Analogy and falsification in Descartes’ physics

Studies in History and Philosophy of Science 43 (2012) 402–411

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Analogy and falsification in Descartes’ physics Gideon Manning California Institute of Technology, 1200 East California Blvd., MC 101-40, Pasadena, CA 91125, USA

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Article history: Received 19 July 2011 Received in revised form 24 January 2012 Available online 20 March 2012 Keywords: René Descartes Analogy Hypothesis Falsification Explanation

a b s t r a c t In this paper I address Descartes’ use of analogy in physics. First, I introduce Descartes’ hypothetical reasoning, distinguishing between analogy and hypothesis. Second, I examine in detail Descartes’ use of analogy to both discover causes and add plausibility to his hypotheses—even though not always explicitly stated, Descartes’ practice assumes a unified view of the subject matter of physics as the extension of bodies in terms of their size, shape and the motion of their parts. Third, I present Descartes’ unique ‘‘philosophy of analogy’’, where the absence of analogy serves as a criterion for falsifying proposed explanations in physics. I conclude by defending Descartes’ philosophy of analogy by appeal to the value scientists assign to simplicity in their explanations. ˘ 2012 Elsevier Ltd. All rights reserved.

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1. Introduction The reception of Descartes’ physics could be described through the various rejections of his many analogies. Take, as an example, his account of magnetism. Descartes claims in the Principles that invisible particles traveling from a magnet’s two poles likely have a shape and twisting motion similar to that of a screw (Descartes, 1996, VIII 275ff.).1 He reasons that when particles emanating from a magnet come into contact with objects they can, depending on their orientation and motion, pull objects toward a magnet or push them away. Although Descartes is citing a common effect in his explanation of magnetism—screws push and pull objects and so do magnets—this analogy, and the evidence Descartes believes it provides about causes in the subvisible world, hardly satisfied the majority of his contemporaries. Later in the century even the one time Cartesian Christiaan Huygens describes the Principles as a ‘‘Romance’’ filled with ‘‘chimeras’’ where ‘‘conjectures [serve] as truths, which can be seen in the grooved particles that [Descartes] employs in the explanation of the magnet’’ (Huygen, 1888–1950, X 405).2 My aim in this paper is to elucidate the role of analogies in Descartes’ physics. In doing so I hope to show that Descartes’ use of

analogy is more defensible—i.e. less a chimera or mere conjecture—than is usually thought; it is part of Descartes’ effort to ‘‘submit [his] reasons to examination by the senses’’ (1996, II 366). More than this, I will suggest that Descartes’ theory of falsification holds considerable appeal if we substitute the ideal of simplicity among explanations for his metaphysical commitment to matter being nothing but extension. I begin in the second section by noting the difference between analogies—comparaisons in French, comparationes in Latin—and hypotheses—hypothèses and suppositions in French, hypotheses, positiones and suppositiones in Latin. In the third section I present Descartes’ famous analogies from the Dioptrics. As Descartes’ scientific practice shows, the primary purpose of analogy is to aid in the discovery of causes and to illustrate how subvisible mechanisms might produce known effects. In either case, analogies utilize what we know of the sensible world. What drives Descartes’ search for subvisible mechanisms is the hypothesis and erstwhile metaphysical truth that the natural world is nothing more than extended matter. In the fourth section I consider Descartes’ remarks about analogy in response to criticism of the Dioptrics. Building upon section three, I reconstruct Descartes’ defense of his use of analogy and show that his

E-mail address: [email protected] When offering my own translation, I cite the original language text in Descartes (1996), including volume in Roman numerals, followed by page number. For similar seventeenth century responses to Descartes’ physics, see the references in Anstey (2005). A fairly recent historian, Larry Laudan, accuses Descartes of resorting to claims supported ‘‘with neither empirical evidence nor a priori reasons’’ (1966, p. 79). 1 2

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G. Manning / Studies in History and Philosophy of Science 43 (2012) 402–411

