1. Introduction
The best-known element of Newton’s methodological views is his rejection of hypotheses. Although his attitude toward hypotheses underwent subtle changes throughout his career, he expressed his general rejection of them on many occasions. For example, in the General Scholium to the Principia, he famously writes that when it comes to the cause of gravity, “I do not feign hypotheses” (P.943). Earlier, in reply to the critiques of his optical paper of 1672, he similarly expressed a strong aversion to accepting hypotheses. “My theory,” he declared, “contain[s] nothing else than certain properties of light which, now discovered, I think are not difficult to prove, and which if I did not know to be true, I should prefer to reject as vain and empty speculation, than acknowledge them as my hypothesis” (NCorres.I.144).
Newton’s rejection of hypotheses has often been interpreted as a rejection of Hypothetico-Deductivism (HD),Footnote 1 which, importantly, is claimed to have been practiced by his contemporaries, such as Descartes, Huygens, and (to a lesser extent) Leibniz.Footnote 2 HD maintains that observed consequences of a hypothesis provide support for it, and this is the only (or the main) avenue through which scientific theories are confirmed. As Steffen Ducheyne correctly observes, “[O]n a hypothetico-deductive rendering, a theoretical statement is confirmed when the consequences drawn from it are verified by observation—and that is basically it” (Ducheyne Reference Ducheyne2012, 57; emphasis added).Footnote 3
I believe it is a significant, but unfortunately widespread, mistake to interpret Newton’s rejection of hypotheses as a mere rejection of HD. It is an equally serious and widespread mistake to think that HD was popular among Newton’s contemporaries. Indeed, I will argue that none of the figures usually associated with HD adhered to it. Of course, Newton rejected HD—or would have, had he known about it. After all, HD was formulated by twentieth-century philosophers of science, such as Hempel (Reference Hempel1966, chapters 2 and 3) and, in a different vein, Popper (Reference Popper2002).Footnote 4 However, Newton’s rejection of HD is not particularly noteworthy. Even at the most abstract philosophical level and to those of us who, unlike Newton, are not adamantly against hypotheses, HD appears too simplistic and hopelessly problematic.Footnote 5 By contrast, there was a far more sophisticated and plausible hypothesis-based account of scientific methodology that enjoyed widespread popularity in the early modern period. I call this method Inference to the Best Hypothesis (IBH). What is particularly noteworthy about Newton’s methodology is his rejection of IBH, and especially of one of its strongest forms, which we may call Inference to the Only Plausible Hypothesis (IOPH).
The main goal of this article is to establish this point. That is, I aim to show that it is a mistake to take HD as the relevant rival to Newton’s “inductive” method. In the context of early modern views on the methodology of natural philosophy, the rival was IBH, especially its stronger variant IOPH. I will briefly introduce the basic features of IBH and IOPH. I will then argue that they enjoyed widespread popularity at the time, not only among those usually considered to be “speculative” philosophers, such as Descartes and Leibniz, but also among some of the most prominent proponents of “experimental” philosophy, such as Boyle and Huygens. I will finally argue that, despite their widespread popularity, Newton rejected IBH and IOPH.
My argument also bears on how we understand experimental philosophy. A central commitment of the experimental philosophers was the rejection of hypotheses adopted on little or no experimental evidence, but this should not be conflated with a general aversion to hypotheses.Footnote 6 Let us call a method hypothetical if it allows that a hypothesis proposed to explain a body of phenomena, P, can achieve a high enough degree of probability to be included in one’s official theory chiefly by plausibly accounting for P. On this definition, HD, IBH, and IOPH are all hypothetical methods. My argument shows that one could be an experimental philosopher and still employ a hypothetical method; indeed, some of the prominent experimental philosophers championed such methods. Newton’s claim that hypotheses of any kind “have no place in experimental philosophy” (P.943) thus reflects a radical version of experimental philosophy, one that would even exclude Boyle and Huygens.
The structure of the article is as follows. In section 2, I will briefly explain how HD and IBH differ. In section 3, I discuss other uses of hypotheses that must be distinguished from their use in hypothetical methods. One could employ hypotheses in these senses while either accepting or rejecting hypothetical methods. Section 4 examines hypothetical methods of Boyle, Descartes, Leibniz, and Huygens. Due to space constraints, my discussion of each is brief. However, I believe it is sufficient to show that none of them championed HD and that, although in different ways, all of them endorsed IBH—the last three primarily in the form of IOPH. Section 5 discusses Newton’s rejection of hypotheses, where I provide evidence that he rejected IOPH in particular.
2. IBH versus HD: What is the difference?
Suppose one is considering whether a hypothesis, H, is true. According to HD, to do this, one must examine H’s “test implications”: statements of the form “certain observable events…should occur under specified circumstances” (Hempel Reference Hempel1966, 197) that deductively follow from H.Footnote 7 If test implications are false, then H “must indeed be rejected” (ibid.). If, however, a number of test implications turn out to obtain, then “while this result does not afford a complete proof for the hypothesis, it provides at least some support, some partial corroboration or confirmation for it” (ibid., 198). In this way, the hypothetico-deductive method places utmost emphasis on the observation of the deductive consequences of a hypothesis.
