ernan mcmullin - conceptions of science in the scientific revolution

Reappraisals of the

Scientific Revolution

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26 l\tvid C. Lindberg

by A. Rupert Hall, In Itit. 72 (1981):90-1; also Butterfield's "History of Sdtnce and the Study of History," Harvard Library Bulletin, 13 (1959):329-47, in which Butterfield discusses the influence of Paul Tannery on the practice of the history of science; and A. Rupert Hall, "On Whiggism," History of Science, 21 (1983):45-59, where Hall touches on Butterfield's shifting historiographic sensibilities.

79 Butterfield, Origins of Modern Science, p. 1. 80 Butterfield, The Origins of Modern Science, rev. ed. (London: Bell, 1957),

pp. 15-16. 81 Ibid., Chap. 11. 82 Others who must be taken into account in any full discussion of the idealist

program in the twentieth century are Ernst Cassirer, Das Erkenntnisproblem in der Philosophic und Wissenschaft der neueren Zeit, 2 vols. (Berlin: B. Cas-sirer, 1906-1907); Emile Meyerson, Identite el realite (Paris: F. Alcan, 1908); Heldne Metzger, Les doctrines chimiques en France au debut du XVII' siecle a la fin du XVIII' siicle (Paris: Presses Universitaires de France, 1923), and Attraction universale et religion naturelle chez quelques commentateurs anglais de Newton (Paris: Hermann, 1938); Robert Lenoble, Mersenne, ou la naissance du micanisme (Paris: Vrin, 1943); and R. G. Collingwood, The Idea of Nature (Oxford: Oxford University Press [Clarendon Press], 1945).

83 See A. R. Hall's recollections, /sis, 75 (1984):22-5; Thomas S. Kuhn's rec-ollections in the same issue, p. 30; I. Bernard Cohen's "Commemoration" of Alexandre Koyr6, /sis, 57 (1966):157-65; and Richard S. Westfall, The Construction of Modern Science: Mechanisms and Mechanics (New York: Wiley, 1971), pp. 160-1.

84 For a survey of some of these currents, see the informative article by Arnold Thackray, "History of Science," in A Guide to the Culture of Science, Technology, and Medicine, ed. Paul T. Durbin (New York: Free Press, 1980), pp. 7-28.

85 For illustrations of this social history, see Steven Shapin and Simon Schaffer, Leviathan and the Air-Pump: Hobbes, Boyle, and the Experimental Life (Princeton: Princeton University Press, 1985), and Margaret C. Ja-cob, The Cultural Meaning of the Scientific Revolution (New York: Knopf, 1988). See also the interesting historiographic reflections by John Pick-stone, Roy Porter, Simon Schaffer, Steven Shapin, and Robert M. Young, under the title "What is the History of Science?", History To-day, 35 (1985):46-52.

Conceptions of science in the Scientific Revolution

E R N A N M c M U L L I N

That the state of knowledge is not prosperous nor greatly ad-vancing, and that a way must be opened for the human un-derstanding entirely different from any hitherto known, and other helps provided, in order that the mind may exercise over the nature of things the authority which properly be-longs to it.1

The sonorous lines with which Bacon's Great Instauration opens re-mind us of the ambition shared by so many in those heady days to make all things new, in the realm of knowledge as in nearly .all else. Bacon insists that the older learning has been quite unable to give any real insight into nature:

The logic which is received, though it be very properly ap-plied to civil business and to those arts which rest in dis-course and opinion, is not nearly subtle enough to deal with nature; and in attempting what it cannot master, has done more to establish and perpetuate error than to open the way to truth.2

A new approach to the knowledge of nature is called for, and this is what Bacon proposes to provide. And so, a few years later, does Descartes. By the time Locke writes his Essay Concerning Human Un-derstanding, half a century further on, he can assume that the change has already occurred:

He that shall consider how little general maxims, precarious principles and hypotheses laid down at pleasure, have pro-moted true knowledge or helped to satisfy the inquiries of rational men after real improvements; how little, I say, the setting out at the end has, for many ages together, advanced men's progress towards the knowledge of natural philosophy; will think we have reason to thank those who in this latter age have taken another course, and have trod out to us,

28 Ertiati McMullin Conceptions of science in the Scientific Revolution 29

though not an easier way to learned ignorance, yet a surer way to profitable knowledge.3

In this essay, 1 want to reflect on this "other course." It was not quite so well defined a " w a y " as Locke implies. My concern will be with the quality of knowledge the "new sciences" were supposed to provide. What conceptions of science did the "new scientists" and those who reflected on their work develop? And how did they come by these conceptions? Most discussions of methodology in the Sci-entific Revolution focus on the methods themselves: on the new im-portance of experiment, on mathematical idealization, and so forth.4

Though I will touch on these, my interest will lie much more in the "metamethodological" issue: What kind of knowledge were the new techniques supposed to deliver? This restriction of focus may help to make an otherwise unmanageably large topic somewhat more tract-able.5 And it could be argued that the shifts that gradually occurred at this deep level over the course of the seventeenth century were those that most clearly, in retrospect, mark this century: a s the age of scientific revolution.

In an investigation of this sort, several different kinds of questions can be put to the historical material. One might ask what the actors themselves thought they were doing, what sort of knowledge they believed their "new science" gave them. Or one might, from a later vantage point, ask how effective (consistent, coherent) their concep-tion of science in fact was.6 We shall be interested here in both ques-tions, but in the former rather more than the latter. Our main concern is with the changes in the notion of natural science that occurred in the seventeenth century. What quality of knowledge did the inves-tigators think they could attain, and how was this knowledge attained? To discover this we have to look at what scientists and philosophers - the two groups were just then beginning to separate - had to say about the achievements and limitations of the new inquiries into nature.

In the Greek tradition, the conception of science employed in nat-ural philosophy did not originate from within the discipline itself; it did not take its shape from the actual achievements of the day in such fields as astronomy, mechanics, or biology. Instead, the notion of episteme was rooted in metaphysics and theory of knowledge and was held up as an ideal to be aimed for. To reach "the eternal and the necessary" was the goal, and as a goal it seemed to need no elaborate justification. The discrepancy between the notion of science outlined by Aristotle in his Posterior Analytics and the accounts of nature given by him in his extensive biological works, as well as in the Physics and On the Heavens, has long presented a problem to historians; there is

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also enabled philosophers to separate off three highly idealized con-ceptions of science, each of which is characterized by an emphasis on one of Peirce's three types of inference at the expense of the other two.10 All three of them have been attributed to various among the authors we are about to survey. Hence it may be worthwhile to de-scribe them briefly, before getting down to the historical task proper.

Deductivism

One begins from "axioms," "principles," propositions that are seen to be true in their own right without need of recourse to any other evidence, and then proceeds by deduction to derive further propo-sitions. Since deduction is entirely rule governed and assumed to be capable, without fail, of transferring truth from one set of propositions to another, the only problem is to find secure starting points. Since these latter will have to stand in their own right, they will have to be seen to be true in their own terms. That is, an understanding of the concepts employed suffices to assure one of the truth of the premises. (The labels "intuitionism" or "conceptualism," sometimes used for this model of science, derive from this latter feature.) To say that the premises must be "self-evident" could be misleading, if this is taken to imply that they are obvious. It may require a great deal of experience or of careful reflection to assure oneself of a necessary relation be-tween concepts.

Aristotle's notion of demonstration provides the primary example of a deductivist conception of science. The logic is that of the syllogism; the premises are to be anchored in an epagoge, an intuitive insight based on an experience of the natures concerned (an induction of a limited and special sort). The deduction mirrors the order of inherence of properties in essence.

Inductivism

One begins from the observation of singulars, noting the regular co-occurrence of certain features, and generalizes to a lawlike statement relating these features to one another in a stable way. The inference takes the form of generalization. One moves to a claim about a class as a whole from the evidence of a sample. Regular co-occurrence is taken to be a sufficient (and perhaps, indeed, the only legitimate) basis for asserting a "lawlike" relationship. Science itself is taken to consist exclusively of " laws" arrived at in this way. Induction will work only with observable features, and so an exclusively inductive science cannot contain terms referring to unobservables.

Conceptions of science in the Scientific Revolution 31

Mill, in his System of Logic, comes closest perhaps to the inductivist ideal. He is concerned, in particular, to trace causal relationships, where a "cause" is taken to be an observable event, linked in terms of constant co-occurrence with its effects. The methods of same-ness, difference, and concomitant variation allow one to test the au-thenticity of the observed co-occurrence as an index of genuine lawlikeness.

Hypothetico-deductivism

One tests a hypothesis by the observational consequences deduced from it. The inference here lies not in the derivation of the original hypothesis (which may have been arrived at in any manner one chooses) but in the manner of testing the hypothesis by the number and quality of the verified consequences to which it gives rise. Ver-ification (or justification) moves backward from consequence to ex-planatory hypothesis and thus can never be conclusive, except when it can be shown that no other hypothesis can account for the evidence. As a result, a hypothetico-deductive argument can ordinarily yield only a greater or lesser degree of likelihood.

It would, of course, be generally conceded that scientists make extensive use of this method. But the logical positivists tended to make an " - ism" of the method by treating it, sometimes, as the single model of scientific inference. In his methodology of "conjecture and refutation," Karl Popper was even more explicit in this regard than the positivists had been, since he entirely rejected induction (or so he said) and ruled out also the deductivist assumptions of what he called "essentialism." A conjecture or hypothesis is to be tested ex-clusively by the empirical consequences derivable from it; no other criterion is to carry epistemic weight. Furthermore, even these em-pirical consequences can be given only negative weight; that is, they may be used to falsify, but not to verify, or even to render probable.

I have deliberately used the label "hypothetico-deductive" here, rather than Peirce's term "retroductive," because Peirce (like William Whewell before him) went to some pains to show that the hypothetical arguments characteristic of science are much richer and more complex than the mere testing of hypotheses by the empirical correctness of the consequences drawn would suggest. I will use the term "retro-ductive" when I want to bring out the fact that effect-to-cause rea-soning encounters problems not only because of the potential multiplicity of possible causes but also, for example, because the lan-guage of the (observed) effect may not suffice to describe an unob-served cause.

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The reader, at this point, may be fretting about the danger of im-posing a sophisticated modern set of distinctions upon a historical situation that does not support it. In point of fact, my intention is in part to underline this very danger. Historians of science have quite often characterized the Scientific Revolution in straightforwardly in-ductivist terms. Alternatively, some have thought that what mattered was a steady turn to the hypothetico-deductive method. And there was, until recently, fairly general agreement that Descartes and his followers were essentially deductivist in their ambitions. We shall see that "pure-case" attributions of this sort must be regarded with sus-picion. A reappraisal of theories of science in the seventeenth century can safely presuppose this.

Descartes: Precursor of the hypothetico-deductive method?

In his youthful work, the Regulae (1628), left unfinished and unpub-lished, Descartes came closer, perhaps, than did anyone else of that time to a deductivist account of knowledge generally, including nat-ural knowledge. Rule II lays down that "only those objects should engage our attention, to the sure and indubitable knowledge of which our mental powers seem to be adequate," 1 1 and this is glossed: "Sci-ence in its entirety is true and evident cognition."1 2 Merely "probable" knowledge is to be rejected; we are to "make it a rule to trust only what is completely known and incapable of being doubted. " Indeed, " w e should busy ourselves with no object about which we cannot attain a certitude equal to that of the demonstrations of arithmetic and geometry . "

Only two mental operations, intuition and deduction, are to be trusted in this task; together, they can accomplish complete dem-onstration (rule III).13 Intuition is the anchor of the process; it is " t h e undoubting conception of an unclouded and attentive mind and springs from the light of reason a lone . " And it is brought to bear on the relationships of simple natures as these are conveyed in clear and distinct ideas.14 Though Descartes is not very specific in describing the process, it would seem that these ideas are themselves to be derived from experience.1 5 He is critical of those who "neglect ex-perience," supposing that "truth will spring from their heads" (rule V).16 Someone who wants to understand the transmission of force (he says) ought not rely on obscure effects like magnetism; rather, they should take their start from the motions of bodies, "be -cause in this domain there is nothing more accessible to s e n s e " (rule IX).17 What he is proposing is, then, systematic deduction from an intuitively grasped empirical starting point; in some respects, at least,


he has not moved far from the conception of science in the Posterior Analytics.18

In the ten years separating the Regulae from the publication of the Discourse on Method (1637), Descartes worked on numerous problems in natural science and began the construction of an ambitious cos-mology (Le monde, interrupted when the news of Galileo's trial reached him). This may explain the reservations that make their appearance in the Discourse in regard to the deductivist program.1 9 In Part 5, he imagines what would happen if God were to create a world and communicate random motion to it. The matter of this world can al-ready be described; indeed, " i t seems to me that nothing in the world could be clearer or more intelligible, excepting what has just been said of God and the soul ." 2 0 Furthermore, the laws according to which this matter must move can also be determined in advance:

I pointed out what the laws of Nature are and, without rest-ing my reasons on any other principle than the infinite perfec-tions of God, I tried to demonstrate all those of which one could have any doubt and to show that they are of such a na-ture that even if God had created other worlds, He could not have created any in which these laws would fail to be ob-served. After that, I showed how the greatest part of the mat-ter of which this chaos is constituted must, in accordance with these laws, dispose and arrange itself in such a fashion as to render it similar to our heavens; and how meantime some of its parts must form an earth, some planets and comets, and some a sun and fixed stars.21

This is an extraordinarily ambitious deductivist claim, and it is hardly necessary to look at Le monde to discover that Descartes came nowhere near to making good on it. He went even farther. He claimed to be able to show " h o w the mountains, seas, fountains and rivers, could naturally be formed in it[the earth], how the metals came to be in the mines and the plants to grow in the fields; and generally how all bodies, called mixed or composite, might arise." 2 2

We can recognize here the sort of evolutionary cosmogony based on mechanics alone to which we are accustomed today. If the universe began in time and came to be through natural laws, then a cosmogony of this sort was the only possible one, given Descartes's deductivist schema and the reductionism to which it committed him.2 1 He con-fesses that he cannot yet see a way to explain animal bodies in this manner, by "demonstrating effects from causes, and showing from what beginnings and in what fashion Nature must produce them." 2 4

In Part 6 of the Discourse, written three years after he set Le monde aside, in order to introduce a set of scientific treatises (Optics, Mete-

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orology, Geometry), a significant reservation makes its appearance. First, he restates the order of his inquiry. One must search first for the principles of "everything that is or can be in the world, without considering anything that might accomplish this end but God himself . . . or deriving them from any source excepting from certain germs of truths which are naturally existent in our souls."2 5

This is perhaps the farthest from empiricism that Descartes gets in any part of his writings. Not only is science to proceed from first principles, but these principles themselves rest not so much upon specific experiences as upon innate "germs of t ruth." And from these principles he goes on to claim (as he had already done in Part 5) to be able to proceed in a purely deductive way to the "heavens , stars, an earth, and even on the earth, water, air, fire, the minerals and some other such things." 2 6

But now, the limits appear at last. In attempting to explain more particular kinds of things on earth, a multiplicity of alternatives opens up, so that

I did not think it was possible for the human mind to distin-guish the forms or species of bodies which are on the earth from an infinitude of others which might have been so if it had been the will of God to place them t h e r e , . . . if it were not that we arrive at the causes by the effects, and avail ourselves of many particular experiences.... The power of nature is so ample and so vast, and these principles are so simple and so general, that I observed hardly any particular effect such that I could not at once recognize that it might be deduced from the principles in many different ways.

This sounds deductivist. But, of course, what he is saying is that the same effect can be produced by many different causes, all of them compatible with the first principles of the science. So deduction alone will not serve. The only expedient open at this point, he concludes, is " to try to find experiences of such a kind that their occurrence would not be the same if it were to be explained in one of the ways as it would be if it were explained in the other." 2 7

These texts have been quoted so often that it may seem an apology ought be given for repeating them yet again. Yet they need careful scrutiny. They are certainly incompatible with a straightforward de-ductivist interpretation. But do they imply that Descartes is advocat-ing a hypothetico-deductive method? Only in a very limited sense, at best. For one thing, his mechanics is still as deductivist as ever; a few pages later, he reminds the reader that the foundations of his physics "are nearly all so evident that it is only necessary to under-stand them in order to accept t h e m . " Indeed, he is still convinced

Conceptions of science in the Scientific Revolution M

that there is not one that he cannot "demonstrate . " 2 8 So there is no change in regard to the axiomatic-deductive character of his basic science, namely, mechanics. The problem does not arise until one asks about particular contingent natures of the kinds found around us on earth. This distinction between mechanics and those sciences where one has to infer from observed effects to hidden causes is, as we shall see, crucial to an understanding of many of the declarations on method of this period, and not just those of Descartes.

It is possible, he supposes, to infer merely from the general laws of matter and motion that an earth will form out of an original chaos. But that is as far as the unaided deduction will go. The more specific sorts of natures can be discovered only by working back from effects to causes, that is, by asking what sorts of causes would be necessary to produce these effects. And when Descartes does this, he realizes that the effects we observe could be brought about by many different sorts of natures consistently with the general laws of mechanics. (A " n a t u r e " is now a configuration of particles whose structure can be inferred only indirectly from the effects it produces.)