provocative claim that ‘‘when someone makes an assertion concerning nature which cannot be explained by any . . . analogy, I think I have demonstrative knowledge that the point is false,’’ depends on his unified view of matter as extension (1991, 122). I conclude by showing that our own interest in simplicity when forced to choose among competing explanations can be used to support Descartes’ ‘‘philosophy of analogy’’. 2. Hypothesis vs. analogy There are now several competing accounts of the proper role of analogy in science but, however one defines analogical reasoning, a good analogy indicates that a certain phenomenon or process is similar to a better-known phenomenon or process in one or more non-trivial ways.3 Descartes’ overwhelming interest when using analogies lies in identifying similar effects and then inferring the existence of a similar cause between the phenomena or processes he is comparing. Schematically then, all Descartes’ analogies appear in the following ratio-like form: Known Effect1 : Known Cause :: Known Effect2 : Unknown Cause. The better known phenomenon (Known Effect1:Known Cause) is almost invariably a mechanical contrivance for Descartes, and the cause being sought (Unknown Cause) is immune to direct observation because of its small size or remote location. To use Descartes’ magnetism example again, a screw with its pulling and pushing action can be observed and understood by anyone. By contrast, the subvisible mechanisms responsible for the pulling and pushing action of a magnet are not well understood and are immune to direct observation. The Known Effect1 is the screw’s pushing and pulling action and the Known Cause is the orientation of the screw’s threads and its motion. Known Effect2 is the pushing and pulling action of a magnet. Thus, the effects in the two cases are similar and observable. On the basis of this similarity, Descartes presents an analogy between the screw and the magnet and concludes that the Unknown Cause—the cause of the magnet’s properties—might be particles that are similar to a screw in their shape and motion.4 From our contemporary perspective, one of the most distinctive features of Descartes’ analogies is his preference to avoid referring to them as ‘‘analogies’’.5 In fact, though for the sake of convenience I will continue to refer to ‘‘Descartes’ analogies’’, as far as I am aware Descartes uses the French ‘‘analogie’’ on only six occasions in all of his writing (e.g., 1996, XI 158). He uses the Latin ‘‘analogia’’ to contrast what he is trying to do with what his contemporaries often do, as in ‘‘nor should it be thought that this is said merely by way of analogy [per analogiam]’’ (Ibid., X 412; Cf. Ibid., V 270).6 The analogies from the Dioptrics are ‘‘comparisons [comparaisons]’’ and those from the Meteors are instances of reasoning by ‘‘example and similarity [exemplum & similitudinem]’’ (Ibid., VI 83 and I 422, respec3

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tively).7 In the Principles, analogies are typically ‘‘comparisons [comparationes]’’ or efforts to ‘‘compare [consero/comparo]’’ (e.g., Ibid., VIII 87 and 110, respectively). In Proposition 8 from the Rules for the direction of the mind, Descartes does not advise us to seek ‘‘analogies’’ when trying to discover the nature of light but to ‘‘enumerate all the other natural powers so that, by means of knowledge of some other one, [we] might come to understand this one, at least by imitation [imitationem]’’ (Ibid, X 395).8 Nevertheless, the presence of what we easily recognize as analogical reasoning in Descartes’ scientific work at every stage in his development, and the emergence of a stable terminology (comparaison/comparatio) in his writing beginning in the 1630s, suggest that analogies are an integral part of Descartes’ method in physics. There is no shortage of discussion about Descartes’ scientific method, and there are many valuable studies of the evolving use of hypotheses and expérience by Descartes and subsequent Cartesians (e.g., Ariew, 2010; Clarke, 1982, 1989, 2010; Garber, 1978; Hatfield, 1988; Laudan, 1966; McMullin, 2008, 2009). What is generally missing from these studies, however, is focused attention on Descartes’ use of analogy as distinct from, or as a special case of, his use of hypotheses (Cf. Statile, 1999; Cf. Garber [Unpublished]). To rectify this situation and in order to provide what I hope will be a more complete account of Descartes’ method in physics, I will spend the rest of this section discussing Descartes’ use of hypothesis in order to prepare us for a closer look at his analogies in later sections. Starting in the 1620s, with the Rules, Descartes appeals to ‘‘suppositiones’’, i.e. hypotheses. In this early work he likens his method to the one ‘‘in geometry when you make certain suppositions about quantity, which in no way weaken the force of the demonstrations, even though in physics you often take a different view of the nature of quantity’’ (1985, 40, modified). Just as the geometer assumes certain principles, so Descartes assumes certain principles for the sake of his demonstrations. In later years, Descartes compares his use of hypotheses to the astronomers’, ‘‘whose suppositions are almost all false or uncertain, but who nevertheless draw many very true and certain consequences from them because they are related to various observations they have made’’ (Ibid., 152–53, modified). This comparison from the Dioptrics is more suggestive than the earlier one from the Rules because Descartes finds a place for ‘‘false and uncertain’’ principles as well as observations, the latter being, as we will see, where analogies enter into his method. Holding this point for later discussion, collectively the comparisons to geometry and astronomy tell us that Descartes’ hypotheses may be false principles or, because his method is a method of physics, the wrong causes for the effects that they are introduced to explain. Still, what matters is that the ‘‘conclusions’’ or ‘‘consequences’’ follow from the hypotheses. Notice that just as one could assume for the sake of argument a principle or cause that may be false, one could also assume for the sake of argument a principle or cause known to be true. In spite of