By contrast, according to IBH, a hypothesis is worthy of adoption only if it is the best among all the available hypotheses compatible with a body of observations—assuming, of course, that the best is good enough.Footnote 8 There is much in common between IBH and what in the twentieth century became known as Inference to the Best Explanation (IBE). Both accounts were developed largely in response to the problem of underdetermination.Footnote 9 And both maintain that this problem is solved if we focus only on the best, as determined by a set of theoretic virtues such as simplicity and explanatory power. However, there is a fundamental difference between IBH and at least some prominent versions of IBE (which is why I distinguish the two). Some contemporary proponents of IBE hold that “our inferential practices are governed by explanatory considerations” (Lipton Reference Lipton2004, 56). And this entails that, as the name suggests, according to IBE, the best hypothesis is the one that offers the best explanation. In other words, on this view explanatory power takes pride of place among theoretic virtues. By contrast, proponents of IBH in the early modern period considered explanatory power as only one, and typically not the most important, among theoretic virtues.
IOPH is a special case and a stronger form of IBH. According to IOPH, one may adopt H only if H is the only hypothesis that satisfies some minimum criteria of plausibility (which, of course, entails that H is the best). The specific criterion of plausibility varies from one philosopher to another. However, as I will argue, many prominent natural philosophers in the early modern period were particularly fond of this method.
The main difference between HD and IBH or IOPH is as follows. According to HD, the level of support or confirmation that a hypothesis, H, receives is essentially determined by the totality of its confirmed test implications, I. In other words, support for H is determined by the contents of H and I and their relationship. Although proponents of HD use additional criteria, like simplicity, as tie-breakers among candidate hypotheses,Footnote 10 these criteria are not central to the core idea of hypothetico-deductivism. Therefore, the more emphasis one places on them, the farther one departs from the core of HD.
By contrast, IBH is holistic in its essence. The merits of H given I cannot be assessed in isolation; they depend on how H compares with its alternatives and on the extent to which it outperforms them. In this respect, IBH is a genuinely comparative method in which theoretical virtues play a central role, standing in contrast to HD, where the primary source of confirmation lies in the deductive consequences of the theory. IOPH imposes an even stronger requirement. According to it, the merits of H depend not only on how well H accounts for the observations but also on how poorly the alternatives fare. Unless all competing hypotheses are deemed implausible, IOPH withholds any positive assessment of a theory. Thus, while HD and IBH allow a hypothesis to be well confirmed even in the presence of serious competitors, IOPH remains silent so long as plausible alternatives remain.
3. Other uses of hypotheses
My claim that IBH can be considered the salient hypothetical method in the early modern period is not intended to suggest that hypotheses were not used in other, independent ways. Hypotheses were used in ways other than what I earlier called hypothetical methods. I will briefly mention three such uses here to distinguish them from both IBH and HD.
(1) Hypotheses as Tools. The first of these uses was as calculation devices or as aids to memory. Although it had its detractors,Footnote 11 this was an influential interpretation of astronomical hypotheses since antiquity.Footnote 12 Osiander was referring to this conception of hypotheses when he wrote in his preface to Copernicus’s De Revolutionibus, that if in astronomy “any causes are devised by the imagination, as indeed very many are, they are not put forward to convince anyone that they are true, but merely to provide a reliable basis for computation” (Copernicus Reference Copernicus, Dobrzycki and Rosen2016, xvi). The idea is that astronomical hypotheses are sometimes devised to “save the phenomena,” which is sufficient for providing reliable predictions. However, a “physically true” account of the motions of heavenly bodies in astronomy—an account of the nature of those bodies—might be impossible to attain, at least given our current epistemic status.Footnote 13
Although the paradigm of this use of hypotheses was in astronomy, it was also considered applicable to other fields. For instance, in a letter of 1693 to Thomas Molyneux, John Locke writes, “[U]pon such grounds as are the establish’d history of diseases hypotheses might with less danger be erected, which I think are so far useful, as they serve as an art of memory to direct the physician in particular cases, but not to be rely’d on as foundations of reasoning, or verities to be contended for” (LCorres.IV.629).
The first review of the Principia in Journal des sçavans, which was published anonymously, alluded to this conception when the reviewer claimed that Newton’s work contains “the most perfect” mechanics but not physics because “it is only by hypotheses that are, most of them, arbitrary” that he has explained the System of the World. Newton’s work will contain physics, instead of mere mechanics, “when he substitutes true motions for those that he has supposed” (Journal des sçavans, August 1688, 153; translated in Koyré Reference Koyré1965, 115). The reviewer made this claim because the third book of the first edition of the Principia started with nine “hypotheses.” Accordingly, the reviewer characterized Newton’s theory of universal gravitation as hypothetical mechanics, arguing that it started with unproved and “arbitrary” hypotheses whose role was merely to save the phenomena without claiming to be true.