In the later Cartesian tradition, this manner of distinguishing be-tween the basic deductivist science of mechanics and a "phys ics" that deals with the detailed configurations of matter responsible for the observed properties of familiar bodies came to be more or less taken for granted. Pierre-Sylvain Regis, for example, in the introduction to the section devoted to physics in his Systtme de philosophie (1690), distinguishes between a physical body "composed of many insensible parts, shaped and arranged in such a way that one can from their configuration and arrangement explain all of the properties that de-pend on t h e m " (the example he gives is a diamond), and a mechanical body "composed of sensible parts, coarse and tangible, which because they are linked together, can by their shape and situation increase or diminish the movement of bodies to which the mechanical body is applied" (the example here is a clock).29

Regis goes on then to emphasize that "speculative physics , " where one reasons from effects back to causes, can be regarded as no more than probable, that "nothing of the demonstrative belongs to i t . " Yet "uncertain as it i s , " it is still in " t h e front ranks" of human knowl-edge.3 0 It is uncertain precisely because in "physico-mechanical" bod-ies one has to have recourse to hypotheses to account for effects that are produced by unobservable causes, the minute parts on which the properties of the whole depend. So that (echoing Aristotle in another context), it would be as unreasonable, he asserts, to seek for dem-onstrations in "phys ics " as it would be to content oneself with prob-ability in mathematics. The hypotheses in "phys ics " must, of course,

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be compatible with the "first truths" regarding quantity, figure, and movement at the summit of his system; these latter are taken to be known with certainty.

Descartes could not bring himself to go so far. The admission of a hypothetical status for the lowest-level claims about natures clearly worried him. He advises the readers of the Optics and the Meteorology not to take offense at his reliance on "suppositions":

For it appears to me that the reasonings are so mutually inter-woven, that as the later ones are demonstrated by the earlier, which are their causes, the earlier are reciprocally demon-strated by the later, which are their effects. And it must not be imagined that in this I commit the fallacy which logicians call circularity, for since experience renders most of these ef-fects quite certain, the causes from which I deduce them serve not so much to prove them as to explain them; whereas on the contrary, it is the causes that are proved by their effects.31

This construal of the linked ascent to causes and descent to effects as somehow demonstrative has its origins in the Posterior Analytics.32

Aristotle distinguished between knowledge of the reasoned fact which proceeds from cause to effect, and knowledge of the fact which works from effect back to cause, and implied that the latter could somehow sustain the former in cases where the subject was not di-rectly known. (The two examples he gave were the steady light of planets, caused by the planets' nearness to the earth, and the waxing and waning of the moon, caused by its spherical shape). The validity of this way of reasoning depended, however, on the convertibility of the middle term of the syllogism involved, or as we would say, on the knowledge that the hypothesis to be demonstrated is the only one that suffices to explain the effects. And this last, of course, is precisely what we do not ordinarily know in the standard case of hypothetical explanation in science. In the passage from the Discourse just cited, the warrant goes from experienced effect to unexperienced cause - that is, in the opposite direction to deduction. Such inference is hypothetical, unless it can be shown that the cause postulated is the only possible one; and even then, the proof is not a deducti-vist one.

Elaborate attempts were made in the later Aristotelian tradition to patch up this all-important gap in the theory of demonstration. As we have already noted, discussions of regressus (as the combined ascent-and-descent argument was called) were especially common in the Paduan Aristotelianism of the sixteenth century; Jacopo Zabarella is remembered for the labor he devoted to showing how the success of the explanatory descent could warrant the probative ascent, in


something approaching a demonstrative manner. Descartes must have been aware of at least the outlines of the regressus argument, since it was a staple of the commentaries on the Posterior Analytics that shaped the teaching of methodology in his time.

But, of course, he could not show that " the causes are proved by their effects," any more than his predecessors had been able to do. In the year after the Discourse appeared, he came back to this issue again and again, prodded by several of his correspondents. In a letter to Plempius, concerning some objections made by Fromondus (Libert Froidmont) to the manner of arguing in the Discourse, he tries to show, for example, that he can prove that the constituent particles of water must be like little eels, whereas the particles of oil must have "branches," as trees do.33 He gives four indicia, "indications," such as that water dries off cloth more rapidly than oil does (the particles of oil grasp those of the cloth) and concludes: "Although each of these, when considered separately, can only persuade in a probable way, when taken together they have the force of demonstration." And he remarks, offhand, that if he had gone on to demonstrate everything properly he would have wearied his readers' eyes. (In the Discourse, the excuse was that although he could have demonstrated the hypothetical claims, he had refrained from doing so in order to prevent others from misapplying his system.)34

In a letter to Jean-Baptiste Morin, shortly after, he tries a variation on the same argument. Morin had said, by way of criticism, that it is easy to adjust a (hypothetical) cause to a known effect. Descartes responds:

While there are indeed many effects to which it is easy to ad-just different causes, one to the other, it is not always so easy to adjust one single cause to many effects, if it is not the ac-tual cause from which they proceed. Indeed, there are often effects which are such that to specify one cause from which they can clearly be deduced is sufficient to prove it to be their true cause. And I maintain that all of those of which I have spoken are of this sort.35

And he goes on to insist that once it is admitted that bodies consist of minute particles, "it is easy to demonstrate" what the shape of these particles has to be to account for the observed effects. His own success in accounting for "vision, salt, the winds, the clouds, the snow, thunder, the rainbow," by contrast with others who have at-tempted the same task, ought to suffice to persuade any attentive person that " the effects which I explain can have no other causes than those from which I deduce them." 3 6

Why was Descartes so eager, against all the odds, to insist on the

38 Ertiati McMullin Conceptions of science in the Scientific Revolution 39

certainty of his claims, even when they were arrived at by means of hypothetical reasoning? He leaves us in no doubt that one of his fundamental concerns is the overcoming of Pyrrhonist skepticism.37

The laborious step-by-step argument of the Meditations, which has so fascinated recent philosophers, was intended to secure the founda-tions of knowledge; on this metaphysical basis, a physics could then be built. Other thinkers of his day had attacked skepticism with equal fervor but had been willing to settle for less than certainty in regard to the natures of physical bodies. Pierre Gassendi, for example, con-structed an atomist doctrine in which knowledge of the actual con-figurations of the atoms was left vague; he seemed to think that the improvement of the magnifying power of the newly invented micro-scope would in time take care of the problem.38 Marin Mersenne restricted certainty to mathematics and to our knowledge of sensible effects, while questioning the possibility of any certain knowledge of the physical essences that are the causes of these effects.39 Descartes evidently thought that to assign only probability to our knowledge of physical causes, as Mersenne did, was to concede to skepticism. And so Descartes had to find ways of construing his claims about the minute constituents of bodies as certain, despite the hypothetical manner by which he arrived at these claims.

Mersenne was not persuaded. It seemed to him that the account of refraction in the Optics, with its metaphors of wine flowing through a vat of grapes and tennis balls passing through loosely woven cloth, could not possibly qualify as demonstration. Responding, Descartes insists that he has provided a demonstration here,

as much, at least, as it is possible to do so in that domain, without having first demonstrated the principles of physics by means of metaphysics (which I hope to do some day, but which has not yet been done), and to the extent that any other question of optics, of astronomy, or of any other matter which is not purely geometrical or arithmetical can ever be demonstrated. But to require of me geometrical demonstra-tions in a subject which depends on physics is to ask of me the impossible. If the proofs only of geometricians were to be called demonstrations, one would have to say that Archi-medes never demonstrated anything in m e c h a n i c s . . . . It is enough in such matters that the authors having presupposed certain things that are not clearly contrary to experience, have then gone on to speak consistently[conséquement] and with-out committing fallacies, even though their suppositions may not be exactly true.40

This is an interesting response, and it indicates a distinct weakening in his notion of demonstration. He calls on the precedent of Ar-

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been deduced from them: because most of the truths which remain to be discovered depend upon certain specific observa-tions, which will never be stumbled upon by chance but must be sought out with care and expense.46

So the principles alone are not enough; observations are needed, presumably in order to specify the effects that are to be explained in terms of hypothetical configurations. Does this affect the certainty of the result? In Part III, he heads a section: "That it can scarcely be possible that the causes from which all phenomena are clearly de-duced are false." The principles, at least, can be secured, not just by their self-evidence, but by the fact that they account for everything:

If the principles I use are very obvious, if I deduce nothing from them except by a mathematical sequence, and if what I thus deduce is in exact agreement with all natural phenom-ena, it seems that it would be an injustice to God to believe that the causes of the natural effects which we have thus dis-covered are false.47

But how about the hidden configurations? He goes on: We have not been able to determine in a similar way the size of the parts into which this (cosmic) matter is divided, nor at what speed they move, nor what circles they describe. For seeing that these parts could have been regulated by God in an infinity of diverse ways, experience alone should teach us which of all these ways He chose.48

This is certainly explicit enough. Yet he does not leave it there. These configurations of cosmic matter, postulated to explain astro-nomical phenomena, "seem to me sufficient for all the effects of this world to result from them in accordance with the laws of nature explained previously, as if they were the causes. And I do not think it possible to devise any simpler, more intelligible, or more probable principles than these."4<) Note the distinction again between the "laws of nature" (the truths that are prior and beyond question) and the configurations (vortices and the like). Yet even these last, the "prin-ciples" of explanation of the astronomical phenomena, are held to be the most probable hypotheses that could possibly be devised.

In Part IV, he faces the more troublesome question of the config-urations of the imperceptible particles that explain the properties of terrestrial bodies. What makes this project at least abstractly possible are two linked assumptions, first that the variety of properties of sensible bodies are "nothing other" in the bodies than "certain dis-positions of size, figure, and motion,"5 0 and second, that the same is true at all levels of size: "It is far better to judge of things which occur in tiny b o d i e s . . . on the model of those which our senses perceive


occurring in large bodies."51 The first, peculiarly Cartesian, assump-tion enabled him to reduce the language of physics to the (known) language of mathematics. The second assumption, which was made by every scientist of the century who reflected on the issue and would for Newton take on the status of a "rule of reasoning," made it pos-sible to extend microscopic science downward without having to worry about needing new concepts. (This assumption would go more or less unchallenged until the advent of quantum theory in our own century.) Without both of these assumptions, the Cartesian enterprise could not even have got under way.

But these are not nearly enough, or, as the author himself puts it, "I attribute determinate figures and sizes and movements to the im-perceptible particles of bodies, as if I had seen them." 52 To the obvious objection, his response is that he argues by analogy from the mac-roscopic to the microscopic. And such argument, he allows, can at best tell us what the hidden configurations "may be like." As long as the effects are correctly described, however, " w e shall do as well as if these were the true causes, even if the postulated configurations are false."53 This is an odd comment; it is as though the aim of his science were to be purely descriptive, were to be confined to getting the observed effects right.

His customary optimism reasserts itself, not quite consistently, in the very next paragraph, where he fears an "injury to truth" unless it be noted "how many things concerning the magnet, fire, and the fabric of the entire world have been deduced here from so few prin-ciples," thus allowing one to conclude that "it could scarcely have occurred that so many things should be consistent with one another, if they were false."54 It is the first principles, of course, that he is defending here, not the hypotheses in regard to specific natures. And, indeed, he strengthens his claim about the principles even further (ignoring the challenge to the more specific hypotheses) by going on to assert that they "seem more than morally certain." Without noting the distinction between the general principles and the specific ret-roductive hypotheses, he proposes that his "reasonings" should be regarded as "absolutely certain," on the grounds of their having been "deduced in a continuous series from the first and simplest principles of human knowledge."5 5 And on this cheerful but less than persuasive note, the Principles ends.

I have traced the convolutions of Descartes's thought on these is sues in some detail because they foreshadow so much of the later debates. But it is time to draw some conclusions. It is clear, first of all, that Descartes attributed a different status to the general principles of mechanics than he did to hypotheses explaining the properties ol

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specific kinds of bodies. The former rest upon the evidence of the ideas they employ. Whether or not to call them a priori depends on what one makes of his references to the "innate" character of the ideas themselves.56 He appears to discount the notion that they are strictly inborn in us; as "germs" they have to be elicited in some way by experience, but they do not depend for their content on any specific experiences. He frequently offers the fact that they serve so well to articulate such experiences as a sort of persuasive confirmation of their truth, but it is clear that for him, at least, they need no such additional support. On the other hand, hypotheses about the unob-servable particles and mechanisms postulated to explain macroscopic phenomena do depend directly upon experience, namely the expe-rience of those phenomena themselves. This is where the amassing of observations is needed. And the explanatory models rely on anal-ogies drawn from everyday experience.

The status attributed to the seven "impact rules" listed in the Prin-ciples is particularly revealing. In Cartesian mechanics, all action is brought about by contact, so that the laws of impact have the basic character that gravitational laws would later have for Newton. Des-cartes seems to suggest that the impact rules can be directly derived from the general principles of his mechanics. But he nowhere shows how this could be done, and it is clear that he would require some further assumptions in order to reach them deductively.57 The prob-lem is more serious than this: Several of the laws run contrary to our ordinary experience of impact and appear to be obviously false, as many of Descartes's correspondents noted.

Descartes was fully aware of the criticisms. His response was that before one can judge whether a particular set of bodies obey his impact rules or not, one would have to be able to calculate the effects on these bodies of the multiplicity of other bodies with which they are surrounded.™ Furthermore, real bodies are rarely perfectly solid, as the bodies in his impact laws are assumed to be; therefore the dis-crepancies can always be blamed on these "impediments" (as Galileo called them), factors that are in practice impossible to estimate.59 The warrant for these impact laws is thus in no sense experimental. They are not idealizations extrapolated from or tested by experience; their warrant is their alleged logical link with the prior general principles of mechanics.60

A second conclusion can be briefly stated. Descartes did not, in the end, concede that certainty lay beyond his grasp in any part of natural science.61 In that respect, he never quite gave up on the ambition of the Rules. Even when he admits the multiplicity of possible explan-atory hypotheses involving unobservable particles, he always goes

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some way to the ever-present, uncontrollable effects of hidden me-chanical agencies.6 6

There is no suggestion here of testing, of modifying the original hypothesis or formulating alternatives, of respecting the apparently refuting experiments, of devising new experimental strategies, and so forth, all of which are part of the "method of hypothesis" as that came to be understood later. Descartes's critic Christiaan Huygens was far closer to grasping what the shift to hypothesis entailed. In his Traite de la lumiere (1690), he retains the Cartesian ideal of a more general set of principles specifying the concepts that make motion intelligible. But he has realized that the explanatory theories in terms of which such phenomena as light are to be understood are in prin-ciple postulational and entirely dependent for their warrant on how well they account for the data.67 It was perhaps to be expected that optics should be the field in which the nature of retroductive inference would first become fully clear.

In a well-known passage in the preface to the Traite, Huygens remarks that his demonstrations ought not be expected to have the certitude of geometry,

since whereas the geometers prove their propositions by fixed and incontestable principles, here the principles are verified by the conclusions to be drawn from them, the nature of these things not allowing of this being done otherwise. It is always possible to attain thereby to a degree of probability which very often is scarcely less than complete proof. To wit, when things which have been demonstrated by the principles that have been assumed correspond perfectly to the phenom-ena which experiment has brought under observation, espe-cially when there are a great number of them, and further, especially, when one can imagine and foresee new phenom-ena which one employs, and when one finds that therein the fact corresponds to our prediction. But if all these probable proofs are found[in my work], as it seems to me they are, this ought to be a very strong confirmation of the success of my inquiry.68

Here in truth is the hypothetico-deductive method, as perceptively presented as it was by any writer of the century. The methodological questions posed by the Cartesian system, and Descartes's own in-ability to handle them, furnished Huygens with his starting point. In this admittedly restricted but nonetheless real sense, Descartes's work can be seen as a stage on the way to hypothetico-deductive method, while not itself embodying it.


Francis Bacon: Exemplar of inductivism?

With Francis Bacon we enter a very different world. Though his work was finished before Descartes's had begun, the separation between Bacon and the older tradition in theory of science was much sharper. He is much easier to treat, since he brought together his thoughts on method in a single work, the Novum organum, which appeared in 1620 shortly before his death.6 9 Since the work was revised over and over, it can be taken to represent his considered view, after a lifetime of reflection on a " n e w w a y " for the science of nature. Nonetheless, as we shall see, it is not easy to extract from it just what the new way amounted to. The method of aphorism he adopted does not lend itself to confident reconstruction of what he really meant. The fact that Book II breaks off at a crucial point may well imply that he had run into difficulties in trying to carry through his original plan for the work.

To the first members of the Royal Society in the seventeenth century, as well as to the Encylopedist chroniclers of science in the eighteenth century and theorists of science like Whewell and Mill in the nineteenth, Bacon was the inductivist par excellence, the herald of a new era in which induction would be recognized as the method of science. Whewell writes: " I f we must select some one philosopher as the hero of the revolution in scientific method, be-yond all doubt Francis Bacon must occupy the place of honor."7 0

What earned Bacon this place is the way in which " h e insists upon a graduated and successive induction," beginning from observa-tion.71 Whewell quotes the Novum organum, Book I, aphorism 19, with satisfaction:

There are and can be only two ways of searching into and dis-covering truth. The one flies from the senses and particulars to the most general axioms, and from these principles, the truth of which it takes for settled and immovable, proceeds to judgement and to the discovery of middle axioms. And this way is now in fashion. The other derives axioms from the senses and particulars, rising by a gradual and unbroken as-cent, so that it arrives at the most general axioms last of all. This is the true way, but as yet untried.72

The contrast between Bacon's " t rue w a y " and Descartes's method could not have been more sharply drawn. Bacon divides the inquiry into metaphysics, " t h e investigation of forms, which are (in the eye of reason, at least, and in their essential law) eternal and immutable," and physics, " t h e investigation of the efficient cause, and of matter,

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and of the latent process and the latent configuration" (II, 9).73 It is to "Metaphysics" that he devotes his attention in his exposition of the method of induction in Book II of the Novum organum:

Though in nature nothing really exists besides individual bod-ies, performing pure individual acts according to a fixed law, yet in philosophy this very law, and the investigation, discov-ery and explanation of it, is the foundation as well of knowl-edge as of operation. And it is this law with its clauses that I mean when I speak of forms, a name which I the rather adopt because it has grown into use and become familiar. (II, 2)

The voluntarist theology informing Bacon's thought shows itself here. The laws are fixed, not because of an intrinsic necessity of nature, but because the creator issues them as his commands. The forms, the correlatives of the laws, are thus eternal and immutable.