Hesse (1966) remains the classic treatment of analogy in science but Bartha (2010) represents a new benchmark for the subject. For the Principles, Descartes commissioned illustrations depicting magnets expelling subvisible screw-like particles (1996, VIII 288). The connection among these illustrations, imagination, vision and conjecture more generally is discussed in Galison (1984), Lüthy (2006) and Bellis (2010). These works show that Descartes’ views develop and change over time. 5 Although Descartes’ magnetism analogy is innovative, many his analogies are quite pedestrian. Such is the case with his analogy between lightning and fire (Descartes, 1996, VI 317; Martin, 2011), his analogy between vision and the tactile sensations caused by a blind man’s stick (Descartes, 1996, VI 84; Sabra, 1967, p. 55), and his analogy between the motion of a celestial body and a boat’s movement in a river (Descartes, 1996, XI 57–58; Palmerina, 2007). Notice though that in all these cases Descartes is using similar effects to infer a similar cause. 6 Descartes’ biased use of ‘‘analogia’’ is noted in Galison (1984). At the urging of an anonymous referee I have consulted the ARTFL database and discovered that ‘‘analogie’’ appears rarely in French texts of the seventeenth century. Comparing it with ‘‘comparaison’’, which is Descartes preferred term for what we think of as his analogies, ‘‘analogie’’ is roughly one tenth as common. To this extent, Descartes’ preference for ‘‘comparaison’’ is consistent with the preferences of his contemporaries. For more on the ancestry of Descartes’ different terminology in connection with ‘‘analogy’’, see note 20. 7 The Meteors is a complicated case because Descartes’ initial analogies from this work are presented as ‘‘suppositions’’ but, as I just indicated, they are later classed with his other comparaisons (1996, VI 233). The analogy between a raindrop and a prism in the Meteros, which serves in the experimental and quantitative success of the account of the rainbow, Descartes calls a comparaison (Ibid., VI 329). 8 Descartes’ use of imitatio here is unusual. The term comes from the rhetorical tradition and is usually reserved for the imitation of a style or manner. Descartes uses the French derivative of imitatio—imiter—when he claims to imitate the method of the astronomer in the Diotrics (1996, VI, 83). 4

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what Descartes writes in the passages above, and what the comparison to astronomy might suggest, it is not true that all of Descartes’ hypotheses are potentially ‘‘false or uncertain’’. First, in some cases Descartes vindicates in his metaphysics what he otherwise labeles as ‘‘hypotheses’’. These hypotheses are not potentially false or uncertain, however, they are metaphysical or ‘‘absolute certainties’’. Second, Descartes’ standards for knowledge or ‘‘demonstration’’ in physics appear to evolve throughout the 1630s. Without appealing to metaphysics, in some places he maintains that his hypotheses are not potentially ‘‘false and uncertain’’ but rather the only ones that can be found that both explain the effects while maximizing separate epistemic values. Before elaborating on these two points, I want to mark the important distinction between hypotheses that are also metaphysical truths and those that are never metaphysical truths. Henceforth I will discriminate between: Stage 1 hypotheses: principles or causes that have an a priori metaphysical justification although they sometimes appear in Descartes’ physics as hypotheses. Stage 2 hypotheses: principles or causes that appear in Descartes’ physics without ever having an a priori metaphysical justification. Stage 1 hypotheses come first in Descartes’ order of exposition and they serve more as theoretical constraints on explanation than as literal efficient causes. There are, as we will see, many instances in which Descartes claims he can ‘‘deduce’’ all of his hypotheses from a metaphysical foundation, but he nowhere suggests that this eliminates the category of Stage 2 hypotheses.9 From the standpoint of Descartes’ physics, as Clarke (1990) emphasizes, the most important point to remember is that both Stage 1 and Stage 2 hypotheses serve as principles for deducing effects from causes. In other words, whether conjectures, known falsehoods or metaphysical truths, the primary role of these hypotheses is to account for effects in the natural world that the physicist takes as given and in need of causal explanation. In order to further clarify the difference between a Stage 1 and a Stage 2 hypothesis, take as an example the Stage 1 hypothesis that matter is just extension. In The World, Descartes writes of planning to ‘‘expressly suppose [supposons expressément] that it [matter] does not have the form of earth, fire, or air, or any other more specific form, like that of wood, stone or metal’’. He adds, continuing his supposition, ‘‘this matter may be divided into as many parts having as many shapes as we can imagine, and . . . each of its parts is capable of taking on as many motions as we can conceive’’ (1985, 91). A decade later, in the Principles, it is one of Descartes’ certainties deriving from Part One’s metaphysical preface that ‘‘all the bodies of the universe are composed of one and the same matter, which is divisible into indefinitely many parts’’ (Ibid., 256). What was once a hypothesis has been converted into a metaphysical certainty.10 More to the point for our discussion, when Descartes offers Stage 1 and Stage 2 hypotheses in his physics they look to be mere