(2) Hypotheses as Axioms and Postulates. This was not Newton’s intention. In calling those propositions “hypotheses,” he was following a tradition in geometry and mathematics in which axioms and postulates of a system were called hypotheses. As Cohen (Reference Cohen1956, 583) observes, Isaac Barrow was, in this matter, the most important influence on Newton. Barrow sometimes used “hypothesis” and “postulate” interchangeably. He also maintained that hypotheses are founded on experience (construed broadly so that they include internal “consciousness” [Barrow Reference Barrow2013, 133]). This view is very much in line with Newton’s later definitions of “Phenomena” and “Rules”Footnote 14 —the titles he gave in subsequent editions to most of those propositions entitled “Hypotheses” in the first edition.Footnote 15
What, then, is the difference between hypotheses as used in hypothetical methods like IBH and HD and hypotheses considered as axioms and postulates, especially if they are justified through experience? Suppose H is a postulate or axiom in a work whose goal is to render a given body of phenomena, P, intelligible. In such a case, H is supposed to be justified based on data independently of P. Thus, although Newton offers some experimental evidence for his “axioms or laws of motion” in the Principia (mostly in the Scholium to the laws), he does not take the theorems he deduces from them to prove the truth of the laws of motion. Rather, he takes them independently experimentally established.Footnote 16 Similarly, although Newton took the Rules of Philosophizing to be justified through experience (as his definition of a rule suggests), he clearly did not think they were justified by the phenomena to which he applied them in book three of the Principia.Footnote 17
By contrast, according to HD, hypothesis H offered to account for phenomenon P is justified because it deductively entails P. According to IBH, H is justified in similar circumstances because it is the best hypothesis compatible with P. Thus, unlike when H is treated as a postulate or axiom for explaining P, both IBH and HD take P as essential to the justification for H.
(3) Hypotheses as Queries. In An Account of the Book Entitled ‘Commercium Epistolicum, which Newton published anonymously in 1715, he writes: “[I]n this [experimental] philosophy hypotheses have no place, unless as conjectures or questions proposed to be examined by experiments” (Newton Reference Newton and Janiak2004, 165; emphasis added). Accordingly, an experimental philosopher should only consider hypotheses insofar as they help her determine the observable consequences of those hypotheses and design experiments to test them. Newton adds that such uncertain hypotheses were “proposed in the end of [his] Opticks in the form of queries” (ibid.). Years earlier, in 1672, he had expressed a similar view: “for hypotheses should be fitted to the properties which call for explanation and not be made use of for determining them, except in so far as they can furnish experiments” (NCorres.I.169; emphasis added).Footnote 18
This use of a hypothesis resembles, though does not fully coincide with, the contemporary notion of a “working hypothesis.”Footnote 19 The important point for my purposes is this: The use of hypotheses as queries was compatible with a wide range of views about hypothetical methods, and one should not conflate the two. I will now turn to IBH, the most popular hypothetical method at the time, and its proponents.
4. The proponents of IBH
4.1. Boyle
Boyle was among the most important figures—if not the single most important figure—in the gestation and development of experimental philosophy as a movement. Before the publication of the Principia, he was probably the most prominent living experimental philosopher.Footnote 20 Therefore, the fact that his method was essentially based on hypotheses (in particular, IBH) provides strong evidence that Newton’s conception of experimental philosophy, in which hypotheses “have no place,” was far from commonplace.
To be sure, Boyle opposes the use of hypotheses adopted based on insufficient experimental grounds. He argues that natural philosophers would do mankind a considerable service if they believed it “uneasie to erect such Theories as are capable to explicate all the Phænomena of Nature, before they have been able to take notice of the tenth part of those Phænomena that are to be explicated” (B.II.14). However, the question that interests us here is whether natural philosophers should employ hypotheses once such a body of experiments has been collected? Boyle’s answer is a resounding “yes,” particularly if those hypotheses exhibit certain virtues. In a manuscript note enumerating the requisites of good and excellent hypotheses, he mentions intelligibility, avoidance of absurdities, and sufficiency for the explanation of (or at least compatibility with) the related phenomena as the requisites of a good hypothesis (Boyle Reference Boyle and Stewart1991, 119). The requisites of an excellent hypothesis are even more noteworthy.
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1. That it be not Precarious, but have sufficient Grounds in the nature of the Thing itself, or at lest be well recommended by some Auxiliary Proofs.
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2. That it be the Simplest of all the Good ones we are able to frame, at lest Containing nothing tht is Superfluous or Impertinent.
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3. That it be the only Hypothesis tht Can explicate the Phænomena, or at lest tht does explicate them so well.
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4. That it enable a skilfull Naturalist to Foretell Future Phænomena, by their Congruity or Incongruity to it: and especially the Events of such Expts as are aptly devisd to Examine it; as Things tht ought or ought not to be Consequent to it. (Ibid.)
This is a list of familiar theoretic virtues that render a hypothesis the best among rivals within the IBH method. Number 3 is particularly interesting: If a hypothesis satisfies it, then it is most likely the only plausible hypothesis among the alternatives. In other words, this requisite (or something similar to it) often marks the difference between IBH and its stronger form, IOPH.
