion. The description in the Opticks is more methodological inexplaining 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 doubthad 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 thenwhat 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 suchpropositions 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 possibledifference between the two statements

is that here he states that conclusions are "exactly or very nearly true" while inthe Opticks that they "may be pronounced generally," i.e., it depends on whether"exactly or very nearly true" differs significantly from "generally".

23 MS Add. 3970, f.621v. The final sentence replaced "Metaphysical proofs ofa Deity not grounded on Phaenomena are dreams."



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which includes all sensations, including internal sensations. Hence

Descartes' celebrated "I think, therefore I am" belongs to experi-mental philosophy. Proofs of God's existence can belong to experi-mental philosophy in the same manner. After all, Newton hadearlier declared publicly in the General Scholium that "to treat ofGod from phenomena is certainly a part of experimental philoso-phy."24 Earlier, in what I take to be an attempt at a draft for the

queries added to the Latin edition, he elaborated on this point:"We see the effects of a Deity in the creation & thence gather the

Cause[,] & therefore the proof [of] a Deity & what are his proper-ties belongs to experimental Philosophy."25 Metaphysics and dis-course about God belong to experimental philosophy providedthey are based on phenomena, otherwise they are hypothetical andhave no place in it.

In the period that Newton was preparing the second Englishedition of the Opticks, he was also working on a third edition ofthe Principia and had drafted the fourth rule as well as new defini-tions and a preface. Most of these passages, as well as other docu-ments to which we will turn shortly, were aimed directly at Leibniz

and the Leibnizians, for the original priority dispute over the in-vention of the calculus had after 1710 burgeoned into a full scalewar over natural philosophy.26 When Newton asserted in the Gen-eral Scholium in 1713 that "Hypotheses are not to be regarded in

experimental Philosophy" he intended to eliminate all objectionsto his theory of gravity, like those of Leibniz, that were not basedon experiment and observation or Phaenomena.

Roughly at the same time that Newton had written his draft to

query 31 and announced that inner sensations are phenomena, he

drafted a number of definitions of this crucial term for his con-templated new edition of the Principia. J. E. McGuire publishedthese manuscripts in 1966 and dated them to 1716 as part of New-ton's campaign against Leibniz. McGuire was primarily concernedwith Newton's concept of body, but in the same set of drafts New-ton also attempted to define his concept of phaenomena. In the

following draft he makes explicit what is only implicit in his draftfor query 31:

24 Newton, Principia, 943. In the third edition he changed "experimental phi-losophy" to "natural philosophy."

25 MS Add. 3970, f. 619v; the square brackets are mine.26 For a complete account of the dispute between Newton and Leibniz, see

Hall, Philosophers at War, especially ch. 8, "The Philosophical Debate."



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200 ALAN E. SHAPIRO

Definition I

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

proper, 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. Heap-parently thought better of it, for it does not appear in the revised

queries of the 1717 edition of the Opticks or the third edition ofthe 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 whathe 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 matterwhich 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 notphenomena, and subject to none of the senses, have no place in experimen-tal philosophy.2"

These imaginary hypotheses clearly differ from the sort of hypoth-eses that Newton pursued in the queries of the Opticks, such as

light 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's

27J. E. McGuire, "Body and Void and Newton's De mundi systemate: Some NewSources," Archive for History of Exact Sciences 3 (1966), 206-48, on 238-9; MS Add.3965, f. 422v. I have edited McGuire's translations since he put all changes-bothadditions and deletions-in italics.

28 McGuire, "Body and Void, " 220-1; MS Add. 3965, f. 422r. The single open-ing bracket is Newton's.



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reason for adding it. Leibniz publicly, but mildly, criticized New-

ton's ideas about attraction in his Essais de Theodicee (1710), but itis not clear when Newton saw this.29 What certainly did catch hisattention was a letter that Leibniz wrote to Nicolas Hartsoeker in

February 1711 criticizing his physical theories. This letter, togetherwith Hartsoeker's response, had been published on the Continent,but when Newton saw the translation published in the Memoirs ofLiterature n 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. 30This is just ten days before he senthis final changes to the General Scholium to Cotes on 28 March1713. These changes (which are indicated by angle brackets in the

quotation 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 b-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 alreadybeen composed and sent to Cotes on 2 March; and that it wasLeibniz's letter to Hartsoeker that prompted Newton to resurrectthe term "experimental philosophy," which he had tentatively usedin the Latin translation of the Opticks before deciding to remainwith the more traditional "natural philosophy." As we shall see,Leibniz's remarks are also responsible for the concluding section

on natural philosophy in Newton's review of the Commercium episto-licum in 1715.