When I speak of forms, I mean nothing more than those laws and determinat ions . . . which govern and constitute any sim-ple nature, as heat, light, weight, in every kind of m a t t e r . . . that is susceptible of them. Thus the form of heat or the form of light is the same thing as the law of heat or the law of light. (II, 17)

The investigation of forms constitutes the principal work of human knowledge (II, 1). We are to look for a "true definition" (II, 20), a "true specific difference" (II, l) .7 4 When a form is present, " the nature infallibly follows"; when it is absent, "the nature infallibly vanishes" (II, 4). Seeking a form is thus something like searching for necessary and sufficient observational conditions for the appearance of the na-ture in q u e s t i o n . F u r t h e r m o r e , we are to look for a "source of being" that is inherent in a broader group of natures to serve as genus. And it ought to be "better known in the natural order of things" than the form itself (II, 4). Thus in the famous example to which much of Book II is devoted, motion is finally discovered to be "the genus of which heat is a species" (II, 20), motion being, of course, "better known in the natural order of things."

But how is this "interpretation of nature" (to be distinguished, Bacon reminds us, from the hasty and speculative "anticipations of nature" of his predecessors) to be carried out? The directions fall into two parts: "one, how to educe and form axioms from experience; the other, how to deduce and derive new experiments from axioms" (II, 10). Bacon never gets to the second part. The first - educing and forming axioms from experience - is, in turn, divided into three phases: the formation of natural histories; the organization of these histories by tables of presence, absence, and degree; and finally the


formation of axioms by an act of the understanding, "guided and guarded," which is the "true and legitimate induction" (II, 10).

The tables (like Mill's methods of sameness, difference, and con-comitant variation, which were inspired by them) link regularly co-occurring observable factors. They are thus typically inductive, in the narrow sense defined earlier in this essay. The evidence for causal relationship comes from finding factors invariably linked in obser-vation or co-varying in a significant way. Evidence against is provided by absence, when presence might have been expected. The method is one of generalization, with an element of testing provided by the tables of absence. Many of the "prerogative instances" he lists in Book II illustrate this. Powdered glass and agitated water become white, where they were previously transparent (II, 23). This suggests that whiteness is due to unequal refraction of the rays of light. Again, we are aided in the discovery of the form of weight by noting that quick-silver is very heavy, though not solid; diamond is solid, but not nearly so heavy (II, 24). Thus, the form of weight is related to the quantity of matter but not to solidity. In short, it would seem as though the discovery of the form of a given simple nature reduces to the discovery of another (better-understood) simple nature that invariably accom-panies the first nature in any complex, and thus may (in a loose sense) be said to "account for" it.

There is another feature of Bacon's exposition that has always linked it with inductivism. He tells us that if the method is used correctly, "there will remain at the bottom, all light opinions vanishing into smoke, a form affirmative, solid, and true and well-defined" (II, 16). Although he immediately adds, "This is quickly said, but the way to come at it is winding and intricate," the implication still seems to be that he can provide the map of that way. And it is a method that anyone can, in principle, grasp: "The course I propose for the disc-. covery of the sciences is such as leaves but little to the acuteness and strength of wits, but places all wits and understandings nearly on a level" (I, 61). It is (he says) like drawing a circle with a compass instead of by hand. And it provides "not pretty and probable con jectures, but certain and demonstrable knowledge."7 6 Axioms are said to be "educed from particulars by a certain method and rule" (I, 103). Induction, if properly carried out "leads to an inevitable conclusion."77

The experiments he prescribes to discover the "natural cause" of an effect "never miss or fail"; indeed, they "settle the question" (I, 99). These and other texts would surely seem to say that Bacon believed his method to work automatically. And this is just what induction was supposed to do, according to its more sanguine later exponents.

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But Bacon was not a strict inductivist. This was already emphasized by Whewell long ago. Bacon "held the balance, with no partial or feeble hand, between phenomena and ideas" ; he expounded a broader notion of induction, not unlike Whewell 's own, though still defective (Whewell argues) in a number of ways.7 8 In recent years, this broader reading of Bacon has become more or less standard, among philosophers and historians of science at least, though not, perhaps, among scientists.79 Indeed, one now finds it claimed that Bacon's approach is "strikingly similar to Popper's falsificationism" (which is supposed to be as far from inductivism as one can get)80 or again that it is in its essentials hypothetico-deductive, as opposed to inductive.81

What are the points at issue here? Critics of the inductivist reading take the main issue to be whether Bacon really does set out to "achieve everything by the most certain rules and demonstrat ions" (I, 122). Their claim is that this must be regarded as no more than "propa-ganda" on his part;82 that his method is really one of hypothesis, involving intuition, creativity, luck - and that he knew this. His op-position to the "anticipation of nature" ought not (they say) to be interpreted, as it sometimes ha§ been,8 3 as opposition to the use of hypothesis; rather, he is expressing a perfectly appropriate, and in-deed insightful, objection to over-hasty generalizing from insufficient evidence, and especially to the " rescue" of an axiom from counter-evidence by a "frivolous distinction," where " the truer course would be to correct the axiom itself" (I, 25).

Let us take these points in reverse order. Bacon certainly did not intend his criticism of the "anticipations" that he found characteristic of the traditional natural philosophy to extend to hypothesis gener-ally. He used the term "hypothes is " himself only rarely, and then usually in the pejorative sense common in his day. But his key term " a x i o m " comes close in meaning to our term "hypothesis . " 8 4 Axioms are the crucial elements in induction, the means of "closing with nature." 8 5 They are put forward for "trial by fire" (I, 47) by means of the various kinds of " ins tances" described in Book II. Though he speaks, on occasion, of "deducing" the axioms from experiments (for example, I, 82), he recognizes that the axioms cannot, because of the "subtlety of nature , " be established by syllogistic argument; when they are "duly formed from particulars," however, they "discover the way to new particulars" (I, 24).

Bacon stresses that the first steps are tentative, recalling that "truth will sooner come out from error than from confusion" (II, 20). One has to guess at possible links between simple natures. At this point, the process of exclusion is the "forcible" one (I, 46); in it "are laid the


foundations of true induction, which however is not completed till it arrives at an affirmative" (II, 19). But he realizes that exclusion itself may not be as decisive as one would desire; indeed, it cannot "possibly be so at first. For exclusion is evidently the rejection of simple natures; and if we do not yet possess sound and true notions of simple natures, how can the process of exclusion be made accurate?" (II, 19).

His answer to this is to propose "more powerful aids for the use of the understanding," notably the " instances of the fingerpost," which, as between two or more natures, show which is to be assigned as " c a u s e " of the nature being investigated; the union between them will be seen to be "sure and indissoluble," and at this point the inquiry may terminate (II, 36). Bacon clearly does think that his exclusions will lead to a single, definitive answer; despite his perceptive admis-sion that the "not ions" he is forced to use are imperfect in the early stages of the inquiry, he believes that the process of testing he outlines will eventually reveal the " f o r m " that is sought.8 6 If there is "prop-aganda" here, it is only in regard to the ease of the method - the "leveling of wits" - and not to its ultimately conclusive character.

Thus, though he employs hypothesis and admits that the original formulation of these hypotheses involved conjecture,8 7 he also holds that in the end hypothesis will be eliminated. He would have to assume, of course, that the investigator has to deal with only a finite, indeed, only a small, number of simple natures or of possible causal hypotheses. And he does make just this assumption, in regard to simple natures, at least (II, 7).88

But, from the mere fact that he allows a hypothetical status to his axioms, one cannot assume that he is implicitly expounding hypothetico-deductive method. An inductivist would (or should), after all, concede a similar status to such generalizations. How is one to decide which of the methods Bacon leans toward? A preliminary point to note is his well-known reservation about the reliability of sense-knowledge:

By far the greatest hindrance and aberration of the human un-derstanding proceeds from the dullness, incompetency and deceptions of the senses . . . For the sense by itself is a thing infirm and erring; neither can instruments for enlarging or sharpening the senses do much, but all the truer kind of interpretation of nature is effected by instances and expert ments fit and apposite, wherein the sense decides touching the experiment only, and the experiment touching the point in nature and the thing itself. (I, 50)

Empiricism and inductivism normally go together, but Bacon is cer-tainly not an empiricist (as that label later came to be used). " T o thi

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immediate and proper perception of the sense, I do not give much weight."8 9 Though he goes on to remind the reader that " the senses supply the means of discovering their own errors ," he is emphatic that observations are not simple " d a t a " from which generalizations may be drawn.9 0 They have to be corrected when incoherences show, not by instruments that improve on the senses directly,91 but by con-trolled experiment and systematic test. This appears to lean in the hypothetico-deductive direction.

But it is not decisive. How in the end does one separate inductive from retroductive inference? Or, for that matter, why does one? Both forms of inference are hypothetical, but they rest on different sorts of evidence. Induction relies on co-occurrence and co-variance. The hypothesis here would simply be that two (or more) observable factors (for Bacon, simple natures) are significantly related, one being either the formal cause (partial definition or difference) or the efficient cause of the other. The notion of test here is a weak one: It amounts to looking at cases that are similar to those where the factors have been found to be together or to vary together, and to discovering whether the postulated causal factor still accompanies the given one in these cases in the expected way. If it does, this constitutes additional sup-port; if it does not, the hypothesis (which bears on causality under-stood as regular co-occurrence) is falsified. The most familiar example of such an inductive hypothesis is the experimental " l a w " relating two quantitative variables, expressed as a curve relating results of a set of controlled experiments.

Retroductive inference is much less direct. It seeks to explain ob-served data in terms of variables or structures that are not themselves observed. The warrant for these cannot be observed co-occurrence or co-variance. The inference must begin from verification of deductive consequences of the hypothesis. Testing thus takes on a very different aspect. The hypothesis has to be supported, not by finding "more of the s a m e , " but by thinking up and verifying consequences that are as different as possible from those that originally prompted the hy-pothesis. Falsification is now much more complicated. When the pre-dicted consequence does not materialize, there are usually many different inferences one can draw from this (for example, the inad-equacy of the "not ions" employed, to draw on a Baconian suggestion); the downright falsity of the hypothesis is only one such inference. In induction, exclusion works much more simply: If the hypothesis is that two factors, A and B, are invariably associated under conditions C, and an instance is found where this is not the case, this inductive conjecture is immediately refuted.

Why should this relatively sophisticated distinction (one that has


been so often mishandled in twentieth-century philosophy of science) be applied to the seventeenth century? There are two reasons. First, the controversy as to whether Bacon's method was or was not in-ductive cannot be resolved without a sharper formulation of the no-tion of induction than one customarily finds; second, Bacon's work affords a perfect illustration of the effects of an ambiguity in this regard. Bacon is, in fact, at the origin of a confusion that has continued right down to the present.

On the face of it, the tables of presence and absence can only be inductive. And the notion of science as a discovery of " f o r m " - of something shared by instances otherwise heterogeneous - is inductive also and has, indeed, obvious affinities with the Aristotelian tradition from which Bacon is so strenuously seeking to separate himself. The natural philosopher's task is to discover such forms as that of redness, which is whatever it is that diverse instances like the "fixed red" of the rose and the "apparent red" of the rainbow or the opal have in common (II, 17). There must, he assumes, be a simple nature re-sponsible for the common attribution of the term " r e d " to all such cases. The gradual movement upward to more and more general axioms, of which he speaks so often (e.g. , I, 19; I, 104) seems to be one of increasing generality only. The deducing of new experiments from axioms (II, 10), which is to be the second part of the interpretation of nature, is never clarified, but its function appears to be only the determination of whether or not a particular postulated nature is present.

But the matter is not so simple. Everything hinges on whether or not the simple natures are always observable, so that the warrant for their presence is a direct one, and the consequent inference one of inductive generalization. What forces one to question this is the dis-tinction drawn in Book II, aphorism 5, between two ways of regarding bodies: first, as a " troop of simple natures" (so that gold is a sum of " the forms of yellow, weight, ductility, fixity, fluidity, solution and so on" ) ; second, as the locus of " latent process , " which "proceeds not by simple natures but by compound bodies as they are found in nature ." And he concedes that the latter may give the better hope for understanding. The tracing of latent process leads us beyond what "can be s e e n " to something that " for the most part escapes the sense" (II, 6). He notes that so far these processes have gone "unknown and unhandled" : "For seeing that every natural action depends on things infinitely small, or at least too small to strike the sense, no one can hope to govern or change nature until he has duly comprehended and observed t h e m " (II, 6).

Presumably by "observed" here, he must mean "discovered." And

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the discovery cannot be by the sense. But this changes everything. He makes it even clearer when he goes on to speak of the "latent configuration" on which the observed properties of things depend but that is itself not accessible to sense. Organisms have a visible structure, but bodies like iron and stone, which are uniform to the sight, must have a "true configuration," far more "subtle and exact , " that can be reached not "by fire, but by reasoning and true induction with experiments to a id" (II, 7). Bacon rejects atomism because he believes that the corollary doctrines of the vacuum and the unchange-ableness of the atoms are false (II, 8). But he asserts the existence of real imperceptible particles and other occult constituents of bodies (such as "spirit") , upon which the observed properties of things de-pend (II, 7).

But how are these to be known? He asks us not to be "alarmed at the subtlety of the investigation," because " the nearer it approaches to simple natures, the easier and plainer will everything become, the business being transferred from the complicated to the s i m p l e . . . as in the case of the letters of the alphabet and the notes of music" (II, 8). And then, somewhat tantalizingly, he adds: "Inquiries into nature have the best result when they begin with physics and end with m a t h e m a t i c s . I t sounds as though the simple natures are to be grasped mathematically: But how? And in what sense are the natures of these occult agencies " s imple"?

His answer appears to be that they are " s i m p l e " in part because they are shared by the largest number of natures. In the case of the heavenly bodies, " w h e r e man has no means of operat ing," investi-gation must depend on " t h e primary and catholic axioms concerning simple natures, such as the nature of spontaneous rotation, of at-tractions or magnetism and of many others of a more general form than the heavenly bodies themselves" (II, 5). Magnetism is " s i m p l e , " then, presumably because it is not to be reduced as a compound would be, and because its numerous effects are attributed to a single kind of nature. But magnetism is obviously not simple in the sense that it is easier for us to understand. (One is reminded of Aristotle's dis-tinction, in the face of a similar difficulty, between things "better known to u s " and "better known in themselves.")9 3

Bacon believes that the investigator can "reduce the non-sensible to the sensible, that is, make manifest things not directly perceptible by means of others which a r e " (II, 40). But the examples of " s u m -moning instance" he adduces to illustrate this simply define the non-sensible cause in terms of its observed effects or postulate untestable mechanisms. Rust, for example, is said to result from the fact that the "invisible and intangible spirit" in things finds " n o pores or pas-


sages through which to escape and is compelled to push and drive before it the tangible parts themselves" (II, 40.)

The tension within the Novum organum between an inductive method of gradual generalization linking observables, and a set of examples that requires a much more complex method of inference, can be clearly illustrated by turning to Bacon's lengthy discussion of heat. He concludes from his survey of instances as disparate as flame, wool, and aromatic herbs, each of them displaying " h e a t " in some way, that heat is a form of motion. This seems plausible in such cases as flame. But in others, like red-hot iron, there does not seem to be any associated motion. Bacon's move here is to postulate minute particles, whose constrained motion is responsible. But this means that the inference is not inductive; it is not based on co-occurrence or co-variance of observed features. It is retroductive in form. The hypothesis is that the violent motion of minute particles is causally responsible for what we interpret as heat in this case. The warrant for this can only lie in the consequences derived from it, since the motion itself is not observed.

It is striking how often Bacon does list unobservable causal factors in the illustrations he gives: the tides as possibly the result of a "mag-netic force" raising the waters, for example, or the downward motion of heavy bodies as possibly due to an attraction for them on the part of the earth (II, 36). What is puzzling here is that he has moved from formal cause to efficient cause in these cases, even though he had earlier maintained that analysis in terms of efficient cause is second-ary. His treasured example of heat may have misled him, because he was able to say not just that heat is caused by the motion of the minute parts but that heat is this motion. In other cases where the latent configuration would be invoked, the relationship of observed property to the postulated particles would have to be one of efficient, not formal, causality. The mode of inference would have to be ret-roductive; the inductive mode associated with his " f o r m s " would not do; And the kind of explanation given would be correspondingly different.