This manuscript is not simply an isolated methodological note.Footnote 21 Boyle’s writings on natural philosophy demonstrate a clear commitment to this comparative method in practice. For example, in a piece entitled “Of the Excellency and Grounds of the Corpuscular or Mechanical Philosophy,” he compares mechanical philosophy with the hypotheses of both Aristotle and the Chemists. The first advantage of the corpuscular hypothesis that Boyle mentions is “the Intelligibleness or Clearness of Mechanical Principles and Explications.”Footnote 22 He then immediately continues, “I need not tell you, that among the Peripateticks, the Disputes are many and intricate about Matter, Privation, Substantial Forms, and their Eduction, &c. And the Chymists are sufficiently puzled” (B.VIII.104). Note here the essentially comparative nature of his argument. Afterward, he discusses various kinds of simplicity (in terms of number and primitiveness) enjoyed by the principles of mechanical hypothesis (B.VIII.105-6). Finally, he claims the principles of mechanical philosophy “being so simple, clear, and comprehensive, are applicable to all the real Phænomena of Nature, which seem not explicable by any other not consistent with ours” (B.VIII.116; my emphasis). Boyle then continues to offer the following disjunctive argument to support this claim. If we appeal to an immaterial agent or principle, then “it will not enable us to explain the Phænomena, because its way of working upon things Material would probably be more difficult to be Physically made out, than a Mechanical account of the Phænomena” (ibid.). And if that agent or principle is corporeal, then it will either be effectively identical with the principles of mechanical philosophy or “because of the great Universality & Simplicity of ours, the new ones propos’d must be less general than they, and consequently capable of being subordinated or reduc’d to ours” (ibid.). In short, no hypothesis can compete with the mechanical one because it either reduces to it or has less explanatory power. It is evident that Boyle is employing an IBH-style argument here: Mechanical philosophy is true because it is the best.
Elsewhere, after mentioning “several ways, not impertinently employable to recommend the Corpuscularian Doctrine of Qualities” (B.VIII.323), he goes on to assert that “there is yet another way of arguing in favour of the Corpuscularian Doctrine of Qualities, which, though it do not afford direct proofs of its being the best Hypothesis, yet it may much strengthen the Arguments drawn from other Topicks” (B.VIII.325; my emphasis). The details of this “other way” are not pertinent to our discussion. What is significant is Boyle’s explicit assertion that he is engaged in seeking the “best hypothesis.”
In short, the inherently comparative nature of Boyle’s method and his explicit methodological assertions make it evident that his hypothetical method is a form of IBH rather than HD.
4.2. Descartes
Many have found Descartes’s method, especially in parts III and IV of the Principle, HD.Footnote 23 Descartes’s views on hypotheses are more complicated than those of the other figures discussed here, largely because in parts III and IV of Principles of Philosophy, he makes contradictory claims about the epistemic status of his hypotheses. I cannot do full justice to his views here, but I believe I can offer sufficient evidence that he was a proponent of IOPH, not HD.
In section 42 of part III of the Principles, Descartes argues that although all terrestrial and celestial phenomena are relevant to his hypothesis, it is not necessary to consider them all. This is because “we shall know that we have determined such causes correctly afterwards, when we notice that they serve to explain not only the effects which we were originally looking at, but all these other phenomena, which we were not thinking of beforehand” (AT.VIII.99/CSM.I.255). He continues, “[I]f a cause allows all the phenomena to be clearly deduced from it, then it is virtually impossible that it should not be true” (ibid.).Footnote 24 These statements suggest that if there is a hypothesis capable of explaining a large number of phenomena, especially if it yields successful novel predictions, we can be virtually certain of its truth.
Descartes expresses very similar ideas at the end of part IV concerning his hypotheses on terrestrial phenomena. These hypotheses typically posit various kinds of imperceptible particles (such as the grooved ones responsible for magnetism) with definite sizes, shapes, and motions whose actions result in the phenomena in question. But given the imperceptibility of these particles, how do we know they exist? Descartes’s reply to this question comes in a few steps. First, he sets out a necessary condition for any plausible hypothesis: It must appeal only to those features of matter of which we can have a clear and distinct notion (size, shape, and motion), and it must be consistent with the laws of nature (discussed in part II of the Principles). In the second stage,
I took the simplest and best known principles, knowledge of which is naturally implanted in our minds; and working from these I considered, in general terms, firstly, what are the principal differences which can exist between the sizes, shapes and positions of bodies which are imperceptible by the senses merely because of their small size, and, secondly, what observable effects would result from their various interactions. [AT.VIII.326/CSM.I.288]
This involves what Descartes calls enumeration, which was an essential part of his method.Footnote 25 In the present case, enumeration is carried out by examining the simplest combinations of intelligible features that could produce the effects under study, and by checking whether their observable consequences agree with the phenomena as observed. Finally, in the third step, “[W]hen I observed just such effects in objects that can be perceived by the senses, I judged that they in fact arose from just such an interaction of bodies that cannot be perceived—especially since it seemed impossible to think up any other explanation for them” (ibid.; my emphasis). Thus, two considerations assure Descartes of the truth (or high probability) of his hypotheses: (1) that they are the simplest hypotheses capable of accounting for observable phenomena by appeal to notions clearly and distinctly understood (size, shape, motion); and (2) that they are the only plausible explanations, where plausibility is determined by the clarity and distinctness of the notions involved in the hypothesis, together, perhaps, with its simplicity. For example, we can imagine an explanation of magnetism according to which “the magnet contains some kind of [soul-like] entity the like of which our intellect has never before perceived” (A.X.439/CSM.I.57). However, we should discard this explanation as implausible, because we cannot form clear and distinct ideas of such entities. To understand them, we “need to be endowed with some new sense, or with a divine mind” (ibid.). What justifies ruling out such hypotheses is, of course, God’s benevolence, which ensures that “the faculty which he gave us for distinguishing truth from falsehood cannot lead us into error, so long as we are using it properly and are thereby perceiving something distinctly” (AT.VIII.328/CSM.I.290).