conjectures or ad hoc assumptions whenever an analogy is not instrumental in their discovery. A good example of this is Descartes’ Stage 2 hypothesis from the Principles that the world was created in an initial state of ‘‘proportion or order [proportio vel ordo]’’ (Ibid., 257).11 This claim is not supported by evidence of any kind except (arguably) the fact that God has the power to do everything that we can conceive. Such a constraint hardly curtails Descartes’ prodigious imagination, however, and in the Principles he acknowledges that we are licensed ‘‘to make any assumption [assumere]’’ about the initial state of matter because ‘‘we cannot determine by reason alone how big these pieces of matter are, or how fast they move, or what kinds of circle they describe’’ (Ibid., 256). God, quite simply ‘‘might have instituted’’ what Descartes describes as ‘‘countless different configurations’’ of matter ultimately producing the effects we now observe. While he does offer the ‘‘sole proviso that all the consequences of our assumption must agree with experience’’, this is not to say that observational evidence led to the discovery of the hypothesis or that his Stage 2 hypotheses are true (Ibid., 256–257). Rather, the hypotheses must allow us to save the phenomena—i.e. to explain all known effects—and, failing this confirmation, the hypotheses can be rejected.12 This brings into sharp relief the second reason that Descartes’ suppositions are not potentially ‘‘false and uncertain’’, for in spite of passages like the one cited in the last paragraph about ‘‘countless configurations’’, Descartes will often claim that his Stage 2 hypotheses could not be false. The literature criticizing Descartes here is vast.13 As we just saw, Descartes acknowledges that God could have created matter in any number of initial states. This implies more than one Stage 2 hypothesis can be used to save the phenomena and, generalizing, it means that no single Stage 2 hypothesis can be judged true and certain.14 But Descartes adds in the Principles that he does ‘‘not consider it possible to invent [non puto . . . posse excogitari] any other principles that are simpler, or more intelligible, or indeed more probable [probabiliora]’’ than the ones he offers (1996, VIII 102, emphasis added). These further standards for assessing competing hypotheses—simplicity, intelligibility and probability—go beyond merely saving the phenomena or agreeing with experience. Applying them, Descartes seems to believe that all his hypotheses must be correct. Later in the Principles, Descartes elaborates on this thought with more technical terminology. He acknowledges that his method has provided only ‘‘moral certainties’’ consistent with God’s goodness. But still, Descartes intimates that his method has led to ‘‘absolute certainties’’. As he writes: there are some matters even in relation to the things in nature, which we regard as absolutely, and more than just morally, certain . . . Mathematical demonstrations have this kind of certainty . . . And perhaps even these results of mine will be allowed into the class of absolute certainties . . . All the other phenomena, or at least the general features of the universe and the earth which I have described, can hardly be intelligi-

9 The scholastic distinction between general as opposed to specific or particular physics is another way to understand this point. Stage 1 hypotheses enter in the context of Descartes’ general physics but Stage 2 hypotheses never do. 10 In spite of this shift from the The World to the Principles, what follows the Stage 1 hypothesis that matter is extension in both works are a series of Stage 2 hypotheses. First come suppositions [supposons / suppositionum] related to how God initially divides up matter and introduces motion into its many parts and then comes a hypothetical matter theory with three discrete elements: fire, air and earth. After this, Descartes conjoins his laws of nature to his suppositions about initial states and to his matter theory. From this combination of principles he infers the most general features of the world: planets, stars, comets, etc. A great deal of criticism has been directed at these inferences, but Descartes deserves credit for his commitment to a naturalized and developmental account of the natural world. 11 This is an initial state the complete opposite of the one Descartes hypothesizes in The World, which was one of chaos entirely lacking ‘‘order or proportion [ordre ni proportion]’’ (Descartes, 1985, p. 91). 12 Descartes sometimes explains away experiences inconsistent with the consequences of his hypotheses by citing the complex interactions between bodies that alter the expected effect (e.g., 1996, VIII 70; for discussion see Sakelleriadis, 1982). More generally we can say that Descartes refuses to give up his hypotheses until an equally all encompassing hypothesis or group of hypotheses can be found. 13 Descartes’ vacillation on the status of his hypotheses is the subject of McMullin 2008 and 2009, which include extensive bibliographies. 14 One can discern this point from Descartes’ account of the competing hypotheses about the Earth’s motion as well (1996, VIII 84-86; see also an earlier remark in defense of the Discourse in Ibid., II 200).