29"Newton knew of the Theodice 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 paper

call'd Memoirs of Literature .... In ye 18th Number ... published May 5th, 1712 Youwill find a very extraordinary Letter of Mr. Leibnitz to Mr. Hartsoeker which willconfirm what I have said "; Newton, Correspondence, 5: 392-3.

31 Ibid., 302, n. 8. We should recall that at the same time Newton also addedthe statement that to discourse about God belongs to experimental philosophy;see note 2 above.



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202 ALAN E. SHAPIRO

In his letter to Hartsoeker Leibniz did not mention Newton byname, 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 wayevery 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 thenidentified Newton's concept of gravity, which "is performed with-out any Mechanism, by a simple primitive Quality, or by a Law ofGod" 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...."" 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 inwhich 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 he

form'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. The

only issue of conjecture for Newton was whether God created the

particles, not whether they existed.

32 "Philosophical Letters Written by M. Leibniz and M. Hartsoeker, " Memoirs ofLiterature 2, no. 18 (5 May 1712), 137-43, on 139.33 Ibid.34 Opticks, 400. Although the second English edition that I cite here differs in

a number of places from the Latin translation that Leibniz saw, they do not affectLeibniz's interpretation and criticism.



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In his draft reply Newton argued, much as he did in the Gen-

eral Scholium, that the existence of gravity has "been proved bymathematical 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 hardness

requires a mechanical cause by expanding it to include all the

universal qualities,So then gravity & hardness must go for unreasonable occult qualitys unlessthey can be explained mechanically. And why may not the same be said ofthe 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 bythe will of God from the beginning of the creation & perfectly uncapable ofbeing explained mechanically, & so may be the hardness of primitive parti-cles of bodies.36

I will examine Newton'sargument

for the existence of universal

qualities later, but we should note that he has attempted to shiftthe issue to less problematic qualities such as inertia and exten-sion, and then rather tentatively argues that hardness also "maybe" a universal quality. One reason that Newton may not have sentthis 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 conceptof

gravitywas "a fiction invented to

supportan 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. IfI 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 Leibnizwho was advocating a hypothetical philosophy. On 28 March New-ton instructed Cotes to make the following addition (in anglebrackets) to the General Scholium:

35 Newton, Correspondence, 5: 299.36 Ibid., 300.



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204 ALAN E. SHAPIRO

and hypotheses, whether metaphysical or physical, or based on occult quali-

ties, or mechanical, 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 theRoyal 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 also

anonymously reviewed it in the Philosophical Transactions in Janu-ary 1715. Most of this long review is devoted to mathematics, butat 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 be

proved 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 Uncertainties

alone.""3 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

37 Newton, Principia, 943; see also note 2 above.38 [Newton], "An Account of the Commercium epistolicum," 222.39 Ibid., 223.



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Phaenomena, and stops where such Evidence is wanting; the other is taken

up 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 Gravitybe Mechanical or not Mechanical: the other that it is a perpetual Miracle ifit 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 itasserts nothing more than can be proved by Experiments, and we cannot yetprove by Experiments that all the Phaenomena in Nature can be solved bymeer 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 [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."41This 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 hisMicrographia, for example, spoke of "the real, the mechanical, the

experimental Philosophy."43 The experimental philosophy-as itsname declares-was always associated with experiment and obser-vation. 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. 586v42 Charles Webster, "Henry Power's Experimental Philosophy," Ambix 14

(1967), 150-178, in n. 66.

43Robert Hooke, Micrographia: Or Some Physiological Descriptions of Minute BodiesMade by Magnifying Glasses, with Observations and Inquiries Thereupon (London, 1665;facsimile rpt.: Bruxelles, 1966), a[3].



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206 ALAN E. SHAPIRO

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 againstJohn Keill's criticism. "We are not now in a Cartesian Vortex," hewrote, "where fancy and contrivance can introduce and hinder anyeffect 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 and

experimental 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 thatWhiston 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

44William 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 NewTheory of the Earth (Oxford, 1698).

45John Harrison, The Library of Isaac Newton (Cambridge, 1978), no. 169246 On Newton's relation to the mechanical philosophy see Alan Gabbey, "New-

ton, Active Powers, and the Mechanical Philosophy," in Cambridge Companion toNewton, ed. Cohen and Smith, 329-57.