In the instances of tides and falling motion, Bacon describes crucial experiments that would, in his view, decide between the alternative explanations. But these are rather special cases, both because he can argue that there are only two or three possible alternatives, thus allowing exclusion to work, and also because the causes are almost synonymous with the effects. In the more important example of heat, he has no such helps, and it is unclear from the text how the inference is supposed to work. Perhaps it is by analogy; one moves gradually from cases where motion is clearly present to cases where no motion

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is apparent but where it can plausibly be postulated with the help of "minute particles." There does not seem to be much reliance on the verification of consequences, on the finding of " n e w particulars" (I, 24) as a mode of evidence. One difficulty is that the hypothesis itself is not sufficiently exactly specified to allow it to be tested by " instances of the f ingerpost ." The simple nature he invokes is, of course, motion. But even if a science of motion were to be granted to him (and he is far from one), it is not clear how he could have proceeded to a test of his fundamental hypothesis about minute particles in motion.9 4

Summing up this discussion, we can conclude that the method Bacon describes in the Novum organum is basically inductive. It is only when, in Book II, he proposes to formulate explanations in terms of latent configuration that the inductive method fails and his procedure becomes somewhat ambiguously retroductive. On his "falsification-i s m " both Popper and Urbach are right, the former in holding that Bacon's method is basically inductivist and hence can be falsificationist in only a limited sense, the latter in drawing attention to Bacon's quite explicit use of a method of conjectures and refutations. Horton is right in contesting Medawar's dismissal of Bacon as a mere inductivist, but she is perhaps overly generous in attributing to Bacon the essentials of the hypothetico-deductive method. He was too firmly rooted in the inductivism of the forms and in the tables of presence and absence. The presence or absence of a form is an inadequate test of a hypothesis about an unobserved cause. Bacon had, indeed, begun to grasp the power of the negative outcome, but his ontology of simple natures prevented him from appreciating the complexity of the positive outcome.9 5

Boyle: The criteria of hypothesis

A new starting point was needed, if the maxims of the Novum organum were to bear fruit. The initial induction had to be based on something other than the kind of verbal bond that led Bacon to classify both flame and wool as heat producing. And it had to focus on limited and controlled contexts, instead of seeking analogies across the entire range of familiar experience. In the next generation of Baconians, it was perhaps Robert Boyle who most clearly grasped what was needed.9 6 His experiments in pneumatics were designed to test causal hypotheses about the " s p r i n g " (pressure) of the air. They also pro-vided quantitative information of an inductive sort, relating changes in one variable to changes in another.

In pneumatics, as well as in his extensive studies of chemical re-actions and of the products of crystallization, Boyle's aim was not just


to describe but to explain: to account for these processes in terms of their underlying causes. And since the causes could not themselves be directly warranted by observation, Boyle was aware of the hypo-thetical character of the explanations he was proposing. Even so fa-miliar an entity as air became problematic as "a tmosphere , " when postulated to explain the behavior of the barometer. The shapes of crystals could be accounted for by supposing that crystals are made up of imperceptibly small corpuscles, themselves geometrically fig-ured in a regular way. The action on metals of acids, salts, or mercury could be explained by supposing pointed corpuscles entering pores and locking together in various ways.9 7 The specificity of the scores of types of chemical reaction and of crystal formation that Boyle stud-ied convinced him that only the corpuscular philosophy had the ex-planatory resources needed.9 8

Boyle said, much more explicitly than Bacon did, that the assess-ment of hypothesis was one of the investigator's chief tasks. In a short unpublished paper, " T h e Requisites of a Good Hypothesis , " Boyle laid down six criteria for a " g o o d " hypothesis, and four additional criteria for an "excel lent" one.9 9 A good hypothesis has to be internally consistent, must explicate the phenomena under consideration, and must not contradict either other phenomena or "manifest physical truth." An excellent hypothesis must, besides, be simple, must not be "precar ious" (forced), must enable the making of further predic-tions that can be tested, and must be " t h e only hypothesis that can explicate the phenomena or at least that does explicate them so well ."1 0 0

The hope of showing that the hypothesis under evaluation is the only one that can explain the phenomena may have been prompted, in part, by Boyle's work in pneumatics, where a finite list of possible causes could plausibly be compiled. But he was very well aware that this would not normally be the case. Even though the general prin-ciples of the mechanical philosophy appeared to him secure, he re-alized that the explanation of such "subordinate principles" as gravity, magnetism, springiness, as well as of chemical reactions and crystallization processes would have to be tentative: "For it is one thing to show it possible for such and such effects to proceed from the various magnitudes, shapes, motions, and concretions of atoms, and another to be able to declare what precise and determinate mea-ures, sizes, and motions of atoms will suffice to make out the proposed phenomena." 1 0 1

He had been able to devise experiments to test his hypotheses in pneumatics, but he had no such experiments in chemistry. His work there had been much more inductive, the cataloging of innumerable

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empirical regularities. Though he could offer hypotheses about pores and pointed particles and the like, these were far too indeterminate to allow test experiments to be constructed. Perhaps it was this that led him to distinguish between excellent and good hypotheses: Know-ing that his own corpuscular explanations could never qualify as ex-cellent, perhaps he hoped that they might pass muster as good. The barriers were just those that Descartes had earlier encountered in his attempts to explain observed processes and properties in terms of the shapes, sizes, and motions of corpuscles. But Boyle had a keener sense than did Descartes of how weak a claim to truth such models had when the link between model and explananda fell so far short of deduction: "I would have such kind of superstructures looked upon only as temporary ones; which though they may be preferred before any others as being the least imperfect, or if you please, the best in their kind we yet have, yet are they not entirely to be acquiesced in, as absolutely perfect or uncapable of improving alteration."102

It was to be a long time before any corpuscular hypothesis could qualify as "excellent." Boyle's "superstructures" were wildly pre-mature. But his conception of science was not. The elements of it had been at hand for some time, and many others at the confluence of the Baconian and the Cartesian traditions were moving in the same direction. Boyle saw more clearly than most what the consequences would be of redefining the methodological canons of the Novum or-ganum within the context of the mechanical philosophy. His concep-tion of science joined induction and retroduction; it relied upon measurement, gave pride of place to causal hypotheses, and recog-nized the role of experiment in sorting between theoretical alterna-tives. "I suppose that I have established forever a true and lawful marriage between the empirical and the rational faculty, the unkind and ill-starred divorce and separation of which has thrown into con-fusion all the affairs of the human family."103 Bacon's famous boast invites all sorts of qualification from the modern reader. The metaphor of betrothal might, for one thing, have been more prudent than that of marriage. The terms of the union were far harder to establish than Bacon had thought they would be. And the facile reductionism of the mechanical philosophy prevented an appreciation of just how difficult the retroductive task would ultimately prove to be. Nevertheless, the readers of Boyle and Huygens already would have had a pretty fair idea of the quality of the knowledge the happy union could produce.

Kepler: Hypotheses of planetary motion

At this point, I want to turn our story in a different direction. So far, we have been dealing with the proponents of large theories of sci-


entific method and those who were influenced by them. Now we will consider a thinker who, in a highly specialized area, but the area to which perhaps the most intensive methodological scrutiny had al-ready been given, seems to have anticipated later thinking about how a "science" should proceed. Johannes Kepler's first problem was to discover the "true form" of the motions of the planets, to hit upon the paths the planets actually followed and the speeds at which they moved. Only then could he go on to explain these motions.104 His first question is therefore: What are the real motions that account for the motions the astronomer can trace in the sky? These motions are hidden from us and can only be inferred indirectly by means of the constructions of the mathematicians. The problematic is thus different from that of mechanics, where the question about causes bears only on the issue of what makes the bodies move as they do. Kepler knows that in astronomy one cannot resolve this latter question without solving the other one first.

In a recent book, Nicholas Jardine has argued for the seminal im-portance of Kepler's appreciation of what the "hypothetical" character of the search for the real motions of the planets amounted to.105 In his Defence of Tycho against Ursus,106 Kepler defended Tycho Brahe against the charges that Nicolas Reimarus Ursus had leveled against him - the charge, among others, that Tycho's astronomy, being "hy-pothetical," amounted to nothing more than "fictions," even if it did account for the phenomena. The arguments used by Ursus were not new; the issue had been debated ever since antiquity, in large part because of the evident incompatibility of the two long-prevailing ac-counts of the planetary system, the "physical" one of Aristotle and the "mathematical" one of Ptolemy.1"7

Kepler distinguishes between two sorts of hypothesis. A geometrical hypothesis proposes a particular mathematical device - for example, an epicycle - as a way of summarizing a set of phenomena. A dis-agreement about such "hypotheses" - about whether to use epicycles or eccentrics to describe the planetary motions, for instance - is of no real consequence, since these are but "conceits" of the astronomer and do not affect the "explaining of nature."1 0 8 That is, though they differ mathematically, they may still describe precisely the same mo-tion.109 An astronomical hypothesis, however, purports to give the truth as to a particular planetary motion. A disagreement here - for example, that separating Ptolemy and Copernicus - is substantive:

If some astronomer says that the path of the moon describes an oval shape, it is an astronomical hypothesis. But when he shows by what circles a drawing of this sort of oval can be constructed, he uses geometrical hypotheses. . . . Accordingly, there are two distinct tasks for an astronomer: one, which

58 Ernan McMullin Conceptions of science in the Scientific Revolution 59

truly pertains to astronomy, is to set up astronomical hy-potheses such that the apparent motions will follow from them; the other, which pertains to geometry, is to set up geo-metrical hypotheses of whatever kind (for there can often be various kinds in geometry) such that from them those prior astronomical hypotheses, that is, the true motions of the planets unadulterated by the distortion of the sense of sight, both follow and can be worked out.110

Having clarified this long-standing source of misunderstanding, Kepler focuses on astronomical hypotheses. His truth-claim for the Copernican hypothesis faced the obvious challenge: How can you assert this hypothesis to be true on the basis of its accounting for the phenomena, if the Ptolemaic system accounts for them more or less equally well? His first response assumes the presupposition of the challenge: that the sole criterion of the truth-value of a hypothesis is the saving of phenomena. He argues that Ptolemy's predictions do not depend on the reality of the motions of the heavens, any more than Copernicus's do on that of the motion of the earth. Rather, both depend simply on a "certain separation"1 1 1 of heavens and earth, the same one in each case. This is all, therefore, that each testifies to (under the prior assumption as to the proper criterion for a hypoth-esis): "S ince , therefore, they are one for the purpose of the demon-stration, for the purpose of the demonstration they certainly are not contradictory propositions. And even though a physical contradiction inheres in them, this is still entirely irrelevant to the demonstra-tion."1 1 2 The contention of the critics that astronomical hypotheses cannot be regarded as truth bearing, since contradictory hypotheses can be equally well supported, thus fails.

Kepler appears to be struggling, in this difficult passage,1 1 3 toward the insight we would now call "kinematic relativity." The two systems may well be kinematically equivalent, even though they are physically incompatible. Kepler grasps the implication quite clearly: The criterion of "saving the p h e n o m e n a " is insufficient of itself to determine the truth of astronomical hypotheses. Where Ursus and the others have failed, he says, is in not seeing that this means one must look more widely for criteria; one must not confine one's thinking to geometry, or even to astronomy alone, ignoring the help that may be obtained from elsewhere.1 1 4

But first there is a preliminary argument against the skeptical view: "False hypotheses, which together yield the truth once by chance, do not in the course of a demonstration in which they have been combined with many others retain this habit of yielding the truth, but betray themselves."1 1 5 Four years earlier, in the Mysterium cos-

mographicum of 1596, Kepler had developed this same theme. Deriving the truth from false premises " is fortuitous, and that which is false by nature betrays itself as soon as it is considered in relation to other cognate matters; unless you would be willing to allow him who argues thus to adopt infinitely many other false propositions and never, as he goes backwards and forwards, to stand his ground." 1 1 6

The false hypothesis shows itself by the ad hoc modifications that must be made over time in order to defend it from refutation. Even more directly, it may be detected once one takes "related sciences" into consideration.117 The systems of Tycho and Copernicus may agree in their basic predictions of planetary positions, but other "physical considerations" may still serve to separate them. Copernicus is will-ing, for example, to allow the immensity of the distances to the fixed stars (because of the absence of observed parallax); Tycho is not. Furthermore, one hypothesis may reveal the cause of a phenomenon, whereas another may merely predict the phenomenon. For example, Copernicus is able to explain why it is at the time of their nearest approach to earth that the superior planets are in opposition to the sun; it is a necessity in his system, whereas it is a contingent, extra postulate in that of Ptolemy.1 1 8 One further clue is that the better astronomer is the one who can claim for his system "simplicity and well-ordered regularity," since this can be assumed to be "what God would have preferred."1 1 9

Kepler thus provides his reader120 with a varied list of criteria that a good astronomical hypothesis should meet in order to qualify as representing the " true mot ion" of the planet. He obviously believed that the criteria themselves could easily be applied and that in fa-vorable cases they could yield certainty. Though he underlines the role of hypothesis, his finished science can still remain what science had always been: a definitive claim to knowledge. The Copernican hypothesis (he makes clear more than once) is in no way provi-sional.121 Nor is there anything tentative about his proclamation of the ellipse as the " true form" of the orbit of Mars.

What made this kind of assurance possible, and what therefore marked off kinematics, was of course the special character of the inference involved in moving from apparent to " t r u e " motion. The hypothesis itself posited a geometrical orbit; the process of fitting the orbit was therefore one of closer and closer approximation. One could more or less tell at any moment how close one was coming; a criterion of mathematical simplicity would be likely to play a major role in the decision between alternatives. The inference, though not simply inductive, was thus much closer to induction than inference to agent cause would ordinarily be. No new concepts were needed;

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the process of "discovery" began from the choice of a particular geo-metrical figure. This may have made it easier for him to employ it without apology.

To critics of hypothesis such as Ursus, his response is direct. If they claim that astronomy knows nothing of the causes of the heavenly motions, because they believe only what they can see, "what is to become of medicine in which no doctor ever perceives the inwardly hidden cause of a disease except from the external bodily signs and symptoms which impinge on the senses, just as from the visible positions of the stars the astronomer infers the form of their mo-tion?"1 2 2 He saw, more clearly than others before him, what the adop-tion of this new conception of science entailed. In particular, he grasped that although the main warrant for a scientific hypothesis must lie in the verification of its consequences, this cannot be the whole story. And he took some long steps toward the elaboration of criteria of hypothesis appraisal that were to carry science far beyond the level attainable by the classical methods of demonstration.

Gali leo: Kinematics as science

In this and the next section, we come finally to the two scientists whose names most easily come to mind when the Scientific Revolution is mentioned. Galileo began a mathematization of nature that Newton carried to its triumphal conclusion. I will argue, nevertheless, that the deceptively simple patterns of inference drawn from Galilean kinematics and Newtonian dynamics were in important ways inap-propriate for the sciences of properties and processes whose begin-nings we have seen. What it is to "unders tand" motion is not at all the same as what it is to "unders tand , " say, chemical change or the action of the atmosphere. But the prestige of the new mechanics was so great, and the achievements in the other sciences so few by com-parison, that the temptation to see in mechanics the ideal of the sort of knowledge natural science can in principle attain became almost overwhelming as the century of the revolution waned.

Galileo's importance to our story lies in the " n e w science" of me-chanics that he announced in 1638. But before we come to that, brief reference should be made to his "astrophysics" and his cosmology. The telescope opened up to him a distant realm where the use of hypothesis appeared unavoidable. The traditional notion of demon-stration could not work for the very distant, any more than for the very small, since the natures of these remote objects did not lend themselves to the intuitive insight into familiar experience on which the starting points of demonstration depended. Thus another mode of warrant was necessary. In the First Day of the Dialogue on Two Chief


World Systems, there is an elegant example of hypothetico-deductive reasoning. Let us assume, Galileo says, that the moon's surface is like that of the earth and ask what observable consequences this would have for us here on earth. Then let us check to see if these are in fact the case. And, of course, they were, in impressive detail. Galileo was much less comfortable with inference to the very small, disturbed by the use of explanatory models in the microdomain.1 2 3

Much of the debate around the Dialogue of 1632 centered on whether Galileo had followed the mandate given him by Pope Urban VIII in 1624 to treat the Copernican view "hypothetical ly ." What Urban clearly meant was that it should be taken as a calculating device, just as Andreas Osiander had recommended in the famous prefatory letter to De revolutionibus. This had been, after all, the standard understand-ing of the mathematical models of the astronomer on the part of most Aristotelian philosophers for centuries. But Galileo had expressed his strong dissent from this view of astronomy long before.124 And he had early on convinced himself that in the phenomenon of the tides he had found the proof he needed of the truth of the Copernican claim.

It would thus have run entirely counter to his understanding of astronomy and to his basic conception of science to present the Co-pernican system as a calculating device only. And in fact, in the Dialogue he made no attempt to restrict it in this way.12S On the other hand, it would have been fatal to his chances of publication to make too overt a claim to conclusive proof. In the text of the Fourth Day, however, he frequently comes close to doing so. Look at his choice of terms:

Now this [the earth's motion] is the most fundamental and effec-tive cause of the tides, without which they would not take p l a c e . . . . The diurnal period of the tides, of which the pri-mary and universal cause has first been proved.... Having estab-lished that it is impossible to explain the movements perceived in the waters and at the same time maintain the immobility of the vessel which contains t h e m . . . . The primary cause of the uneven motion of the vessels, and hence of that of the tides, consists in the additions and annual m o t i o n . . . . We shall dem-onstrate that the causes for all the various events perceived in the tides reside in things previously recognized and accepted as unquestionably true.126

It is no wonder that the examiners appointed by the Holy Office found that he had departed from the authorized "hypothetical" form;127 there could be no denying that he treated the Copernican position as potentially provable. Indeed, they could claim with some justice that he had to all intents and purposes presented it as proved,


both by positive argument and by exclusion of the alternative hy-pothesis (fixity of the earth, common to both the Ptolemaic and the unmentioned Tychonic positions). Galileo conceded (as Kepler had) that the planetary data alone could not provide a conclusive proof -although they were, he emphasized, sufficient to refute the Ptolemaic model. What he needed, he realized, were phenomena that could only be attributed to the earth's motion, so that he could argue con-clusively from effect to cause.128 But how could one exclude the pos-sibility of alternative causes, the difficulty that (as we have seen) troubled all the early exponents of hypothetical argument? Galileo called upon several innocent-seeming methodological prescriptions: (1) A given effect can have one and only one " t rue and primary cause";1 2 4 and (2) A single true and primary cause must hold good for effects that are similar in kind.130

With the aid of these two principles, it was not difficult to construe the tidal argument as conclusive. For, if the double motion of the earth really could account for the basic features of the tidal phenomena (leaving local variations to be explained by such "secondary causes" as the sizes and depths of the ocean basins),131 then one would not have to worry about the phenomena being explainable by another cause equally well. This would presumably be excluded, since any given phenomenon can be adequately explained in one way only, according to the maxim. But surely this begs the question, or at least equivocates on the notion of adequate explanation.