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bly explained except in the way I have suggested (1985, 290– 291). Descartes appears to be vacillating in this, the second-to-last paragraph of the Principles, and there is no obvious solution to his rhetoric in favor of absolute certainty. While in the end he affirms only that the ‘‘general features of the universe and earth’’ are absolutely certain, he holds out the possibility that more than this is absolutely certain. Ignoring the complication introduced by ‘‘absolute certainty’’, I propose to understand Descartes as claiming that none of his hypotheses are actually ‘‘false and uncertain’’. In Descartes’ judgment, not only do they explain the phenomena (something other hypotheses can also do), no other hypotheses have the same degree of collective simplicity, intelligibility and probability. This is an important part of Descartes’ developing view of hypotheses, but the main result of my discussion here in section two lies elsewhere. I can summarize what we have learned by returning to the complaint of Huygens noted earlier: Descartes’ reference to ‘‘grooved particles’’ is a conjecture. In referring to one of Descartes’ analogies and not to one of his hypotheses, Huygens is mistaken if he is asserting that Descartes simply offers an analogy between visible screws and sub-visible particles without any basis in experience. This is false because in the effect of pulling and pushing Descartes clearly registers a specific similarity identified through experience. But even if Huygens’ general characterization of the Principles as a fiction is correct because, for example, Descartes introduces Stage 2 hypotheses without using analogies, there is now at least a question about where precisely we find Descartes engaged in idle speculations and arbitrary conjectures. If Descartes’ hypotheses seem to fit this description when he introduces them without any evidence save the power of God, what about when analogies are is used to introduce hypotheses? Are these hypotheses or the analogies themselves arbitrary conjectures? In the following sections I try to show that the answer is no. 3. Descartes’ scientific practice With the background of the previous section in place, two strategies suggest themselves for discussing Descartes’ view of analogy: examining his practice and examining his methodological reflections, i.e., his philosophy of analogy. It will not always be easy to pursue these two strategies separately from one another, but in this section I focus on Descartes practice, as exemplified by work published in the mid-1630s. In the next section I will detail his philosophy of analogy. Descartes’ earliest reference to analogy dates from the 1610s. In a notebook preserved by Leibniz, Descartes writes that: Man has knowledge of natural things only through their resemblance to the things which come under the senses. Indeed, our estimate of how much truth a person has achieved in his philosophizing will increase the more he has been able to propose some similarity between what he is investigating and the things known by the senses. (Ibid., 5) This is clearly a commitment to analogy and to the epistemological significance of sense experience. Already we can see that Descartes believes our knowledge of the natural world depends on our ability to find analogies between what the senses reveal and ‘‘natural things’’. These pregnant ideas about the role of analogy and the foundational status of what we can observe reach mature expression only in the 1630s.15 Descartes’ most ambitious and original effort in physics, The World, dates from this period. Although it is

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summarized in Discourse Five, where Descartes acknowledges a hypothetical method involving fables and suppositions, the hypotheses and analogies that attract the most attention among Descartes’ readers are the ones found in the Dioptrics (e.g., Galison 1984; Garber, Unpublished; Statile, 1999). It is for this reason that I will be concentrating on the Dioptrics, where analogies and the evidence of sense experience figure prominently. Early in the Dioptrics, Descartes refrains from stating light’s ‘‘true nature’’. His official reason for this modest approach is his narrow interest ‘‘to explain how [lights] rays enter into the eye, and how they may be deflected by the various bodies they encounter’’. As a result, he will examine light but he ‘‘need not attempt to say what is its true nature’’. He continues: It will . . . suffice if I use two or three comparisons [comparaisons] which help to conceive light in the way [qui aydent a la conceuior en la façon] that seems most suitable for explaining all those of its properties that we know through experience and then for deducing all the others that we cannot observe so easily (Descartes, 1985, 152; modified). The procedure announced in the Dioptrics involves using analogies to introduce a Stage 2 hypothesis about light’s nature that will then serve to explain light’s effects. These include the transmission of light from a luminous body to our eye—Descartes’ first two analogies deal with this effect—and light’s reflection and refraction— Descartes’ third analogy deals with this effect. If Descartes’ hypothesis implies these effects, then by his own standard he has a good hypothesis. At the same time, Descartes’ claim that analogies can be used ‘‘to help conceive’’ his hypothesis suggests another measure of a good hypothesis. His phrasing is ambiguous between the use of analogy to discover a hypothesis and, having a hypothesis already in hand, the use of analogy to make the hypothesis more plausible or easier to accept. Descartes’ practice in the Dioptrics shows that he means both. Analogies aid in discovery. They also serve to illustrate how hypothesized causes might produce effects, thereby making the hypothesis more plausible. It is important to see that this measure of a good hypothesis is independent of what the hypothesis allows us to infer about light’s effects. A plausible hypothesis by the ‘‘measure of analogy’’ might fail to save the phenomena even though how it would do so, if it could, might be easy to understand and fully intelligible because of the wealth of analogies available. Writing to Vatier in 1638, Descartes returns to this early passage from the Dioptrics. ‘‘As for light, if you look at the third page of the Optics, you will see that I have said there expressly that I was going to speak about [light] only hypothetically [par hypothese].’’ He adds that he specifically tried ‘‘to convey some idea of [light’s nature] by comparisons [comparaisons]’’ (1991, 87, modified). The rest of Descartes’ letter indicates that the alternative method would involve supporting his Stage 2 hypothesis by deducing it from ‘‘the first principles of . . . metaphysics’’ (1985, 87). Whereas the Dioptrics gives ‘‘a posteriori’’ proofs, Descartes tells Vatier that the alternative to arguing hypothetically is to ‘‘prove a priori what I had supposed [que i’ai suposé]’’ (Ibid., 87; modified). It is interesting that Descartes does not think that he would need to change his hypothesis about light if he had followed the alternative method. It is time to see how Descartes uses analogy in his practice, in the method he actually follows. The first of the three analogies offered in the Dioptrics is the analogy of the blind man’s stick. Descartes introduces this analogy by likening the way in which we