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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.47Mathematization also was not widely seen as an essential aspect ofthe mechanical philosophy. Although the mechanical philosophywas 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 Nature

from 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 and

Boyle.From the beginning of his career Newton operated within the

framework of the mechanical philosophy, but he never adhered

strictly to all of its elements, except for the corpuscular nature ofmatter 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), butrather more restricted terms like "mechanical hypotheses" or "me-chanical causes."'5 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 TheWorks 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 PhilosophicalQuestions: 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, : 174; and his letter to Huygens on 3 April1673, 264. In a draft of his reply to Hooke Newton referred to the "mechanicallcauses" of properties, MS Add. 3970. f. 433v. For "mechanical explanations" and"mechanism" see query 28, Opticks, 369; and for "mechanical sciences" (mecha-nicarum scientiarum) see "De Gravitatione," in Newton, Unpublished Scientific Papersof Isaac Newton. A Selection from the Portsmouth Collection in the University Library,Cambridge, ed. A. Rupert Hall and Marie Boas Hall (Cambridge, 1962), 99, 131.



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208 ALAN E. SHAPIRO

"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 the

holy grail of the mechanical philosophy, and serious mechanicalphilosophers-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 was

searching 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 an

empirical 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 gravityshows just how much the term had changed.

That the "experimental philosophy" could serve as a useful wea-

pon against Cartesians and Leibnizian mechanists becomes furtherevident 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, butCotes 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 mechanical

philosophers who opposed the first, but, Cotes tells us, they have

drifted off to speculative "dreams" by imagining invisible particlesand fluids and are left with a "romance."

See also Gabbey, "Newton, Active Powers, and the Mechanical Philosophy," 338-9.



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There remains then the third group, namely, those who profess experimen-

tal philosophy. Although they too hold that the causes of all things are to bederived from the simplest possible principles [i.e., the mechanical philoso-phy], they assume nothing as a principle that has not yet been thoroughlyproved from phenomena. They do not contrive hypotheses, nor do theyadmit them into natural science otherwise than as questions whose truth

may be discussed. Therefore they proceed by a twofold method, analytic and

synthetic. ... This is that incomparably best way of philosophizing which ourmost celebrated author thought should be justly embraced in preference toall others. This alone he judged worthy of being cultivated and enriched bythe expenditure of his labor.51

Cotes thuspresents

Newton with his"experimental philosophy"

as

reforming and transcending the mechanical philosophy.A rhetorical device such as the "experimental philosophy" was

aimed as much at the wider audience of readers to persuade themof the justness of Newton's cause as at Leibniz himself. Butwhat was Leibniz's response to "experimental philosophy"? In 1671Leibniz had identified with "experimental philosophers" (philo-sophis experimentalibus), and he was not later prepared to abandonthat identification to Newton.52 In November 1715, after Newton's

perorationin

the reviewof

the Commercium epistolicum,Leibniz

added a postscript intended for Newton to a letter to AntonioConti, who was serving as an intermediary. He declared his ap-proval of deducing things from phenomena without invoking hy-potheses, but he still insisted that hypotheses had a role to play innatural philosophy:

when the data are insufficient, it is permitted (as one does sometimes in

deciphering) to imagine hypotheses, and if they are successful, they may beheld provisionally until new experiments provide us new data, which Baconcalls crucial experiments, or choosing between the hypotheses. ...I am stronglyin favor of experimental philosophy, but Mr. Newton departs very far from

51 Newton, Principia, 385-6; I have modified the translation of the first sen-tence.

52 Gottfried Wilhelm Leibniz, "Summa hypotheseos physicae novae," SiimtlicheSchriften und Briefe, ed., Deutsche Akademie der Wissenschaften zu Berlin (Berlin,1966), Ser. 6, 2: 340. Leibniz included mechanics, chemists, and physicians (me-chanicos, chemicos, medicos) amongst experimental philosophers. Twenty five yearslater Paolo Boccone referred to "botanists and students of experimental philoso-phy (filosofia sperimentale)," Museo di piante rare della Sicilia, Malta, Corsica, Italia,

Piemonte, e Germania (Venice, 1697), 1; see also 4. Boccone's inclusion of botanistswith experimental philosophers and Leibniz's broad group suggest that "experi-mental philosophy" had a more inclusive meaning on the Continent than in Eng-land. A study of the term "experimental philosophy" in England and on theContinent in the twenty-five years on either side of 1700 could prove to be valu-able.