The issue was a very old one, going right back to the Posterior Analytics, as we have seen. William A. Wallace has recently argued132

that Galileo's youthful notes on this work (which were, Wallace ar-gues, copied with some reworking from the class notes of a logic course given by Paulus Valla at the Collegio Romano in 1588)133 testify to Galileo's early knowledge of the Aristotelian scholarship of the day regarding the nature of science.134 To the point here is Galileo's dis-cussion in these notes of the possibility of a demonstrative regressus.135

Critics had often pointed out that the inference from effect to cause, in a regressus, is logically invalid, except where the major premise can be shown to be convertible - that is, where the cause can be shown to be the only possible cause of this effect.136 Galileo - or perhaps, more exactly, Valla - defends the regressus, while including convert-ibility as one of the conditions to be satisfied in order for the inference as a whole to work as demonstration.

But convertibility requires a separate argument; the argument link-ing effect to possible cause (the Aristotelian argument quia) of itself does not guarantee it, as Galileo admits. And how is this argument to run, where the cause is unknown? Zabarella, the authority on

whom Valla principally relies, was never really able to circumvent this difficulty, and Galileo himself makes no attempt to address it. His use in the Dialogue of the principle that a given effect can only have one " true and primary cause" might be an echo of that earlier discussion, except that what had earlier been a condition that might or might not be satisfied in a given argument quia seems now to have become an exceptionless maxim relating effect and cause.137 It is ironic that Galileo should have relied on the maxim in this particular context, since there was an alternative possible cause for the tides (lunar at-traction), one that the maxim absolved Galileo from seriously consid-ering. On the Copernican issue Galileo seems to have displayed far less methodological acumen than did Kepler.

Perhaps it could be argued, however, that Galileo was entirely aware of the fallacy involved in this use of the one-effect, one-cause maxim to convert hypothetical reasoning into demonstration but that he employed it in an ad hominem way, knowing that his Aristotelian opponents would be likely to accept it. But would he have wanted to claim demonstrative proof for the Copernican position, given the restriction that Urban had laid on him, unless he really believed he had constructed such a proof? In his Letter to the Grand Duchess Chris-tina of 1615, one set of arguments he used had implied that a view that contradicted the literal reading of a passage of Scripture could not be defended unless it were "demonstra ted . " Was this in his mind here?138 Did he really think he could demonstrate the truth of the Copernican doctrine? Did he think he had demonstrated it in the Dialogue? Part of the problem was that he admitted only two categories of suppositions: true and fictive; the all-important third alternative of "highly likely" (or "wel l -supported" or "best available") is not men-tioned by him and would hardly have been admissible as yet in natural philosophy, since it would have suggested opinion, not science.139 It may well have seemed to him, then, that his only option was to propose the Copernican position as true and thus to claim a form of "demonstrat ion" for it. In that case the notion of demonstration he could have remembered from the class notes of his youth would have proved useful.

In our survey of conceptions of science, our main interest, however, must lie in Galileo's " n e w science" of mechanics. In what sense, first of all, did he have a science of mechanics at all? He had left aside quite deliberately the question of what causes falling motion, in order to focus on a kinematic description of the motion itself. This is not, he says, " a n opportune time to enter into an investigation of the cause of the acceleration of natural mot ion . " Better simply to "demonstrate some attributes of a motion so accelerated (whatever be the cause of

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its acceleration)."140 And this proved to be a very wise, if interim, step. But it did leave unanswered the question that all of his prede-cessors would have regarded as the key to a proper "science" of motion.

His success was partly a matter of luck. Aristotle had required two dynamic factors - weight and resistance - in his analysis of fall. Galileo was able to show that as long as one restricted one's concern to fall in vacuo, weight did not affect speed. Thus neither weight nor re-sistance had to be taken into account. It was, then, simply a matter of relating space fallen to time taken. The simplest hypothesis was that the acceleration was uniform. A test of the implications showed that this was indeed the case. And so the hypothesis was demon-strated. Was this not a paradigm of science?

Let us go back over the story a little more slowly. Galileo faced two quite different tasks in the second part of the Two New Sciences. One was to explore the implications of the mathematical concept of uni-formly accelerated motion. This was not as easy as it may sound today; the steps from the "uniformly difform" motion of the scholastics to the geometrical formulas of Galileo had been halting ones, requiring much conceptual effort. The second task was to show that fall in vacuo is, in fact, uniformly accelerated in nature. This was (for the most part) a matter of experiment. But since the means of measure-ment available to him were much too crude to enable him to measure falling motion directly, he had to derive some consequences of the definition of uniformly accelerated motion that could be tested. The one he chose to rely on was the inclined plane.141 The results were what he expected: "By experiments repeated a full hundred times, the spaces were always found to be to one another as the squares of the times, and this for all inclinations of the plane."1 4 2

This afforded an answer to the challenge he put in the mouth of Simplicio, the speaker who represents empiricism in the Dialogue, who was perfectly willing to accept the mathematical consequences of the proposed definition but wondered "whether this is the accel-eration employed by nature in the motion of her falling heavy bodies" and asked for experimental proof.143 Salviati, who represents Galileo's own views, allows that this demand is quite proper "in those sciences which apply mathematical demonstrations to physical conclusions," where principles must be confirmed by "sensory experiences that are the foundations of all the resulting structure." Earlier, when intro-ducing his definition of uniformly accelerated motion, Salviati an-nounced that his confidence that the definition corresponds to the "essence of naturally accelerated motion" rests "chiefly" on the fact that its consequences "correspond to that which physical experiments


show forth to the sense."1 4 4 This certainly sounds hypothetico-deductive. The warrant for holding that his definition really does apply to motion in nature lies, he says, in the fact that consequences of the definition can be verified empirically. Vet he also says that he is "demonstrating" the path that falling bodies and projectiles actually follow.145 How can demonstration and hypothetico-deductive infer-ence be joined in this way? Can he have it both ways?146

Part of the problem lies in the way in which he moves without notice from the mathematical to the physical; he can use a term like "demonstrate," indifferently of proof in either order.147 But there is a more fundamental issue. He repeatedly claims to have discovered the "causes" of local motion from the "properties" of the motion. But in what sense of "cause"? The inference from a property of a motion to the motion itself is relatively simple; it is not at all like inferring from effect to efficient cause. Uniform acceleration and the odd-number rule are "convertible," in the sense that one can infer in either direction. If a motion is known to satisfy one, it will satisfy the other. This is just the sort of "convertibility" that we have seen to be prob-lematic in standard contexts where the scientist is trying to work back from effect to efficient cause. One condition required for regressus to be demonstrative is indeed satisfied, when "effect" and "cause" de scribe mathematically the same motions. But the cause here is formal, not efficient. Kinematics is obviously an altogether special case, of fering no help as a guide to scientific inquiry generally.

There is a further problem. For Galileo's kinematics to be demon strative, another condition must be satisfied. The "consequence" on which it rests must be verified in nature. Motion on the inclined plane must in fact be uniformly accelerated. Newton was later to show that the acceleration of fall is not precisely uniform; the departure from uniformity was, in fact, a direct consequence of his theory of gravi-tation. Galileo was convinced that his postulate was true; departures from it he explained as being due to "impediments" like friction, resistance of the medium, and idealized assumptions about the con-figuration of the bodies studied.148 The divergence between Galileo's " law" and Newton's is not, however, due to an "impediment." It is not due to an idealization of the sort employed by Archimedes (and used also by Galileo in calculating the path of a projectile), where the vertical is taken to be movable parallel to itself. Such an idealization is introduced in order to allow a simple diagram to be used. But the "truth of nature" is in no way obscured by it; it is a simplification that can be allowed for, if necessary. Galileo's law is not an idealization in that sense; taken empirically, it is an approximation that holds quite well over short distances.

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The distinction is crucial. Galileo's definition is not absolutely "true in nature," and hence his reasoning cannot be demonstrative. Early in his Two New Sciences, Galileo remarks that it is " the most admirable and estimable condition of the demonstrative sciences that they arise and flow from well-known principles, understood and conceded by all."149 Are there principles of this sort in mechanics? In the opening lines of the treatise on naturally accelerated motion he incorporates in the Two New Sciences, he writes:

It is as though we have been led by the hand to the investiga-tion of naturally accelerated motion by consideration of the custom and procedure of nature herself in all her other works, in the performance of which she habitually employs the first, simplest, and easiest m e a n s . . . . Thus when I consider that a stone falling from rest at some height successively acquires new increments of speed, why should I not believe that those additions are made by the simplest and most evident rule?150

Why not indeed? But the warrant now lies in the rule rather than in the empirical confirmation. What relative weight did Galileo give to the one as against the other? It is hard to know, since in this case they pointed in the same direction. But there is a revealing comment in a letter Galileo wrote to Giovanni Battista Baliani shortly after the appearance of the Two New Sciences, commenting on the methodology he had followed in that treatise:

I argue ex suppositione about motion, so that even if the conse-quences did not correspond to what happens in the natural motion of falling heavy bodies, it would matter little to me, just as it takes nothing away from the demonstrations of Ar-chimedes that no movable is found in nature that moves along spiral lines. But in this I have been, I can say, lucky; for the motions of heavy bodies correspond precisely to the events demonstrated by me from the motion I defined.151

It would "matter little" to him, he says. But, of course, it would have undermined any claim on the part of his "demonstrations" to count as physics, unless (like Descartes) he was prepared to invoke a doc-trine of "impediments" so strong that it would have detached his "science" from empirical test entirely. Ought one to take comments like this one as evidence of a Pythagorean strain in his thought or simply as an expression of pride in the significant mathematical achievement of the De motu locali? Or ought we to suspect irony, from an author surely capable of it?

One way or another, it seems safe to conclude that Galileo was not the inductivist in mechanics that so many have claimed him to be.


There was, of course, much that separated him from the Aristotelian tradition: his techniques of experiment and of idealization, for ex-ample, and his mathematizing of the language of nature. Yet there were still unmistakable echoes of the deductivism of that older tra-dition within which his quest for demonstration had first taken shape. And these echoes would still be heard in the age that followed, es-pecially among those for whom mechanics was the science of nature.

Newton: Deducing from the phenomena

In this essay, we have traced three very different currents in early seventeenth-century science. One was the search for the unobserved causes of observable effects, a search that led to a growing sophisti-cation in, as well as at least partial acceptance of, hypothetical rea-soning in science. A second was the quest for "laws of nature," to be discovered through a process of generalizing from regularities an-chored directly in experience. And the other was the pursuit of the traditional ideal of demonstration, finding its most plausible reali zation, up to this point, in the kinematics of Galileo. The collision between these currents was nowhere as much in evidence, however, as in the work of Newton; the wide variety of readings that subsequent generations have given to the remarks on method scattered through out his writings testify to the tensions that Newton himself so ob-viously felt in regard to the expectations proper to his "experimental philosophy."

In the formal Latin account he left of his first lectures at Cambridge, we find him already setting his course. The topic is the theory of light and colors, and he wants to justify the mathematical approach he proposes to follow:

I can thus attempt to extend the bounds of mathematics somewhat, just as astronomy, geography, navigation, optics, and mechanics are truly considered mathematical sciences even if they deal with physical t h i n g s . . . . Thus although colors may belong to physics, the science of them may be con sidered mathemat ica l . . . . [In this way,] instead of the conjec-tures and probabilities that are being blazoned about everywhere, we shall finally achieve a natural science sup-ported by the greatest evidence.152

Newton's distrust of the merely probable already shows. To achieve a natural science, one must find a way to separate "mathematics" from "physics ." The association of each color with a light-ray of a

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particular refrangibility is all that is needed (he argues) to convert the theory of colors into a properly mathematical science. In his first communication to the Royal Society (1672), he sets out his new theory, " t h e oddest if not the most considerable detection which has hitherto been made in the operations of Nature." 1 5 3 He describes an experi-ment in which sunlight from a small hole is allowed to pass through two prisms in succession. It is, he claims, an "experimentum crucis" (a Baconian phrase he later discards), since the results refute the usual view (that the colors are modifications brought about by the prism) and prove that colors must be "original and connate properties" of the light before it strikes the prism. Sunlight is, therefore, a mixture of rays of differing refrangibility, each color corresponding to a ray of a particular refrangibility. "I t can no longer be disputed," he con-cludes, that the rays themselves must be substances, since they are the subjects of the quality of color. But to determine what light itself is and how refraction is actually brought about " is not so easy. And I shall not mingle conjectures with certainties."1 5 4 This manner of separating certainty from conjecture by setting aside the question of underlying causal mechanisms will serve him well in his later work.

But Robert Hooke, for one, was unpersuaded that Newton had successfully separated mathematics from physics: "I cannot think it to be the only hypothesis, nor so certain as mathematical demon-strations."1 5 5 He was prepared to admit that Newton's "hypothes i s , " as he kept calling it, did, in fact, explain the phenomena; but then, so did others. To hold that light is a pulse instantaneously transmitted in an ether, and not a stream of corpuscles moving in straight lines, was far preferable in terms of the mechanical philosophy.

Newton's sense of outrage at this questioning of the theory he had thought indisputable shows in his barely civil response. His concern, he insists, had been with the properties of light, "considering it ab-stractly as something or other propagated in straight l ines,"1 5 6 not with the physical question of its underlying nature. His suggestion that light is a body had been no more than that, a "plausible con-sequence" of his theory, but not part of the theory itself, since it was possible that other mechanical accounts of light might also explain these same properties. His theory is not a "hypothetical explica-tion";1 5 7 it is determined by the experiments themselves.

Modern commentators have been divided as to the merits of this controversy. Newton had assuredly refuted Hooke's original "mod-ification" theory. But could he properly claim to have deduced his own theory from the phenomena, banishing hypothesis to the further issue of underlying causal mechanism? It all depends on how physical


an interpretation is given to the " l ight-ray." By describing it as a substance, by calling the white sunlight a mixture of rays that prop-agate in straight lines, it sounds as though he is specifying an un-derlying mechanism that would exclude a wave interpretation. But if the light-ray is no more than a geometrical device to calculate the path of transmission from source to screen, the claim that sunlight consists of "rays differently refrangible" might reasonably be said to be deducible from the prism experiments. Precisely the same sort of ambiguity reappears later when Newton turns to mechanics.

In a letter to Oldenburg at this time, Newton sums up his response to those who rely on the explanatory power of hypotheses:

I cannot think it effectual for determining truth to examine the several ways by which phenomena may be explained, unless where there can be a perfect enumeration of all those ways. You know, the proper method for inquiring after the proper-ties of things is to deduce them from experiments. And I told you that the theory that I propounded was evinced to me, not by inferring 'tis thus because not otherwise, that is, not by de-ducing it only from a confutation of contrary suppositions, but by deriving it from experiments concluding positively and directly.158

Why this opposition to hypothesis, which had, by the 1670s, be-come common coin in natural philosophy? O n e answer often given is psychological: Newton was dogmatic, averse to challenge, inclined to overestimate the certainty of his own claims, as the early brush with Hooke shows. He would thus be inclined to exclude the dis-putable from science proper, in order to secure his retreat there. A second suggestion is that the ingenuity of the Cartesians had led to the multiplication of hidden mechanisms that, though "explanatory" in the sense of being able in principle to account for the data at hand, were incapable of being tested in any precise way by means of em-pirical consequences drawn from them. Newton often voices his im-patience with " h y p o t h e s e s " of this sort, which had clearly, to his mind, become an abuse.1 5 9

But there was another reason too. He was convinced that he could divide the task of the inquirer neatly in two, just as Galileo had done in his mechanics. The properties of the nature under investigation are to be determined directly by experiment. The further matter of explaining the properties in causal terms is an optional affair, one that he is happy to leave until later. Huygens challenged him on this point, saying that until Newton has found an hypothesis that explains the behavior of light passing through prisms, " h e has not taught us

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what it is wherein consists the nature and difference of colours, but only this accident (which certainly is very considerable) of their dif-ferent refrangibility."160 But Newton was not to be persuaded:

To examine how colours may be explained hypothetically is beside my purpose. I never intended to show wherein con-sists the nature and difference of colours, but only to show that de facto they are original and immutable qualities of the rays which exhibit them; and to leave it to others to explicate by mechanical hypotheses the nature and difference of those qualities: which I take to be no difficult matter.161

" N o difficult matter": This was Newton's jab at those who could so imaginatively conjure up explanatory schemes. To Ignace Pardies he writes in 1672 that although hypotheses may be used to explain properties established by experiment, he has in this work on color "thought necessary to lay aside all hypotheses as foreign to the pur-pose"; otherwise, "I see not how certainty can be obtained in any science."1 6 2 Since he believes that certainty can be achieved by finding a way to separate, in each case, the "mathematical" from the "phys-ical," he can see no reason to abandon the traditional link between science and certainty.

But he was loath to let explanation go entirely. In 1675, he sent to the Royal Society a paper entitled, surprisingly, "An Hypothesis Ex-plaining the Properties of Light." The covering letter opens: "I had formerly purposed never to write any hypothesis of light and colours, fearing it might be a means to engage me in vain disputes."1 6 3 What led him to overcome his scruples was the hope, he says, of rendering his earlier papers on color "more intelligible." And so he proposes an ethereal medium, compounded of a variety of "spirits," to help explain not only optical phenomena (though he insists that light can-not simply be a vibration of the medium) but also electrical attraction, muscular action, and even gravitational motion. This was just the sort of generalized explanation, unconnected to precise experimental con-sequence, that he had earlier seemed to scorn.