15 These ideas are also present in the Rules. In Proposition 14 Descartes insists that ‘‘ . . . in all reasoning it is only by means of comparison [per comparationem] that we attain an exact knowledge of the truth’’ (1985, p. 57). To which he adds a few lines later ‘‘ . . . all knowledge whatever—save that which is obtained through simple and pure intuition of a single solitary thing—is obtained by means of comparison between two or more things.’’

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gain knowledge of the world through sight to the way a blind man gains knowledge of his surroundings through the use of a stick. ‘‘[O]ne might almost say that they see with their hands, or that their stick is the organ of some sixth sense given to them in the place of sight’’ (Ibid., 153). Descartes thinks it equally obvious— and presumably a fact we can learn from sense experience—that a blind man’s stick gains him knowledge ‘‘through the action of these bodies [in the world] when they move against his stick, but also through the action of his hand when they do nothing but resist the stick’’. In other words, in the case of the blind man, having sense experience of the world is the effect of a rigid body’s contact with objects in the world. ‘‘In order to draw a comparison [comparaison] from’’ the example of the blind man and his stick—that is, if we pursue the analogy between sight and touch—we should infer: light in bodies we call ‘luminous’ to be nothing other than a certain movement, or very rapid and lively action, which passes to our eyes through the medium of the air and other transparent bodies, just as the movement or resistance of the bodies encountered by a blind man passes to his hand by means of his stick. (Ibid., 153) In this example of his practice, Descartes uses an analogy to discover an unknown cause.16 The cause is a Stage 2 hypothesis about the nature of light. Although hardly a formal syllogism, Descartes follows the above passage by stating that his newly-discovered hypothesis makes the instantaneous propagation of light less ‘‘strange’’. If light is just the motion of a rigid body, like a stick, then movement in a luminous body would instantly be felt in the eye. Now that we have glimpsed how Descartes uses analogy and sensory knowledge to discover a hypothesis, it is worth asking again what precisely the distinction is between an analogy and a hypothesis. And what happened to my suggestion in section II that analogies are related directly to observation but that hypotheses are not? I believe the answer to these questions lies in the fact that Descartes’ Stage 2 hypothesis about light in the Dioptrics itself presumes the Stage 1 hypothesis that matter and motion are the defining features of the natural world. Every genuine phenomenon must be a manifestation of matter and motion, and this includes light. Adopting this Stage 1 hypothesis allows the similarity between a blind man’s use of a stick and our use of vision to have the right significance—it enables the analogy to call our attention to a subvisible mechanism. This only happens because a further similarity exists between the two cases being compared beyond the one Descartes explicitly cites since both must work through a species of contact motion. Thus, instead of a self-standing analogy introducing a Stage 2 hypothesis, I propose that what is really going on in the Dioptrics is that Descartes has a Stage 1 hypothesis supporting the analogy. The Stage 1 hypothesis and the analogy together lead him to his Stage 2 hypothesis. If this is right, the answers to the questions asked at the beginning of the last paragraph are the following: an analogy is always supported by some hypothesis or other, even when analogies are used to discover a hypothesis. Additionally, hypotheses themselves