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210 ALAN E. SHAPIRO

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 are

nothingmore then

imaginations, conjectures,&

suspicions&

ougtnot to be

propounded as Truths or Opinions nor admitted into Philosophy as suchuntil they are verified & established by experiments. And if you consider his

Philosophy 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 February1716 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 apparentlyjudged to be fruitless.56

The Meaning of 'Experimental Philosophy'

We are now in a position to clarify what Newton meant by his

enigmatic statement in the General Scholium that "in this experi-

55 Newton, Correspondence, : 252; the phrases in italics are in Latin, while the

body of the letter is in French.54 Alexandre Koyre and I. Bernard Cohen, "Newton & the Leibniz-Clarke

Correspondence 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: 285-6.56 Leibniz to Conti, 29 March 1716, ibid., 307. Newton chose not to reply to

Leibniz through Conti (because of Leibniz's "insolent" behavior), but around

May 1716 he composed some "Observations upon the Preceding Epistle" that he

privately circulated and then arranged to have published after Leibniz's death inNovember 1716; ibid., 349, n. 1.



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mental philosophy, propositions are deduced from the phenom-ena and are made general by induction." There is a large litera-ture by philosophers, starting with Pierre Duhem in the beginningof last century, on Newton's methodology in the Principia and hisformulation of it in the General Scholium. Philosophers have

largely been critical of the logic of Newton's method, but more

recently there has been growing support for "deduction from the

phenomena." My aim is not to enter into this debate, but ratherto understand what Newton actually meant by "deduction" and "in-duction."57

Since Newton defined his "experimental philosophy" and elabo-rated its meaning in a number of documents in this period, manyof which I have already presented, a useful way to proceed in clari-

fying his meaning is to compare the different statements while

bearing in mind their different contexts. It will be helpful if I state

my conclusion at the beginning, namely, I believe that Newton was

using the words "deduce" and "induction" in their general mean-

ing and not in any technical, philosophical sense, although he was

certainly familiar with those meanings. As an undergraduate he

had studied logic, and from his contemporary reading he knew ofvarious meanings of "induction" such as mathematical and Ba-conian induction. The Oxford English Dictionary gives as a meaningof "deduce": "To derive or draw as a conclusion from somethingalready known or assumed; to derive by a process of reasoning orinference; to infer"; and for "induction": "The bringing forward,adducing, or enumerating of a number of separate facts, particu-lars, etc., esp. for the purpose of proving a general statement."58

In a draft of his letter to Cotes on 28 March 1713, in which

Newton included his final changes to the General Scholium, hecommented on Cotes' sketch of his preface:

I like your designe of adding something more particularly concerning themanner of Philosophizing made use of in the Principia & wherein it differs

57 In contemporary philosophy "deduction from the phenomena" is alsoknown as "eliminative induction" and "demonstrative induction." Although JohnWorrall considers the philosophical problem from the point of optics rather thanmechanics, he provides a useful summary of the problem and the literature fromthe "classical" works of Duhem, Popper, and Lakatos to recent reconsiderations

by John Dorling and John Norton; "The Scope, Limits and Distinctiveness of theMethod of 'Deduction from the Phenomena': Some Lessons from Newton's 'De-monstrations' in Optics," British Journal for the Philosophy of Science 51 (2000),45-80. On Newton's use of induction in the Principia see E. B. Davies, "The New-tonian Myth," Studies in History and Philosophy of Science 34 (2003), 763-80.

58 Oxford English Dictionary Online, 2nd edition, 1989.



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212 ALAN E. SHAPIRO

from the method of others, vizt by deducing things mathematically from

principles derived from Phaenomena by Induction. These Principles are the3 laws of motion. And these Laws in being deduced from Phaenomena byInduction & 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 heavenlybodies.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 in

turn derived from phenomena by induction. He even specifies theprinciples as the Laws of Motion and also adds that he had to applyfurther 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 have

argued, 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 as

general when ye consent is general without exception, tho the

generality cannot be demonstrated a priori."61 We should note thathe now "argues" from phenomena. And rather than appealing to

induction, he more specifically explains that it is by "the consentof phaenomena" that conclusions are rendered general. By this he

presumably 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 Optickswhen he first set forth his methods of analysis (resolution) and

synthesis. He explained that,

The method of Resolution consists in trying experiments & considering all

the Phaenomena of nature relating to the subject in hand & drawing con-

59 Newton, Correspondence, : 39860 Ibid., 299.61 Ibid., 399.



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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 does

aptly 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 obser-

vations, but rather ordinary occurrences of nature and the arts,such as planets moving in their orbits, spinning hoops, and the

changing 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

heterogeneousthat it is

apparentthat he

had 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 the

planets 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 ho

newton's (experimental philosophy).pdf

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