This tension between an official policy of exclusion of explanatory hypotheses from science proper and a reluctant admission that they serve to make the properties of Nature "intelligible" is particularly clear in the Opticks (1704), where he finally brings together his re-searches on light and colors of thirty years before. His aim, he says in the opening lines, "is not to explain the properties of light by hypotheses, but to propose and prove them by reason and experi-ments."1 6 4 But when he attempts to lay out a geometrical science, he is faced with a variety of periodic phenomena and is forced to pos-


tulate "fits of easy reflection and transmission" along regular intervals of the light-ray, brought about by the refracting surface.165

It is possible, of course, to take this simply as a disposition of the light, established by experiments like the colored rings that are pro-duced when a lens is pressed on a glass plate. Newton says he is content with the "bare discovery that the rays of light are by some cause or other alternately disposed to be reflected or refracted" as they propagate.166 But the need for a causal analysis is now becoming urgent, in order to unify the disturbingly disparate properties that have been postulated. After the introduction of the "fits," the Opticks contains a long section in which dozens of assorted new observations of color phenomena are recounted. The work then breaks off suddenly ("I was suddenly interrupted . . . " ) , leaving the observations unan-alyzed. It is hard to avoid the conclusion that he was unable to carry his aim of a nonhypothetical science of properties any farther. Instead, he ends with a series of "queries" in which causal hypotheses are introduced without embarrassment, and all his pent-up imaginative vigor asserts itself.167 Query 1 opens: "Do not bodies act upon light at a distance?", and on successive pages he introduces "aether-pulses," active principles, corpuscles that attract and repel, and a host of other ingenious explanatory devices.

Here we still find strictures against hypothesis, but now more muted.1 6 8 And we also find, in query 31, (the query that would fuel so much later debate in chemistry, optics, and even theology) perhaps the most considered expression of his conception of science. One must begin with the "method of analysis," which consists basically of two steps: the making of experiments, and "drawing general con-clusions from them by induction."169 What is interesting here is the admission that deduction is not enough but that inductive inference is also critically involved. It is, in fact, the "highest evidence that a proposition can have in this philosophy," he notes in a letter to Roger Cotes, in regard to the General Scholium for the second edition of the Principia (1713).170 In the Scholium itself, his manner of expressing this is less felicitous: "For whatever is not deduced from the phe-nomena is to be called an hypothesis, and hypotheses, whether meta-physical or physical, whether of occult qualities or of mechanical, have no place in experimental philosophy. In this philosophy, par-ticular propositions are inferred from the phenomena, and afterwards rendered general by induction."1 7 '

As Newton's contemporaries well knew, there is a great difference between "deducing from the phenomena" and "making general by induction," the latter being hypothetical by the very definition New-


ton himself gives here. This was a difference that Newton was not disposed to acknowledge; the third rule of reasoning in the Principia explicitly attempts to circumvent it. In query 31, he is willing to make a further concession, one that appreciably softens the rigid deductivist insistence of his earlier writings:

And although the arguing from experiments and observations by induction be no demonstration of general conclusions, yet it is the best way of arguing which the nature of things ad-mits of, and may be looked on as so much the stronger, by how much the induction is more general. And if no exception occurs from phenomena, the conclusion may be pronounced generally. But if at any time afterwards any exception shall oc-cur from experiments, it may then begin to be pronounced with such exceptions as occur.172

So that one cannot deduce properties from the phenomena after all; there is a step of generalization involved, and this is open to exception. What we have, then, is not certainty but a degree of like-lihood that depends on circumstances. This was the notion of induc-tion, the "method of analysis ," as he calls it here, with which Newton later came to be identified, the method that would be so widely ad-vocated in the eighteenth century. But it is worth noting that it appears explicitly in very few places in his writings, and significantly qualifies his earlier declarations on the certainty and deductive character of the experimental philosophy.

The reader will have noted that the Principia has barely been men-tioned so far, even though it is this work that is most often cited in discussions of Newton's conception of science. Part of the reason for this order of proceeding is a conviction that the references to method in the optical works are more revealing.173 But more important is the peculiarity of mechanics as science, a peculiarity that Newton perhaps did not appreciate, and one that may help us understand why he so seriously underestimated the importance of retroduction to science proper. Not everyone, of course, would count this an underestima-tion. There are those who have seen in his exclusion of hypothesis a prescient declaration of positivist principle. But Newton was no pos-itivist, unless taking mechanics as a paradigm for all natural science be accounted positivism.

The peculiarity, to be brief, is this.174 The central concepts in the Principia are force, attraction, and gravity. Are they explanatory or descriptive? Do they signify causes or effects? Or both? There is a Janus-like ambiguity to these concepts, of a type we have already noted in light-ray but now much more marked, because light-rays can be conceived "physical ly" as substances (Newton) or modifica-

tions of a substance (Hooke). But what are forces? And where are they? How can the "mathemat ics" be given a "physical" interpre-tation here? When Newton says, for example, that gravity "really does exist , " he seems to mean no more than the inductive claim that falling bodies and planets behave in a particular way. Gravity "suff ices" for all these motions, he says in the General Scholium, meaning that it describes or predicts them.1 7 5 Ought forces be taken as causes, as explanation? The language of the definitions and axioms often suggests that they should be: Forces are said to be "ac t ions" on bodies; they " c o m p e l " bodies to change their state of motion; they "draw as ide" the planets from the rectilinear courses they would otherwise follow. But forces are also described as "propensi t ies , " themselves requiring causes.

The ambiguity enables Newton to claim that he can determine forces directly from motions, and at the same time represent this as deducing causes from effects: " B y this way of analysis we may proceed . . . from motions to the forces producing them, and in general from effects to their causes." 1 7 6 But if the force be supposed to explain why the body acts as it does, the inference ceases to be deductive. Retroduction is involved, since a cause is being postulated that is not itself observed. O n e can observe planets departing from a rectilinear path. But one cannot observe them being "drawn aside" from that path by gravitational forces, nor can one infer that forces are at work without calling upon a theory that requires independent jus-tification.177

The " c a u s e " here is arrived at simply by redescribing the effect, relying on the second law of motion. This technique does not seem to work anywhere else in the natural sciences. The cause to which one is inferring is ordinarily a separate event (e.g. , evacuating the receiver) or a postulated entity (e.g. , corpuscle, atmosphere). It will therefore not be contained in the effect in the convenient way in which force is contained in the very description (in theoretical terms) of the motion produced. Newton seems to have thought that the way ahead lay in finding the laws of force at each level; thus the short-range forces operating between corpuscles could (he hoped) reduce chem-ical transformation to law, as the inverse-square attractions of the Principia had done for the planetary motions. But experience later showed this to be a premature suggestion. One has to find out some-thing about the corpuscles first. And this would involve retroduction of the sort Newton had questioned, hypothesis that is warranted in an indirect and provisional way by its consequences and not by de-duction from, or generalization of, the phenomena.

He makes much in the Principia of a distinction we have already

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noted: "For I here design only to give a mathematical notion of those forces, without considering their physical causes and seats" (Defi-nition VIII). But this distinction tended to obscure the possibility that in contexts other than mechanics one might infer retroductively to such physical causes as corpuscles, relying on acceptably quantitative modes of testing, without this in any way constituting a "deduction" of cause from effect. In one passage, he suggests a rather different conception: "In mathematics, we are to investigate the quantities of the f o r c e s . . . then when we enter into physics, we compare those proportions with the phenomena of N a t u r e . . . . And this preparation being made, we argue more safely concerning the physical species, causes, and proportions of the forces."178 But despite the fact that the "preparation" seems to have been made, he never does go on in the Principia to this third stage.179

There was a special reason why he should make light of any such attempt. If he tried to specify the "cause of gravity," he faced, as he well knew, unpalatable alternatives. The solution favored by defend-ers of the mechanical philosophy, an interplanetary medium, he had shown to be inconsistent with the stability of the planetary system. All were agreed that action at a distance was unthinkable. As to what was left, Newton had some ideas but was well aware that all of them were wide open to criticism.180 It was much more prudent to refuse to engage in the search for causes, even though he knew that this would lead to the criticism that the Principia fell short of science be-cause it did not explain the motions it described, the objection that was in fact forcibly urged by critics as diverse as Leibniz, Huygens, and Berkeley.

This, then, may have been one further reason he inveighs so strongly against hypothesis in his later years: "Hitherto I have not been able to discover the cause of these properties of gravity from phenomena, and I feign no hypotheses."1 8 1 He saw the difficulties - no one better - of finding a "cause of gravity" that would fit the canons of explanation of the day. It was tempting to settle for the safely "deductive" road of a mechanics based on force and thus, in effect, to take mechanics as the model of what a science should be. The generation that followed was not difficult to convince on this score. Many prior to Newton, as we have seen, had recognized that deduction and induction have to be augmented by a more complex form of inference leading to the assessment and provi-sional acceptance of retroductive hypothesis. The force of New-ton's example, if it did not reverse the current entirely, at the very least served to discourage attempts to broaden the channels.182


Locke: The twilight of probability

But there were other voices, not least that of Newton's perceptive friend John Locke, who saw more clearly than did Newton what the consequences of the new approach to nature were for the traditional notions of knowledge and demonstration. Much of Book IV of his Essay Concerning Human Understanding is devoted to this issue. His conclusion is that a "science of bodies," in the classical sense of the term "science," is almost certainly out of the reach of human under-standing. To explain the perceived qualities and powers of the bodies of our everyday experience in terms of the shapes and motions of the constituent corpuscles of those bodies would require us to discover, not only these shapes and motions, but also the necessary conceptual connections between them and the perceptible qualities they are to explain. Neither stage seems possible.

Though we do have an adequate understanding of the primary qualities themselves,

yet not knowing what is the particular bulk, figure, and mo-tion of the greatest part of the bodies of the universe, we are ignorant of the several powers, efficacies, and ways of opera-tion, whereby the effects which we daily see are produced. These are hid from us in some things by being too remote, and in others by being too minute.183

Furthermore, in order to understand the substances around us, we have to take into account "those invisible fluids they are encompassed with, and upon whose motions and operations depend the greatest part of those qualities which are taken notice of in them."1 8 4 The "corpuscularian hypothesis," he goes on, is assuredly the one that goes farthest to explain the qualities of bodies. Yet, since it does not yield the necessary conceptual connections on which demonstration, and therefore knowledge, depend, "I doubt, whether with those fac-ulties we have, we shall ever be able to carry our general knowl-e d g e . . . in this part much farther."185

But Locke had come to realize that another alternative, entirely unconventional from the point of view of classical conceptualist no-tions of science, may be possible. Though the "broad daylight" can-not, in most cases, be reached, the "twilight of probability" may still be attainable.186 Probability is a "likeliness of truth," and it is based not on relations of ideas but on the experience of particulars. It may concern matters of fact; we learn by "constant experience" what reg-ularities occur in the world around us, such as that lead melts when heated sufficiently.187 Or it may be "speculative"; it may concern

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things which the senses of themselves cannot discover. "Analogy in these matters is the only help we have, and it is from that alone we draw all our grounds of probability."188 Since the causes of most of the effects we perceive in nature are hidden, we can only conjecture as to their nature. Hypothesis is thus permissible, but it has to be tested carefully against experiment; one must be careful not to attrib-ute a greater likelihood to it than the evidence warrants.1 8 9

Locke thus recognizes the distinction between (in our terms) in-duction and retroduction, and is quite clear that the best either can give is high probability (in the case of induction, sometimes ap-proaching complete assurance). He is vague about how retroduction is to work; his assumption that the hidden causes can be exhaustively described in terms of a few "primary" qualities drawn from everyday experience made analogy seem more effective an instrument than it ultimately turned out to be. But these "shortcomings" simply reflect the scarcity of successful retroduction in the science of his day.

It was only when the achievements of wave optics and of the chem-ical theory of the elements came to rival those of mechanics, in the early nineteenth century, that the potentialities of the retroductive mode of inference could be grasped, though even then only partially. By that time also, Kant had enlarged the understanding of the creative role of mind in the introduction and validation of such constructs as force and light-ray sufficiently to show the relation between phenom-ena and theory to be far more complex than the deductivist and inductivist accounts of science had allowed. But our story does not reach that far. It ends with Locke, meditating on the advances that we have come to call collectively the Scientific Revolution and con-cluding that the older conception of science would not fit the sort of knowledge the new inquiries into nature would produce.

Notes c 1 Francis Bacon, preface to The Great Instauration (1620), published as an

introduction to The New Organon, ed. Fulton Anderson (Indianapolis: Bobbs-Merrill, 1960), p. 7.

2 Ibid., p. 12. 3 John Locke, Essay Concerning Human Understanding, Bk. IV, Chap. 12,

Sec. 12. 4 See, for example, A. R. Hall, The Scientific Revolution, 1500-1800 (London:

Longmans, Green, 1954); I. B. Cohen, The Newtonian Revolution (Cambridge: Cambridge University Press, 1980). I have discussed some of the meth-odological innovations in "Medieval and Modern Science: Continuity or Discontinuity?", International Philosophical Quarterly, 5 (1965):103-29;


"Galilean Idealization," Studies in the History and Philosophy of Science, 16 (1985):247-73.

5 I have surveyed the period from a somewhat different perspective in "Empiricism and the Scientific Revolution," in Art, Science and History in the Renaissance, ed. Charles Singleton (Baltimore: Johns Hopkins Univer-sity Press, 1968), pp. 331-69.

6 At least three kinds of question might be asked about the "rationality" of an episode in the history of science. A historian might want to know what the scientists involved themselves said, or believed, they were doing and what made it science ("explicit rationality"). Or a historian might ask what sort of rationality, or linking of evidence and claim, was implicit in the procedures actually followed ("implicit rationality"). Or someone (prob-ably a philosopher) might impute a particular logical structure to the episode, in order to account for the "success" of the outcome as science ("imputed rationality"). See section 3 of my essay "The Rational and the Social in the History of Science" in Scientific Rationality: The Sociological Turn, ed. J. R. Brown (Dordrecht: Reidel, 1984), pp. 127-63.

7 See, e.g., Jonathan Barnes, "Aristotle's Theory of Demonstration," Phro-nesis, 14 (1969):123-52. The recent literature is surveyed in William Wians, Aristotle's Method in Biology, Ph.D. diss., University of Notre Dame, 1983

8 See, for example, Nicholas Jardine, "Galileo's Road to Truth and the Demonstrative Regress," Studies in the History and Philosophy of Science, 7 (1976), 277-318.

9 For the notion of a "conception of science," see my essay "The Conception of Science in Galileo's Work" in New Perspectives on Galileo, ed. R. Butts and J. Pitt (Dordrecht: Reidel, 1978), pp. 209-57.

10 "First of all I must establish, as well as I can, the proposition that ail Reasoning is either Deduction, Induction, or Retroduction.... In the course of a long life of active study of reasonings . . . if I had ever met with an argument not of one of these three kinds, I must certainly have per ceived it. But I have never found any such kind of argument except Analogy, which [ i s ] . . . a mixture of the three recognized kinds." "Kinds of Reasoning," in Collected Papers of Charles Sanders Peirce, ed. Charles Hartshome, Paul Weiss, and Arthur Burks, 8 vols. (Cambridge, Mass.: Harvard University Press, 1965-1967), 7:61.

11 Descartes, Rules for the Direction of the Mind, trans. E. S. Haldane and G. R. T. Ross (New York: Dover, 1955), pp. 3-5; for the Latin text, see Oeuvres de Descartes, ed. Charles Adam and Paul Tannery, 13 vols. (Paris: Cerf, 1897-1913), 10:362. Subsequent references to the Rules will give the Haldane-Ross page numbers in the standard English translations first, followed by the Adam-Tannery reference. (The latter is cited hereafter as AT.) The Haldane-Ross translations are in some cases modified.

12 In the enormous secondary literature on the Regulae, there is much stress on the difficulty of translating Descartes's Latin into a modern language. Descartes himself notes that he appropriates Latin terms to his own pur-poses (rule III, p. 7; AT, 10:369). Gregor Sebba provides a helpful discus-sion of the consequent burdens laid on interpreters of Descartes:

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"Retroversion and the History of Ideas," in Stuiiia Cartesiam I (Amsterdam: Quadratures, 1979), pp. 145-64.

13 Daniel Garber argues that the demonstration here need not be more geo-metrico (in geometrical style), in part because "deduction" is not to be taken in the strict sense: "Science and Certainty in Descartes," in Descartes: Critical and Interpretive Essays, ed. Michael Hooker (Baltimore: Johns Hop-kins University Press, 1978), p. 117. Weakening the sense of "deduction" will, he hopes, enable him to defend a consistently "deductivist" account of Descartes's remarks on method. Descartes's criticism of the syllogism on the grounds that the premises already implicitly contain the conclusion (rule X) is not, to my mind, a strong argument for the claim that Descartes wishes the term "deduction" to be taken in a looser sense than that in which it is employed, for example, in geometry, where deductive recon-structions of argument-forms ought always to be available, even if prem-ises are not always fully stated in practice.

14 Though the criteria of clarity and distinctness are not fully developed until later in the Discourse on Method, they are already explicitly functioning in rule XII (Rules, p. 41; AT, 10:418).

15 See Desmond M. Clarke, Descartes' Philosophy of Science (Manchester: Manchester University Press, 1982), pp. 166-79.

16 Rules, p. 15; AT, 10:380. 17 Rules, p. 29; AT, 10:402. 18 For a detailed reading of the Rules as a "timeless dialogue" with Aristotle,

see J. L. Marion, Sur l'ontologie grise de Descartes: Science Cartesienne et savoir Aristotelicienne dans les Regulae (Paris: Vrin, 1975).