make no direct reference to sense experience, but the analogies used to discover them do. And, finally, though we will see this more clearly in our analysis of the second analogy from the Dioptrics, an analogy makes a hypothesis intelligible by likening it to a familiar and well-understood observable phenomenon, such as the contact motion passed through the blind man’s stick. Descartes’ second analogy, the vat of wine analogy, enters where the first analogy leaves off. In his words, ‘‘because our blind man’s stick differs greatly from the air and the other transparent bodies through the medium of which we see, I must make use of another comparison [comparaison]’’ (Ibid., 154). Assuming his Stage 2 hypothesis that light is a ‘‘movement or very rapid and lively action’’, Descartes acknowledges here that light travels from a luminous body instantly in all directions and it does this without a series of rigid stick-like bodies being present. The trouble identified here is conceptual: the medium for light is very different from the analogue that aided in the initial discovery of Descartes’ hypothesis. The second analogy compares light to the pressure placed on the sides of a vat of wine by the liquid it contains and the pieces of grape as they ferment. The vat is supposed to illustrate how the instantaneous straight line propagation of light could occur through pressure or ‘‘the action or tendency to move’’. Punch a hole in the bottom of the vat and wine will flow out. Punch another in the side and the same will happen. This occurs instantly, according to Descartes, and in spite of the fact that the still solid grapes are collected near each of the holes. ‘‘In the same way, all the parts of the subtle matter in contact with the side of the sun facing us tend in a straight line towards our eyes at the very instant they are opened’’ (Ibid., 154-55). Light, Descartes infers, is a tendency to motion, a kind of pressure, that is always present waiting to be felt and, like the wine, it is capable of making its way through or around other bodies in its path. I claimed earlier that Descartes’ analogies serve both in the discovery of hypotheses and in making hypotheses more plausible. Here in the vat of wine analogy, Descartes has shifted to plausibility.17 His Stage 2 hypothesis was discovered using the analogy of the blind man, but the first analogy between light and the blind man’s stick is not altogether satisfying. It raises the prospect of a significant dissimilarity between the medium through which light travels and the medium of the stick such that an accepted fact of light—its instantaneous propagation in a straight line and around obstacles— cannot be explained. To handle this dissimilarity Descartes needed to show that an asymmetry that is true with respect to the first analogy is not necessarily true with respect to the hypothesis about light and other well known phenomena involving motion. Thus, the second analogy helps us understand how the Stage 2 hypothesis could still be true even if the analogy used to discover it is not consistent with all of light’s properties or effects.18 In the third and most famous of the analogies from the Dioptrics, Descartes compares light to a tennis ball or a series of tennis balls. His aim in using this analogy is to illustrate the manner in which something like light could produce color, reflect off a surface and refract through a medium. Although this analogy holds significant historical interest for its relation to Descartes’ convoluted derivation of the sine law of refraction, it follows the pattern set by the

16 The ratio-like scheme introduced in the last section can be used to convey Descartes’ first analogy. Blind man’s knowledge of the world: Motion by contact between bodies, a stick and the blind man’s hand :: Sighted man’s knowledge of the world : Motion between luminous bodies, a medium and the sighted man’s eyes. 17 Gabbey (1990) maintains that this analogy diverges from the first in that it is only an ‘‘illustrative analogy’’ and not a ‘‘working model’’ (p. 277). For more on this point, though put in terms of simulation and what simulation can contribute to physics, see Des Chene (2001). 18 The fact that Descartes’ analogies identify distinct effects of the causes he is seeking to discover or illustrate has led some to treat his analogies as ‘‘models’’ in the modern sense (e.g., Rodis-Lewis, 1978; Clarke, 1982; Gabbey, 1990). Such assimilation obscures a serious objection to Descartes’ multiple analogies in the Dioptrics. Specifically, if each analogy breaks down in some way, then the subvisible world is not identical to any of them. In that case, Descartes does not appear to have a Stage 2 hypothesis supported by an analogy but, at best, partial analogies supporting a hypothesis. The objection is that any hypothesis can be supported by some assembly of partial analogies. (In the next section, we will see that this is very similar to the objection Descartes receives from Jean-Baptiste Morin). However, Descartes’ built in constraint on acceptable analogies tied to his Stage 1 hypothesis limits which hypothesis can be supported even with partial analogies because all the causal analogues must involve matter in motion. I discuss this further in the next section.

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previous two.19 Descartes begins by noting an effect of light that is not consistent with the previous analogies, both of which presume straight line propagation—when making contact with some bodies light ‘‘is liable to be deflected by them, or weakened’’ (Ibid., 155). Next Descartes points out that these effects are similar to ‘‘the movement of a ball or stone thrown in the air [and] deflected by the bodies it encounters’’. The ball’s motion is controlled by the laws of motion and Descartes infers that light too must ‘‘obey the same laws as motion itself’’. It may be hard to think of the laws of motion as causes but two points are relevant here. First, Descartes does in fact think the laws of motion are causes (Ibid., 240). Second, what matters most in the analogy is the fact that the behavior of a ball hitting a surface, something knowable through sense experience, illustrates how matter in motion can sometimes behave. Light is just one species of motion according to Descartes’ Stage 2 hypothesis and his first two analogies, and the third analogy simply illustrates that if light is motion it will conform to the laws of motion. To sum up, Descartes’ scientific practice shows him using analogies to discover possible causes that serve as Stage 2 hypotheses. He also uses analogies to make his hypotheses more intelligible or plausible by comparing them to better-understood phenomena. Additionally, we saw that when proposing an analogy he seems to proceed with at least one hypothesis in hand, the most important being his Stage 1 hypothesis that matter is just extension. In the next section we will see how Descartes defends his use of analogy when it is challenged and why he believes explanations without analogies cannot be accepted. 4. Descartes’ philosophy of analogy In discussing Descartes’ analogies thus far, I have maintained that they help to discover or illustrate causes of natural phenomena, the effects of which are similar to the effects of a well-understood phenomenon of process. Described in this way, there is nothing especially new or innovative in Descartes.20 A comparison is just that, a comparison between two things meant to issue in a plausible conclusion. But Descartes does have a unique philosophy of analogy as part of his philosophy of science. This will be the main focus of this section. After the Discourse and its companion Essays were published, Descartes corresponds with several hostile critics. Among them is Jean-Baptiste Morin, who questions Descartes’ hypotheses as well as his analogies.21 Taking issue with the significance of analogies generally and the specific use Descartes makes of them in supporting his Stage 2 hypothesis about light, Morin notes ‘‘every comparison [comparaison] is between things that are different; thus according to you light is not action or motion’’ (1996, I 543). Yet Morin also recognizes that Descartes wants to infer more from his analogies, for he expresses his willingness to ‘‘criticize [Descartes’] essence or nature of light, which you [Descartes] say is action, or motion, or the inclination to motion, or like action or motion, etc. of a subtle matter,