Recall that in part III, Descartes argues that if a hypothesis explains a large number of phenomena and makes novel predictions, we can be virtually certain of it. He repeats this claim in part IV, where he argues that we can have at least moral certainty of the truth of his hypotheses. Moral certainty is the kind of certainty in which, for all practical purposes, we can act as if we are absolutely certain; the opposite is only theoretically possible (CSM.I.289n2). What is most interesting here, however, is the reason he offers for this. He uses an analogy with a key to a cryptograph.Footnote 26 Suppose someone has found a key to a cryptographic letter, which involves replacing letters of the alphabet with their immediate successors.
If, by using this key, he can make up Latin words from the letters, he will be in no doubt that the true meaning of the letter is contained in these words. It is true that his knowledge is based merely on a conjecture, and it is conceivable that the writer did not replace the original letters with their immediate successors in the alphabet, but with others, thus encoding quite a different message; but this possibility is so unlikely especially if the message contains many words that it does not seem credible. Now if people look at all the many properties relating to magnetism, fire and the fabric of the entire world, which I have deduced in this book from just a few principles, then, even if they think that my assumption of these principles was arbitrary and groundless, they will still perhaps acknowledge that it would hardly have been possible for so many items to fit into a coherent pattern if the original principles had been false. [AT.VIII.328/CSM.I.290]
This explains why hypotheses that account for a large number of phenomena and offer novel predictions are virtually or morally certain.Footnote 27 First, a false key that is only accidentally applicable to an initial set of letters will sooner or later fail to yield meaningful results as it is applied to more and more letters. Second, the number of simple keys that are applicable even to a small number of letters is typically very limited. Therefore, it is exceedingly unlikely for two simple keys to be applicable to a large number of cryptographic letters.Footnote 28 Thus, if one knows that the true key is simple and possesses a simple key applicable to many letters, one can be virtually certain that it is the true key. The idea that laws of nature are simple enjoyed widespread acceptance among early modern thinkers (even Newton would agree with this). For Descartes, this was justified on the basis of God’s benevolence, which is why he surveyed the “simplest and best known principles, knowledge of which is naturally implanted in our minds.”
The upshot is that Descartes did not believe in merely HD justification for his hypotheses. Rather he emphasized theoretic virtues such as simplicity and having novel predictions not only to argue that his hypothesis was the best, but also to claim that it was the only plausible hypothesis (given his restrictions on what counts as plausible). Thus, he was a proponent of IOPH, not HD.
Although I think this captures Descartes’s considered view, I have so far ignored his claims that appear to undermine this reading, which I must briefly discuss. In section 44 of part III, he writes, “I want the causes that I shall set out here to be regarded simply as hypotheses” (A.VIII.99/CSM.I.255). His discussion makes it clear that by “hypotheses,” he means predictive tools that save the phenomena but may nonetheless be false (the first sense discussed in section 3). He continues, “I shall even make some assumptions which are agreed to be false” (AT.VIII.99/CSM.I.256). His elaboration of this point indicates that these “assumptions” are related to his “imaginary” cosmogonic hypothesis, which, on account of being different from the biblical story, he treats as false.
Why, then, does he make these assumptions, if they are false? Because their falsity “does not prevent the consequences deduced from them being true and certain” (AT.VIII.101/CSM.I.257). Even so, what happened to the virtual certainty claimed only a couple of sections ago? I believe two factors are at play here. First, it is well-known that the condemnation of Galileo deeply influenced Descartes’s thinking, or at least its presentation.Footnote 29 Thus, it was imperative for him to state explicitly that his cosmogony was not intended as an account of how things happened, but merely as a hypothesis. Second, he believed that the laws of nature will turn almost any initial conditions into the world as it currently is (A.XI.34-5/CSM.I.91; AT.VIII.103/CSM.I.257-8). Thus, the choice of initial conditions (cosmogony) doesn’t affect the consequences of the hypothesis. It is prudent, then, to choose the simplest conditions for convenience. However, this does not apply to his other hypotheses. As discussed earlier, he claimed his hypotheses were morally certain because they were uniquely plausible. There is no indication that when there is no danger of censure by the church, we should treat his hypotheses as anything less than morally certain.
4.3. Leibniz
Despite his acquaintance with experimental philosophy, Newton did not identify with it until relatively late, around the time he was about to publish the second edition of the Principia. This suggests that his identification as an experimental philosopher was, at least in part, a polemical tool against Leibniz’s attacks (Shapiro Reference Shapiro2004, 185). Newton’s strategy was a familiar one at the time. He made a distinction between “experimental philosophy” and “hypothetical philosophy” and argued that while the former is based upon phenomena, the latter involves “imaginary explication of things and imaginary arguments for or against such explications.” He continues, “[T]he first sort of philosophy is followed by me, the latter too much by Cartes, Leibnitz and some others” (NCorres.V.398-9).
As we shall see, Leibniz’s methodology was far more sophisticated than suggested by Newton’s caricature. On Leibniz’s view, “[T]he most perfect method involves the discovery of the inner constitution of bodies a priori from a contemplation of the author of things, God. But this method is difficult and not to be attempted by just anyone” (A.VI.4.1998). Given the difficulty of this method, however, the next best thing is the “conjectural method a priori [which] proceeds by hypotheses, assuming certain causes, perhaps, without proof, and showing that the things which now happen would follow” (A.VI.4.1999/L.283). This is the method Newton called hypothetical and on which I will focus hereafter.