19 Paul Olscamp, one of the strongest defenders of the thesis that Cartesian method is basically hypothetico-deductive in form, extends this interpre-tation back even to the Rules; see his introduction to his translation of the Discourse on Method (Indianapolis: Bobbs-Merrill, 1965). He finds support in rule XII, specifically in the following text, where the proper method of discovering the nature of the magnet is laid down: Since "there can be nothing to know in the magnet which does not consist of certain simple natures evident in themselves," the inquirer "will first collect all the ob-servations with which experience can supply him about this stone, and from these he will next try to deduce the character of that intermixture of simple natures which is necessary to produce all those effects . . . . He can (then) boldly assert that he has discovered the real nature of the magnet insofar as human intelligence and the given experimental obser-vations can supply him with this knowledge" (Rules, p. 47; AT, 10:427). But this is precisely not hypothetico-deductive method. Descartes's dis-cussions of the role of deduction in the analytic stage of inquiry and also of the role of conjecture (both of them in this same rule XII) to my mind exclude any hypothetico-deductive reading of the Rules.

20 Descartes, Discourse, p. 107; AT, 6:42. (I have used the Olscamp translation of the Discourse throughout; page references are to this translation.)

21 Discourse, p. 108; AT, 6:43. 22 Discourse, p. 108; AT, 6:44.


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34 Discourse, p. 129; AT, 6:77. 35 Descartes to Jean-Baptiste Morin, 13 July 1638, in AT, 2:199. 36 Ibid. 37 See Richard Popkin, The History of Scepticism from Erasmus to Spinoza (Berke-

ley and Los Angeles, University of California Press, 1979), Chap. 10; Phil-lip Sloan, "Descartes, the Sceptics, and the Rejection of Vitalism in Seventeenth-century Physiology," Studies in the History and Philosophy of Science, 8 (1977):l-28.

38 See, for example, Pierre Gassendi, Animadversiones, 2 vols. (Lyon, 1649), 1:203-20; quoted in Lynn Sumida Joy, Gassendi the Atomist: Advocate of History in an Age of Science (Cambridge: Cambridge University Press, 1987), pp. 176-7. Joy discusses at some length the ambiguous character of Gas-sendi's atomism as a scientific doctrine. Gassendi is content to secure atomism against traditional philosophical criticism, without concerning himself much with the inherent problem of how causal relations could be discovered between the shapes and motions of the atoms and the ob-servable properties of sensible bodies.

39 See Peter Dear, "Marin Mersenne and the Probabilistic Roots of 'Mitigated Scepticism,'" journal of the History of Philosophy, 22 (1984):173-205. Popkin, History of Scepticism, Chap. 7, argues that Mersenne is entirely skeptical about the possibility of any knowledge of unobserved natural causes, relying on passages such as this (p. 137): "For it can be said that we see only the outside, the surface of nature, without being able to enter inside, and we shall never possess any other science than that of its exterior effects, without being able to find out the reasons for them, and without knowing how they act, until it pleases God to deliver us from this misery": Les questions théologiques, physiques, morales, et mathématiques (Paris, 1636), p. 11. Dear argues for a more probabilist account, asserting that Mersenne, in the end, allows for probable knowledge in the domain of natural causes.

40 Descartes to Mersenne, 27(?) May 1638, in AT, 2:111 2. 41 Ibid., p. 143. 42 I do not see a shift in principle, of the sort Morris and others have claimed,

between the Discourse and the Principles, regarding the role of demon-stration and the status of hypothesis.

43 Abbé Claude Picot published a French translation of the Principia in 1647, incorporating many revisions and much additional material (Les principes de la philosophie, Paris). The differences between the two texts are partic-ularly revealing. They show that Descartes was wrestling with the epis-temic issues we have been examining here. See Ralph Blake, "Experience in Descartes' Theory of Method," in Theories of Scientific Method, ed. R. Blake, C. Ducasse, and E. Madden (Seattle: University of Washington Press, i960), pp. 98-9.

44 Descartes, Principles of Philosophy, trans. V. R. Miller and R. P. Miller (Dordrecht: Reidel, 1983), p. xxii; AT, vol. 9, pt. 2, p. 10. I have used the Miller and Miller translation of the Principles throughout, sometimes with slight modification; page references are to this translation, hereafter cited as Principles. n

45 Principles, p. xxi; AT, vol. 9, pt. 2, p. 9.


46 Principles, p. xxvii; AT, vol. 9, pt. 2, p. 20. 47 Principles, pp. 104-5; pt. Ill, sec. 43. (For the main text of the Principles,

the part and section numbers, found in the original at AT, vol. 8, pt. 1, will be given). The headings of the next sections (44-5) are, I think, to be understood as induced by theological caution: "That I nevertheless wish those [causes] I am proposing here to be taken as hypotheses" and "That I shall even assume here some which it is certain are false." The context is the theologically sensitive one of the formation of the planetary system and the motion of the earth. The reader is left to decide for himself what Descartes means by saying that even if the hypotheses he proposes are false, they will be as "useful" as though they were true, if they can account for everything.

48 Principles, p. 106; pt. Ill, sec. 46. The voluntarist-sounding language ought not to mislead us into supposing that Descartes is setting God's freedom as first principle here, as other scientists were to do later in the century. The freedom he alludes to is in regard to the configurations only, and it is invoked only because Descartes's first principles cannot of themselves specify these.

49 Principles, p. 107; pt. Ill, sec. 47. 50 Ibid., p. 283; pt. IV, sec. 199. 51 Ibid., p. 284; pt. IV, sec. 201. 52 Ibid., p. 285; pt. IV, sec. 203. 53 Ibid., p. 286; pt. IV, sec. 204. 54 Ibid., p. 287; pt. VI, sec. 205. 55 Ibid., p. 287; pt. IV, sec. 206. 56 For a review of these references, see Clarke, Descartes' Philosophy of Science,

pp. 186-94. Clarke argues against the rationalist reading and takes Des cartes to mean that the laws of mechanics rest on the most general features of everyday experience.

57 See Richard Blackwell, "Descartes' Laws of Motion," Isis, 57 (1966):220-34; "The Impact Rules of Cartesian Dynamics," Appendix 2 in Clarke, Descartes' Philosophy of Science, pp. 211-33.

58 Principles, p. 69; pt. II, sec. 53. 59 See Spyros Sakellariadis, "Descartes' Use of Empirical Data," Isis, 73

(1982):68-76. 60 In the French version, a very strong sentence is added: "And the dem-

onstrations [of the impact rules] are so certain that, even if experience were to appear to show us the opposite, we would nevertheless be obliged to place more trust in our reason than in our senses." It appears likely that Descartes wrote (or at least authorized) this, but one cannot be certain of it. See Principles, p. 69, translators' footnote.

61 I am, therefore, led to disagree with Larry Laudan's claim that the Des-cartes of the Principles is "the modest inquirer after truth who admits, especially throughout the latter half of the Principles, that science is an hypothetical and conjectural enterprise which offers its followers only a probable story": Science and Hypothesis (Dordrecht: Reidel, 1981), p. 34.

62 See Blake, "Experience in Descartes' Theory of Method," p. 92, and es-pecially Garber, "Science and Certainty," sec. 3.

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63 Olscamp's support of this thesis has already been noted. Laudan (Science and Hypothesis, p. 32) speaks of "Descartes' endorsement of the hypo-thetical method" in Part IV of the Principles. Other examples would not be difficult to find.

64 Principles, p. 243; Pt. IV, sec. 133. 65 Descartes to Mersenne, 18 December 1629, in AT, 1:100. See Sakellariadis,

"Descartes' Use of Empirical Data," pp. 69-71. 66 One might, perhaps, recall in his defense the Kuhnian doctrine that a

paradigm is not to be abandoned in the face of anomaly until there is another paradigm available to take its place. But Kuhn does emphasize that the occurrence of anomalies puts a paradigm under pressure, and it is the failure to acknowledge this that separates Cartesian method from what would ordinarily be regarded, even in a broad sense, as hypothetico-deductive method.

67 See A. I. Sabra, Theories of Light from Descartes to Newton (London: Old-bourne, 1967), Chap. 6.

68 Christiaan Huygens, Treatise on Light, trans. S. P. Thompson (London: Macmillan, 1912), pp. vi-vii; translation slightly modified.

69 There are important passages on method in Bacon's Valerius terminus (writ-ten 1603, published 1734); The Advancement of Learning (1605), expanded as Part I of his grand project The Great Instauration, under the title De augmentis scientiarum (1623); and in the natural histories (1622-1623); but the Novum organum was to be the definitive account of method, consti-tuting Part II of The Great Instauration.

70 William Whewell, The Philosophy of the Inductive Sciences Founded upon Their History, 2nd ed., 2 vols. (London: John W. Parker, 1847), 2:230.

71 Ibid., p. 232. Hereafter book and aphorism numbers will be given in parentheses.

72 For Bacon's New Organon I have used the translation by James Spedding et al., vol. 8 in The Works of Francis Bacon, ed. Spedding, 15 vols. (Boston: Taggard & Thompson, 1860-1872); reprinted in Fulton Anderson, ed., The New Organon (New York: Bobbs-Merrill, 1960).

73 See Lisa Jardine, Francis Bacon: Discovery and the Art of Discourse (Cam-bridge: Cambridge University Press, 1974), Chap. 4. Bacon realizes that his use of such terms as "metaphysics" and "form" is novel and asks the reader to recall that he is "taking the received terms (which come near-est to express the thing) in a sense agreeable to my own views" (II, 9).

74 There has been much debate as to how best to understand Bacon's use of the term "form." See, for example, C. Ducasse, "Francis Bacon's Phi-losophy of Science," in Blake et al., Theories of Scientific Method, Chap. 3; M. Hesse, "Francis Bacon," in A Critical History of Western Philosophy, ed. D. J. O'Connor (New York: Free Press, 1964), pp. 141-52.

75 Mary Horton, "Reply to Hattaway: Bacon's 'Knowledge Broken,'" journal of the History of Ideas, 43 (1982):487-504, esp. pp. 501-3.

76 Bacon, Preface to the New Organon, p. 36, in Anderson's edition. A couple of pages previously he says that in induction the business is done "as if by machinery" (p. 34). This is often quoted as though he were equating


induction with a mechanical process. But the metaphor of machinery is used here only to suggest that, just as machinery multiplies the energies of the unaided hand, so the new method of induction multiplies the effects attainable by the understanding with its aid.

77 Bacon, Preface to The Great Instauration, p. 20, in Anderson's edition of The New Organon.

78 Whewell, Philosophy of the Inductive Sciences, 2:237. Whewell argues that Bacon insufficiently appreciated the complexity of the first stage, where laws are formulated, and "did not justly appreciate the sagacity, the in-ventive genius, which all discovery requires" (p. 240).

79 John Piatt, a biophysicist, advocates "the simple and old-fashioned method of inductive inference that goes back to Francis Bacon," which is "like climbing a tree," in that it gives "clean results" by the constant devising of crucial experiments: "Strong Inference," Science, 146 (1964): 347-52. Peter Medawar follows Popper in rejecting (strict) induction as the method of science; see "Hypothesis and Imagination," in The Art of the Soluble (London: Methuen, 1967), pp. 131-55.

80 Peter Urbach, "Francis Bacon as a Precursor to Popper," British journal for the Philosophy of Science, 33 (1982):113-32. Urbach argues, on the basis of a textual comparison of passages from Bacon and Popper, that there are startling parallels of detail between the two. There is a touch of irony about this, in that Popper more than once dismisses Bacon as an "induc-tivist." Urbach argues (correctly, I think) that Popper misrepresents his predecessor.

81 Mary Horton, "In Defence of Francis Bacon," Studies in the History and Philosophy of Science, 4 (1973):241-78. This is the most thorough recent treatment of Bacon's methodology. In her detailed defense of Bacon against the charge of narrow inductivism leveled against him by Medawar, she leans too far, perhaps, in the opposite direction, making induction, for Bacon, an "intuitive leap" (p. 271). Ducasse, "Bacon's Philosophy of Science," argues that Bacon made use of the "method of hypothesis" in much the way the modern scientist does. Sabra (Theories of Light, pp. 173-81) argues exactly the opposite view.

82 Horton argues that "in Book I Bacon the propagandist can be seen at work, exaggerating differences, simplifying descriptions, persuading the reader of the utility of the method he is going to put forward" ("In Defence of Bacon," p. 242), so she chooses to rely on Book II for her exposition, where the "infallible" character of the new method is less in evidence (though not entirely absent). Urbach speculates that Bacon may have exaggerated the value of his method in order "to secure grants from the king" ("Bacon as Precursor," p. 131).

83 Notably by Popper: "Bacon's term 'anticipation' means almost the same as 'hypothesis' in my way of using the term": Logic of Scientific Discovery (London: Hutchinson, 1959), p. 279. Since Bacon rejects "anticipations," Popper takes him to be rejecting the role of hypothesis and testing. Horton ("In Defence of Bacon, pp. 248-50) and Urbach ("Bacon as Predecessor," pp. 116-8) have no difficulty in showing just how serious a misreading of Bacon this is.

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84 Horton, "In Defence of Bacon," p. 247. 85 Preface to The Great Instauration, p. 20. 86 See Jardine, Bacon, Chap. 6. 87 "One contradictory instance overthrows a conjecture as to the form" (II,

18). Horton claims that for Bacon the method of induction is "explicitly an alogical process," an "exercise of the intuition": "In Defence of Bacon," p. 262. She relies on terms like "invention" and "liberty of the under-standing," from the Montagu translation; Works of Francis Bacon, ed. Basil Montagu (Philadelphia: Hart, 1851). The Spedding translation has "dis-covery" and "indulgency of the understanding," which do not lend them-selves so easily to her argument.

88 See De augmentis scientiarum, Bk. Ill, Chap. 4. Urbach's comment that even a small number of simple natures can yield an infinite variety of theories ("Bacon as Precursor," p. 129) is unpersuasive, if we are asking what Bacon himself thought his method could yield.

89 Preface to The Great Instauration, p. 21. 90 See also, Bk. I, aphorism 69. One of his best-remembered aphorisms (I,

95) is the parable of the insects, where he sees himself as a bee, not an ant (the "men of experiment" who "only collect and use"), at one extreme; and not as a spider (the "reasoners" who "make cobwebs out of their own substance"), at the other. The bee both gathers and transforms; likewise, the natural philosopher must gather from nature but transform what is gathered by the power of the understanding. In that way, a "league" may be made between the "experimental" and the "rational" faculties.

91 In Bk. II, aphorism 39, he concedes that the telescope has furnished some "noble discoveries" but says that he regards demonstration of this kind "with suspicion," because it stops short with "those few discoveries" and fails to search out other "equally worthy things." His suspicion of instru-mentation suggests a narrower empiricism than was really characteristic of him.

92 Tantalizing because mathematics plays such a small part in his general account of method. This is, in fact, one of the very few places (Urbach lists some others) where he attaches importance to its role in natural inquiry. Urbach's contention (against the received view) that the emphasis Bacon places on the importance of mathematics for the advancement of science "could hardly be greater" ("Bacon as Precursor," p. 125) is surely overstated.

93 Aristotle, Posterior Analytics, 1.2. 94 It is worth noting that although a belief in corpuscles became almost

universal among natural scientists in the seventeenth century, there was no strong warrant for the belief until very much later - not until John Dalton's work in the nineteenth. It would be interesting to inquire just why the belief became firmly fixed long before any sort of quantitative argument was available to support it, but that would lead us far afield.

95 Urbach ("Bacon as Precursor," p. 130) notes a similarity of sorts here between Bacon and Popper; neither is able to give a good account of the force of the positive outcome. But the accounts they do give are al-


together different, since Bacon has none of Popper's qualms about verification.

96 Laudan argues that Boyle's method was more Cartesian than Baconian (Science and Hypothesis, p. 55). But this is because he makes the Descartes of the Principles a conjectural thinker (p. 34), whereas Bacon is said to believe that principles "will emerge in [a] mechanical way from a study of nature" (p. 37). We have seen reason to question both of these char-acterizations earlier, and hence we will situate Boyle (as he situated himself) within the Baconian tradition, while not denying the affinities between his notions of method and those of Descartes in certain respects. But, as Laudan himself notes (p. 44), these affinities may ultimately be more easily accounted for by the fact that both Boyle and Bacon defended corpuscular modes of explanation at the microlevel than by the assump-tion of any strong, direct influence of Descartes on Boyle. See Rose-Mary Sargent, "Robert Boyle's Baconian Inheritance," Studies in the History and Philosophy of Science, 17 (1986):469-86.

97 See Norma Emerton, The Scientific Reinterpretation of Form (Ithaca, N.Y.: Cornell University Press, 1984), Chaps. 5 and 8.

98 See The Excellency and Grounds of the Corpuscular or Mechanical Philosophy, in The Works of the Honourable Robert Boyle, ed. Thomas Birch, 6 vols. (London 1772), 1:68-78.

99 See R. S. Westfall, "Unpublished Boyle Papers Relating to Scientific Method," Annals of Science, 12 (1956):63-73, 103-17.

100 Ibid., pp. 116-17. 101 Boyle, Works, 2:45. See Laudan, Science and Hypothesis, pp. 32-44. 102 Boyle, WorJts, 1:303. 103 Preface to The Great Instauration, p. 14. 104 See Robert Westman, "Kepler's Theory of Physical Hypotheses," section

3 of "Kepler's Theory of Hypotheses and the 'Realist Dilemma,'" Studies in the History and Philosophy of Science, 3 (1972):233-64, and my "Kepler's Dynamics of Planetary Motion," section 3 of "The Explanation of Distant Action: Historical Notes," in Philosophical Consequences of Quantum Theory, ed. J. C. Cushing and E. McMullin (Notre Dame, Ind.: University of Notre Dame Press, 1989), pp. 272-302.