First, notice that by calling this method “a priori,” Leibniz is not claiming that it has no need for experience. Rather, he is using the term in its traditional sense of a proof from cause to effect,Footnote 30 which here works by assuming a hypothesis and “showing that the things which now happen” follow from it. Because, for him, our knowledge of such contingent facts requires experience (A.VI.4.1381/CP.125), this method heavily relies on experience.Footnote 31 Indeed, as I shall argue, this method works only if there is a large body of experiments or observations.
Leibniz continues the previous passage:
A hypothesis of this kind is like the key to a cryptograph, and the simpler it is, and the greater the number of events that can be explained by it, the more probable it is. But just as it is possible to write a letter intentionally so that it can be understood by means of several different keys, of which only one is the true one, so the same effect can have several causes. (Ibid.)
As this passage shows, Leibniz was clearly aware of the main worry about his hypothetical method, namely, underdetermination. Elsewhere he writes, “[I]f two people claim to have found the key to a cryptographic letter, it is difficult for them to prove a priori and without application that one key is to be preferred over the other” (A.VI.3.231). However, and importantly, this is a problem only if they cannot test their respective keys on new letters (i.e., “a priori and without application”). If they can apply those keys to more and more letters not used in the original deciphering process, it becomes exceedingly unlikely for both to remain plausible keys.
Using the same analogy with a cryptograph, Leibniz endorses a view on the epistemic status of hypotheses surprisingly similar to Descartes’s and based on a similar argument.Footnote 32 He writes:
A hypothesis becomes the more probable as it is simpler to understand and wider in force and power, that is, the greater the number of phenomena that can be explained by it, and the fewer the further assumptions. It may even turn out that a certain hypothesis can be accepted as physically certain if, namely, it completely satisfies all the phenomena which occur, as does the key to a cryptograph. Those hypotheses deserve the highest praise (next to truth) [post vertitatem], however, by whose aid predictions can be made, even about phenomena or observations which have not been tested before; for a hypothesis of this kind can be applied, in practice, in place of truth [pro veritate]. [A.II.1.603-4/L.188]
Simple hypotheses that account for a broad range of phenomena and make novel predictions are “physically certain.” As the cryptograph analogy shows, the reason for this is that, with very high probability, there is no other plausible hypothesis compatible with the data. Thus, Leibniz’s hypothetical method was a clear instance of IOPH.
Interestingly, he occasionally appealed to this method to argue for some of his cherished metaphysical views. For example, in a very important piece called “A New System of Nature,” he writes about the “hypothesis of agreement” (preestablished harmony) that, “besides all the advantages that recommend this hypothesis, we can say that it is something more than a hypothesis, since it hardly seems possible to explain things in any other intelligible way, and since several serious difficulties which, until now, have troubled minds, seem to disappear by themselves when we properly understand the system” (G.IV.486/AG.145; emphasis added). Rival metaphysical hypotheses are unable to offer an intelligible account of phenomena and suffer from problems that only preestablished harmony can resolve. For this reason, he considers the hypothesis to be well established (“is something more than a hypothesis”).
It is misleading to call Leibniz’s method mere HD. It is far more nuanced and based on much firmer grounds than that, at least by Leibniz’s own lights. It is also clear that this method is not speculative. As a matter of principle, it requires large bodies of observational evidence, because the moral certainty of the hypothesis depends on the broad range of phenomena for which it accounts.
4.4. Huygens
When it comes to evidence for the popularity of HD among the early moderns, no passage has been cited as frequently as the following from the preface to Huygens’s Treatise on Light, which is worth quoting in full.
One will see here demonstrations of a kind that do not produce a certainty as great as those of geometry, and that even differ from them greatly, since whereas geometers prove their propositions by certain and incontestable principles, here the principles are verified by the conclusions drawn from them; the nature of these matters not allowing it to be otherwise. It is always possible to attain thereby to a degree of probability, which very often hardly is scarcely inferior to complete proof [evidence entiere]. To wit, this occurs when the things demonstrated on the basis of these assumed principles correspond perfectly to the phenomena that experience has revealed, especially when there are many such phenomena, and even more so when one predicts and foresees new phenomena that ought to follow from the hypotheses employed, and finds that in this the effect corresponds to one’s expectation. Now, if all these proofs of probability are found in what I have undertaken to treat, as it seems to me they are, this ought to be a very great confirmation of the success of my inquiry, and it can hardly be that things are not more or less as I have presented them. [H.XIX.454]
To a contemporary reader familiar with HD, it may seem that Huygens couldn’t have defended it more clearly. Isn’t verifying principles from “conclusions drawn from them” a clear allusion to HD? In fact, it is not. Huygens is alluding to a distinction, well known since medieval scholasticism and going back to Aristotle’s Posterior Analytics, between two kinds of demonstrations. The first (demonstration propter quid or a priori) is a method in which one starts from incontestable principles that are prior in nature to prove things that are posterior in nature. It is through this method that one may have scientia (science) in its Aristotelian sense. This is the method in geometry. The second (demonstration a posteriori or quia) is the less perfect method, more proper to natural philosophy, where one starts from knowledge of effects (things prior only in relation to us) and proves principles that are prior in nature.Footnote 33 Thus, Huygens emphasizes the collection of experiments and natural histories “more or less following the design of Verulam [Bacon]” to build “a natural philosophy, in which it is necessary to proceed from the knowledge of effects to that of causes” (H.VI.95-6).
It was also well known that the same effect can be produced by more than one cause. A famous example at the time was that of a clock. Simply by looking at an unfamiliar clock one wouldn’t know the internal mechanism by which it works; it could operate, for example, either by weights or by springs.Footnote 34 Partly for this reason, proofs in natural philosophy are less certain than those in geometry. In a letter to Perrault of 1676, Huygens writes: “[I]n matters of physics there are no certain demonstrations, and that one can know causes only through effects, by making suppositions based on some known experiments or phenomena, and then testing whether other effects agree with these same suppositions” (H.VII.300). Because we must proceed from the knowledge of effects to those of causes, there cannot be demonstrations in natural philosophy as certain as those in geometry.
One might object that this remains compatible with HD. Demonstration quia can be achieved hypothetico-deductively. To answer this objection and to explain how Huygens’s method differs from HD, we must look at other passages. In the same letter to Perrault, Huygens writes:
In matters of physics there are no demonstrations other than those in the deciphering of a letter. Where, having made suppositions based on some slight conjectures, if one finds that they are verified thereafter, so that following these suppositions of letters one finds words well arranged in the letter, one holds with very great certainty that the suppositions are true, even though there is no other demonstration, and although it is not impossible that there could be others even more correct. [H.VII.298]
Huygens’s conception of method is very similar to Leibniz’s “conjectural method” and Descartes’s method of hypotheses. He uses the same analogy with cryptography to justify it. And just as in Descartes’s and Leibniz’s case, the mere fact that a hypothesis entails observed phenomena does not make it probable. Rather, the hypothesis becomes highly probable because of the extreme implausibility of alternatives,Footnote 35 especially when it accounts for a large number of phenomena and makes successful novel predictions (recall Huygens’s words in the preface to the Treatise on Light, quoted earlier).
This idea is clear in Huygens’s comments on the particular hypotheses he endorses in natural philosophy. In his preface to the Discourse on the Cause of Gravity, he writes:
I do not offer [this Discourse] as something beyond the reach of doubt, or as something against which one cannot make objections. It is too difficult to go that far in researches of this nature. It is, however, my belief that if the principal hypothesis on which I stand is not the true one; there is little hope that [such a true hypothesis] can be found, while remaining within the limits of the true and sane Philosophy. [H.XXI.446, translated in Sabra Reference Sabra1967, 165]
Huygens is very clear that what gives him high confidence (short of certainty) in his “principal hypothesis” about the cause of gravity (namely, that an imperceptible subtle matter causes gravity) is the implausibility of alternatives. Indeed, he expresses the same attitude toward mechanistic philosophy as a whole in the Treatise on Light. There he refers to the “true philosophy in which one conceives the causes of all natural effects in terms of mechanical reasons. This is what one must do in my opinion, or else give up all hope of ever understanding anything in physics” (H.XIX.461). Thus, not only his particular hypothesis about the cause of gravity but also mechanical philosophy as a whole are highly probable, based on an inference to the only plausible hypothesis. In the present case, the implausibility of alternatives lies in their inability to make phenomena intelligible.Footnote 36 Notably, Leibniz expressed a very similar view on this issue. “Unless physical things can be explained by mechanical laws, God cannot, even if he chooses, reveal and explain nature to us” (A.II.1.605/L.189). Accordingly, the truth of mechanical philosophy comes down to the fact that without it, even God could not explain (i.e., render intelligible) nature to us. Given God’s omnipotence, this is another way of saying that without mechanical philosophy, explaining nature is impossible.
This demand for mechanical explanations was at the heart of the debate between Newton and those like Leibniz and Huygens, who could not accept his theory of universal gravitation. Here we can appreciate the difference between interpreting Newton’s rejection of hypotheses as a mere rejection of HD or as a rejection of IOPH. Newton was surely aware of the reason why the proponents of mechanical philosophy insisted on the necessity of a mechanical explanation for gravity (for otherwise, we should “give up all hope of ever understanding anything in physics”). His rejection of this demand, therefore, was far more significant than a mere rejection of HD. I will now turn to Newton’s rejection of hypothetical methods.
5. Newton
Newton’s rejection of hypotheses is well documented, and I will not rehearse the evidence here.Footnote 37 Some of the nuances of his usage of the term, however, merit clarification.Footnote 38 In a letter of March 1713 to Roger Cotes, he writes, “[T]he word hypothesis is here used by me to signify only such a proposition as is not a phænomenon nor deduced from any phænomena but assumed or supposed wthout any experimental proof” (NCorres.V.397). The main characteristic of a hypothesis is the absence of “experimental proof,” which should be distinguished from what in the Opticks he calls “proof by experiments.” The latter refers to relatively direct experimental evidence for particular propositions within the Opticks. By contrast, Newton’s appeal to “experimental proof” in his letter to Cotes expresses a more general methodological requirement: that theories be “deduced from phenomena.” Relatedly, Newton distinguishes between hypotheses and theories. The latter are general propositions established by deduction from phenomena and generalization by induction.Footnote 39 By “deduction from phenomena,” Newton meant exploiting what Ducheyne calls “systematic dependencies,” allowing the phenomena to guide theory revision.Footnote 40 Finally, one must distinguish hypotheses lacking “experimental proof” from the propositions Newton called “hypotheses” in the first edition of the Principia, where (as explained in section 3) the term followed its use in mathematics as denoting postulates or axioms.