105 Nicholas Jardine, The Birth of History and Philosophy of Science (Cambridge: Cambridge University Press, 1984), Chap. 7.

106 Kepler's Apologia Tychonis contra Ursum was composed under the insistent prodding of Tycho Brahe in late 1600 but was not published until 1858. Jardine's Birth of History is a translation of, and commentary on, the Apol-ogia. Page references here are to the Jardine edition. In an earlier article, Jardine outlined the essentials of Kepler's analysis of hypothesis in the Apologia: See "The Forging of Modern Realism: Clavius and Kepler against the Sceptics," Studies in the History and Philosophy of Science, 10 (1979):141-74.

107 See section 3 of my "Goals of Natural Science," Proceedings of the American Philosophical Association, 58 (1984):37-64.

108 Apologia, p. 143. 109 It had been known since the time of Hipparchus that two mathematically

86 Ernan McMullin

different techniques, the epicycle and the eccentric, could describe the same celestial motion.

110 Apologia, pp. 153-4. Kepler identifies the astronomical hypothesis with the true motion in a way that the modern reader might find troublesome. It appears less strange if we consider his definition of "hypothesis": "We call a 'hypothesis' generically whatever is set out as certain and dem-onstrated for the purpose of any demonstration whatever" (ibid., p. 138). He may have framed the definition in these terms because of his op-position to the traditional fictionalist account of astronomical hypotheses. Kepler wanted to insist that even though such hypotheses are postulates, they are postulated to be true. Galileo later makes the same point re-garding the Copernican hypothesis.

111 In a parallel passage in the Mysterium cosmographicum, Kepler expressed this idea more clearly as a "separation of motions between the earth and the heaven": Kepler, Mysterium cosmographicum, in Gesammelte Werke, ed. W. van Dyck, M. Caspar, and F. Hammer, 19 vols. (Munich, 1937-1975), 1:15. See Jardine, "Forging of Modern Realism," p. 158.

112 Apologia, p. 142. 113 Made all the more difficult by a clumsy use of the categories of Aristo-

telian demonstration. In "Forging of Modern Realism," pp. 172-3, Jardine gives a persuasive reading of these categories in terminology more ap-propriate to Kepler's context.

114 Apologia, p. 142. 115 Ibid., p. 140. 116 Mysterium cosmographicum, 1:15; Jardine's "Forging of Modern Realism,"

p. 157. 117 Apologia, p. 142. 118 Ibid., p. 141. 119 Ibid., p. 155. 120 Although the Apologia was not published during Kepler's lifetime, many

similar remarks on hypothesis occur in his published works (see West-man, "Kepler's Theory," sec. 3). However, these remarks were not much noted by his contemporaries, as far as we can tell. Their importance lies rather in the testimony they afford of how far reflection on the status of hypothetical constructs could have progressed by 1600.

121 Kepler remarks, as early as the Mysterium cosmographicum, that although Copernicus's original discovery had been "like that of a blind man feeling his way with a stick," it can now be warranted "by being correctly deduced from a priori reasons, from causes, and from the concept of creation" (1:26). Kepler was evidently aware that the issue as to which body "really" was at rest required him to call on broader physical, meta-physical, and theological considerations.

122 Apologia, p. 151. 123 Lorraine Daston argues that Galileo's forays into the microdomain were

limited by "his vision of natural philosophy as the mathematical rede-scription of the phenomena, coupled with his suspicion of the imagi-nation on traditional Aristotelian grounds": "Galilean Analogies: Imagination at the Bounds of Sense," Isis, 75 (1984):302-10. Still, as she


notes, he was not entirely averse to retroduction in this domain; witness, for example, his analysis of fire, in The Assayer, in terms of a multitude of minute particles. The diffidence he sometimes displays regarding his attempts to call on the imagination to reconstruct hidden causes might also have proceeded, one supposes, from his realization that such spec-ulation could not be tied to experiment in any way.

124 Galileo expressed his dissent in notes written for a response to Robert Bellarmine's letter to Paolo Foscarini in 1615, where Bellarmine says that the "hypothetical" mode of speech proper to "mathematicians" excludes them from making a truth-claim about the models they use; see Bellar-mine to Foscarini, 12 April 1615, in Le opere di Galileo Galilei, ed. Antonio Favaro, 20 vols. (Florence: Barbera, 1929-1939), 12:171. Galileo distin-guishes between "natural" suppositions in astronomy, which are claimed to be true, and "chimerical" ones, known to be false and intended only for purposes of computation ("Considerations on the Copernican Opin-ion," in Opere, 5:357). He insists that the Copernican position must be regarded as "true and real" (ibid., Opere, 5:362).

125 Apart from a single protective comment, in a preface obviously written to conform to the censor's specifications.

126 Galileo, Dialogo sopra i due massimi sistemi del mondo, Opere, 7:454, 470, 450, 471, 473; English translation, Dialogue Concerning the Two Chief World Systems, by Stillman Drake (Berkeley and Los Angeles, University of California Press, 1953), pp. 428, 444, 424, 446, 448. Emphasis added.

127 Commission Report on the Dialogue, Opere, 19:326. 128 Dialogo, in Opere, 7:443; Dialogue, p. 417. 129 Opere, 7:447, 417; Dialogue, pp. 421, 445. 130 Opere, 7:444; Dialogue, p. 418. 131 Opere, 7:458; Dialogue, p. 432. 132 William A. Wallace, Galileo and His Sources (Princeton: Princeton Uni-

versity Press, 1984). 133 What complicates Wallace's reconstruction of the story is that no copies

exist of the 1588 lecture notes, and the only clues we have to them are a plagiarized version published by Ludovicus Carbone in 1597 and Valla's own much later Logica of 1622.

134. Wallace, in fact, makes the much stronger claim that these notes can be taken to represent Galileo's own philosophical position at this early stage of his intellectual career: Galileo and His Sources, Chap. 6. This would seem an extremely risky inference, given Wallace's own well-documented tracing of the sources of Galileo's youthful works to the class notes published by the faculty of the Collegio Romano. The notes of a young teacher, in his first couple of years of teaching, who copies a senior colleague's lecture notes for his own use, are hardly a reliable testimony to the beginner's own views at the time. But they do testify to some knowledge, at least, of what was in the passages copied.

135 Wallace, Galileo and His Sources, pp. 122-6. 136 For an analysis of the convertibility condition required to make the rea-

soning demonstrative, see my "Truth and Explanatory Success," sec. 1.

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137 The maxim owes its innocent look to a notorious ambiguity in the cor-relative notions of effect and cause. Taking them to designate singulars, it is correct to say that this particular effect can only, have been caused by one particular cause. But if they designate kinds (as they do here for Galileo, and as they ordinarily do in science), then it is not true that this kind of event must, in principle, proceed from only one specific kind of cause. There is a further ambiguity in the notion of cause, which can be taken either ontologically or epistemologically. A particular effect can only have one cause in the first sense. But it may have more than one explanation; there may be more than one account that would satisfactorily explain it. The basic flaw in the maxim is that it presupposes full knowl-edge of both effect and cause, which is precisely what is lacking in the situation of scientific inquiry.

138 This possibility is discussed in some detail in my Introduction to Galileo, Man of Science, ed. E. McMullin (New York: Basic Books, 1967), pp. 33-5.

139 At the end of the Dialogue, Galileo concludes that "we have strong evi-dences in favor of the Copernican system, among which three have been shown to be very convincing" (Dialogo, in Opere, 7:487; Dialogue, p. 462). But it seems quite clear that this is a diplomatic form of wording, not a claim for high likelihood as opposed to demonstrative certainty. Ian Hacking notes that the word probabilita, which occurs several times in the Dialogue, has the older sense there of "supported by authorities"; see Hacking, The Emergence of Probability (Cambridge: Cambridge Uni-versity Press, 1975), p. 26. What Galileo is after is "knowledge, not opinion," and hence this sort of "probability" would have been insuf-ficient. Hacking adds, however, that Galileo wrote with insight about games of chance and also that in the Two New Sciences he speaks once of "increasing the probability" of a particular postulate by means of an experiment, "so that it will fall little short of demonstration" (Opere, 8:205). This last is close to the later concept (clear, for example, in Leibniz) that relates probability to evidence. But Galileo never (so far as I can see) attaches this notion of probability to any significant claim he is himself making in his natural philosophy.

140 Galileo, Discorsi e dimostrazioni matematiche, in Opere, 8:202; English trans-lation, Two New Sciences, Stillman Drake (Madison: University of Wis-consin Press, 1974). Drake's translation of Two New Sciences is used throughout. Drake gives the pagination of the Opere, so a reference to the Opere will suffice to locate the translated passage.

141 There were three other possibilities. He tried to derive the proposition that bodies falling from the same height on planes of different inclination attain the same speeds, but he was unable to do so. (In 1638, he attempted the proof again and wrote a version that Vincenzo Viviani added to the second edition; see Discorsi, in Opere, 8:214.) His intuition (lume naturale; Discorsi, in Opere, 8:205) assures him of the truth of the proposition, and he then uses pendulum experiments, "which leave no room for doubt as to the truth of our assumption" (ibid., p. 207). What is interesting here is that experiment is being used, not to test a definition by a con-


sequence mathematically derived from it, but to supplement mathemat-ical intuition. The experiment supports the central claim of the uniformity of acceleration of falling bodies, therefore, only in a very indirect way, as Galileo appears to realize. A second consequence is the parabolic shape of projectile trajectories. There is only a passing allusion to an experi-mental test of this consequence in Two New Sciences (p. 185), which is curious, in the light of interpretations recently given of some working notes dating from around 1605, suggesting that Galileo had already at that time found an experimental way of showing projectile paths to be parabolic: See Stillman Drake and James MacLachlen, "Galileo's Discov-ery of the Parabolic Trajectory," Scientific American, 232 (March 1975): 102-10; R. N. Naylor, "Galileo's Theory of Projectile Motion," Isis, 71 (1981):550-70. A third consequence is that the maximum projectile range occurs at a 45-degree angle of projection, a phenomenon already well known before Galileo's day. The derivation of this by "mathematical demonstration" is welcomed by him, not as affording an additional war-rant for the truth of his postulates, but because it "opens the mind" to a "certainty" about "other effects without need of recourse to experi-ments" (p. 296). He is obviously assuming that after his success with the inclined plane, his postulates do not need further testing.

142 Opere, 8:213. 143 Ibid., p. 212. 144 Ibid., p. 197. 145 Ibid., p. 190. 146 Wallace argues that he can (see Galileo and His Sources, Chap. 6, sec. 4)

and that this had been shown by the Aristotelians of the Collegio Ro-mano, who supposedly formed Galileo's view on this topic in their ac-count of ex suppositione reasoning. Winifred Wisan raises doubts about the basic presumption of this argument, namely that there is a consistent doctrine underlying Galileo's use of the term ex suppositione, a common term at the time; see Wisan, "On Argument ex suppositione falsa," Studies in the History and Philosophy of Science, 15 (1984):227-36.

147 See Winifred Wisan, "Galileo's Scientific Method: A Reexamination," in New Perspectives on Galileo, ed. Butts and Pitt, pp. 1-58.

148 The many complications in Galileo's notion of "impediment" cannot be dealt with here. See my "Galilean Idealization."

149 Discorsi, in Opere, 8:131. 150 Ibid., p. 197. 151 Galileo to Giovanni Battista Baliani, 7 January 1639, in Opere, 18:12-13.

A similar passage occurs in a letter to Pierre de Carcavi on 5 June 1637, where Galileo says that his "demonstrations" would "lose nothing of their force and conclusiveness," even if falling bodies were found not to behave as his principle required them to (Opere, 17:90).

152 Lectiones opticae: The Optical Papers of Isaac Newton, ed. Alan Shapiro, (Cambridge: Cambridge University Press, 1984), 1:439. See Alan Shapiro, "Experiment and Mathematics in Newton's Theory of Color," Physics Today, 37 (1984):34-42. I am indebted to Dr. Shapiro for our many dis-cussions of Newton's comments on method.

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153 As he describes it in a letter to Henry Oldenburg, secretary of the Royal Society, on 18 January 1672; see The Correspondence of Isaac Newton, ed. H. W. Turnbull (Cambridge: Cambridge University Press, 1959), 1:82.

154 "New theory about Light and Colours," in Isaac Newton's Papers and Letters on Natural Philosophy, ed. I. B. Cohen (Cambridge, Mass.: Harvard Uni-versity Press, 1958), p. 57

155 Hooke's response to Newton was given in a paper to the Royal Society, delivered a week after Newton's, on 15 February 1672; in Papers and Letters, p. 114.

156 Newton's response to Hooke, communicated to the Royal Society; in ibid., p. 119.

157 Ibid., p. 129. 158 Newton to Oldenburg, 8 July 1672; in ibid., p. 93. 159 In a detailed analysis of Newton's use of the term "hypothesis," Alex-

andre Koyr6 distinguishes among five senses: (1) a proposition posed in order to deduce the logical consequences, as in mathematics; (2) a prop-osition for which there is not yet adequate evidence, but one that is, in principle, capable of being "demonstrated" from experience; (3) a prop-osition put forward to "save the phenomena," without any commitment, one way or the other, as to truth; (4) a proposition incapable in principle of quantitative observational test; (5) a proposition known to be false but postulated as a premise from which to draw true conclusions. Koyre says, "In the first edition of the Principia, this term is taken in its classical sense, as a fundamental proposition of a theory. In the second edition, on the contrary, a hypothesis is taken to be a fiction, and mostly a false one, or, at the very least, an unproved assertion." See Koyre, "Concept and Experience in Newton's Scientific Thought," in Newtonian Studies (Chicago: University of Chicago Press, 1965), p. 40. Koyre explains the evident tension between Newton's declarations about hypothesis and the actual practice evidenced in his writings by this fivefold ambiguity in the key term. He argues that the negative senses of the term predom-inated more and more in the later writings (p. 37). See also Anita Pam-pusch, "'Experimental,' 'Metaphysical' and 'Hypothetical' Philosophy in Newton's Methodology," Centaurus, 18 (1974):289-300.

160 Huygens, communication to the Royal Society; Papers and Letters, p. 136. 161 Newton, response to Huygens, 3 April 1673; Papers and Letters, p. 144.

After reviewing the variety of Newton's use of the term "hypothesis" over the years, especially in the successive editions of the Principia, I. B. Cohen concluded that Newton's "open hostility" to "any form of hypothesis" developed only after 1692. See Cohen's "Hypotheses in Newton's Philosophy," Physis, 8 (1966):163-84, and "Newton's Use of the Word Hypothesis," Appendix 1 to Cohen's Franklin and Newton (Cam-bridge, Mass.: Harvard University Press, 1966). But texts like the one cited here seem to indicate pretty strong antipathy to hypothesis on Newton's part, from the beginning of his career.

162 Newton to Ignace Pardies, in Papers and Letters, p. 106. 163 Newton to the Royal Society, in Papers and Letters, p. 178. 164 Newton, Opticks (New York: Dover, 1952), p. 1.


165 Ibid., Book II, Part 3, Props. 12-20; see p. 281. 166 Ibid., p. 281. 167 The first edition of the Opticks (1704) ended with sixteen queries (1-16);

seven more were added to the Latin edition of 1706 (now numbered as 25-31); and finally eight to the third edition of 1717 (now numbered 17-24). The fact that he continued to add queries until 1717 (when he was seventy-five years old) indicates how actively he remained engaged in "hypothesis."

168 When he writes, "The main business of natural philosophy is to argue from phenomena without feigning hypotheses" (Opticks, p. 369), this is clearly directed against the overly speculative practices of the mechanical philosophers, though he still supposes here that science consists of de-ducing causes from effects. The famous statement, "For hypotheses are not to be regarded in the experimental philosophy" (p. 404), is aimed at those who urge fanciful hypotheses against those who (like Newton) claim to derive their conclusions directly from experiments.

169 Opticks, p. 404. 170 Newton to Cotes, 28 March 1713, in Correspondence, 5:397. 171 Newton, Principia, trans. A. Motte and F. Cajori (Berkeley and Los An-

geles, University of California Press, 1934), p. 547. 172 Opticks, p. 404. 173 See Thomas Kuhn, "Newton's Optical Papers," in Papers and Letters, pp.

27-45. 174 This topic is more fully treated in "Realism in the History of Mechanics,"

Chap. 13 of my Rationality, Realism, and the Growth of Knowledge (Dor-drecht: Reidel, 1990).

175 The Motte-Cajori translation of the Principia is misleading here. Gravity is said to act "according to the laws which we have explained, and abundantly serves to account for all the motions" (p. 547). But expono and sufficio do not readily support this causal rendering as "explain" and "account for." The passage is better read as "according to the laws we have expounded and suffices for all the motions." Cohen, however, attributes the stronger causal sense to this passage (Newtonian Revolution, pp. 113-14).

176 Opticks, p. 404. 177 See my essay "The Significance of Newton's Principia for Empiricism,"

in Religion, Science and Worldview, ed. M. J. Osier and P. Farber (Cam-bridge: Cambridge University Press, 1985), pp. 49-53.

178 Newton, Principia, Bk. I, Prop. 69, Scholium, p. 192. 179 I. B. Cohen characterizes the "Newtonian style" in science in terms of

three "phases," the first a purely mathematical development of an im-aginative construct, the second a comparison of the consequences of this construct with nature, and the third an elaboration of the construct with a view to new and broader applications. But there is a "sequel" to phase 3, he says, namely the search for causes, which Newton acknowledges but does not engage in; aee The Newtonian Revolution (Cambridge, Mass.: Harvard University Press, 1980), p. 64 Elsewhere, however, Cohen says: "The style I have called Newtonian does not consist merely of deter-

ernan mcmullin - conceptions of science in the scientific revolution

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