All such clarifications aside, the important question for my purposes is: What counts as “experimental proof” for Newton? More specifically, does an IOPH-style proof count? In this section, I argue that the answer is no. (Because IOPH is a stronger form of IBH, rejecting it as inadequate entails a rejection of IBH too.) This is important because some scholars have argued that Newton’s methodological assertions were at least partly polemical.Footnote 41 Thus, one may argue that despite his explicit assertions, Newton was not opposed to accepting a hypothesis in natural philosophy (in the sense of including it in his official theory as an axiom or proposition and not merely as a query),Footnote 42 if it was the only plausible hypothesis compatible with a sufficiently large body of observations. On this view, Newton was only against acceptance of hypotheses based on little or no experimental evidence. If so, his view was not radical at all. Everyone associated with experimental philosophy would have agreed. For example, Boyle argues that to establish a system, it is paramount that “men in the first place would forbear to establish any Theory, till they have consulted with…a considerable number of Experiments in proportion to the comprehensiveness of the Theory to be erected on them” (B.II.14).
Newton’s rejection of IOPH implicitly follows from his assertions about experimental philosophy: “[I]n this experimental philosophy, propositions are deduced from the phenomena and are made general by induction” (P.943). A hypothesis adopted through IOPH is typically not adopted through a combination of deduction from phenomena and induction, but rather because it is uniquely plausible. However, Newton’s rejection of IOPH goes back much earlier, to his first optical letter of 1672: “[W]hat I shall tell concerning them [the origin of colors] is not an Hypothesis but most rigid consequence, not conjectured by barely inferring ‘tis thus because not otherwise or because it satisfies all phænomena (the Philosophers universall Topick,) but evinced by ye mediation of experiments concluding directly” (NCorres.I.96-7). Accordingly, Newton’s method is not hypothetical: He does not merely argue that his theory is the only plausible hypothesis but also directly deduces it from phenomena.
However, I suspect no amount of evidence from Newton’s methodological assertions can be decisive on this issue, for it is always possible to dismiss them as mere polemic. Here his actual practice is far more decisive, and I think we have excellent evidence that Newton rejected IOPH in practice too. Here I will offer only one particularly strong piece of evidence, leaving an extended discussion for another occasion. In a draft “Conclusion” to a Fourth Book of the Opticks written in the 1690s, Newton includes five “hypotheses.”Footnote 43 I don’t wish to emphasize the mere fact that these are labelled as “hypotheses.” What is interesting is Newton’s commentary on “Hypothesis 2.” This hypothesis asserts that just as great motions are caused by gravity, small motions “depend upon certain kinds of forces whereby minute bodies attract or dispell one another at little distances” (Cohen Reference Cohen1969, 319). In his commentary, Newton argues that “if Nature be most simple & fully consonant to herself she observes the same method in regulating the motions of smaller bodies wch she doth in regulating those of the greater” (ibid.). Thus, the hypothesis receives some justification through an analogy with gravity and by the principle of uniformity of nature. He then continues with a striking passage:
The truth of this Hypothesis I assert not, because I cannot prove it, but I think it very probable because a great part of the phænomena of nature do easily flow from it wch seem otherways inexplicable: such as are chymical solutions, precipitations, philtrations, … volatizations, fixations, rarefactions, condensations, unions, separations, fermentations, the cohesion, texture, fluidity and porosity of bodies, the rarity & elasticity of air, the reflexions and refraction of light, the rarity of air in glass pipes & ascention of water therein, the permiscibility of some bodies & impermiscibility of others, the conception & lastingnesse of heat, the emission & extinction of light, the generation & destruction of air, the nature of fire & flame, ye springinesse or elasticity of hard bodies. (Cohen Reference Cohen1969, 319–20)
This passage offers strong evidence that Newton did not endorse IOPH. The range of phenomena that, according to Newton, “easily flow from” this “hypothesis” but are inexplicable without it is very remarkable. Despite all this evidence for the hypothesis, however, Newton does not assert its truth, because he does not have a proof for it! Any proponent of IOPH would have taken the hypothesis’s unique ability to explain such a broad range of phenomena as an extremely strong proof for it, but not Newton. He does say that the hypothesis is “very probable,” which shows that an IOPH-style argument can provide evidence for a hypothesis and make it very probable. However, what matters for my purposes is that the level of certainty does not rise to what is required for Newton to assert its truth, as he did about all the axioms and propositions of the Opticks and the Principia. Later, he expressed the main idea behind this hypothesis in query 31 of the Opticks, where he goes into more detail about the reasons for his claim that short-range forces can account for a broad range of phenomena. His discussion in query 31 indicates that he still found the hypothesis very probable. However, the fact that he expresses it as a query shows that he was still not willing to assert its truth.
I conclude that IBH, and especially IOPH, were popular hypothetical methods in the early modern period, even among some prominent experimental philosophers. They were more plausible and nuanced than HD. However, Newton rejected them. For him, any proposition not established through a combination of deduction from phenomena and induction remained a hypothesis, even if it was uniquely plausible, and “hypotheses are not to be regarded in experimental philosophy” (O.404), except as queries.
Acknowledgments
I am grateful to Domenica Romagni, Curtis Haaga, and two anonymous referees for their helpful comments.
Funding statement
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