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etc.’’ (Ibid., I 547). Morin appears to believe Descartes’ analogies evade giving specific details about his ‘‘subtle matter’’ and, in any case, the analogies do little to make plausible his Stage 2 hypothesis about the nature of light, whether light is action or motion or an inclination to action or motion, as the vat of wine analogy implies. The extent of the disagreement between Descartes and Morin is especially clear where Morin objects to Descartes’ explanation of color production with a prism using his Stage 2 hypothesis and the analogy of spinning balls.22 In the Meteors, Descartes first recalls his description of light from the Dioptrics ‘‘as the action or motion of a certain very subtle matter whose parts must be imagined as small balls rolling in the pores of earthly matter’’ (Ibid., VI 331). Descartes goes on to infer that what diversity we find in light’s effects is not the result of the small balls as such but is a product of the way the balls—the material analogue of his ‘‘very subtle matter’’—move (Ibid., VI 333-4). In his own words: I understand that these balls can roll in diverse ways according to the diverse causes which determine them; and in particular, that all the refractions that occur on the same side cause them to turn in the same direction; but when they have no neighboring balls that are moved notably faster or slower than they, their turning is almost equal to their linear motion; whereas when they have some on one side that move more slowly, and others on the other side that move as fast or faster, as occurs in the confines of shadow and light, then if they meet those that move more slowly on the side toward which they are rolling . . . this causes them to turn less quickly than if they were moving in a straight line; and it is just the opposite when they encounter them on the other side. (Ibid., VI 331) Using his hypothesis about light’s nature and the analogy of spinning balls, Descartes’ conclusion is that refraction can be understood as a change in the rotational and translational motion of subtle matter. Prior to refraction the balls of subtle matter in a beam of light share a common translational motion in their direction of propagation. When entering a new medium with a refracting surface there is no question of stopping the translational motion, and so long as the ‘‘neighboring balls’’ to a given beam of refracted light are moving at the same speed as the balls in the beam of light, then refraction will occur without producing color. This is because the rotational motion is the same as the motion in the direction of propagation, or as Jed Buchwald has put it, ‘‘translation couples to rotation in the same way that it does for a ball rolling without slipping’’ (Buchwald 2007, 38). In other words, according to Descartes mere change of direction coupled with rotational motion that exactly matches the translational motion will not produce color. However, if the ‘‘neighboring balls’’ are moving at different speeds, say because of the presence of a shadow, which Descartes identifies with a lack of motion, then the spinning balls will spin at different rates in relation to their translational motion.23 Depending on the motion of the particles

Schuster (2000) provides a persuasive reconstruction of Descartes’ derivation of the sine law. To provide a more thorough background for Descartes’ terminology and the models he follows or rejects, we would need to investigate, at least, the following: (1) rhetoric, where the trope of comparatio and the use of exemplum and similitudo abound; (2) logic, where distinctions between demonstratio quia, identified as ‘‘analysis’’ or reasoning a posteriori from effects to causes, and demonstratio propter quid, identified as ‘‘synthesis’’ or reasoning a priori from causes to effects exist; (3) mathematics, where proceeding according to ordo, finding instances of ratio, and comparing by means of proportio are features of geometry and algebra; (4) astronomy, where the practice of using conjecture and hypothesis to save the phenomena are standard fare in dealing with heavenly bodies; (5) medicine, where medical induction and semiology make a fine art of observation and inference from effects, understood as signs (signum, indica), to hidden causes; (6) theology, where disputes over God’s being, the being of his creation, and other characteristics seemingly shared between the two, are conducted in terms of comparationes; (7) chemistry, where analogy is a fundamental troupe in explanation; and (8) meteorology, where conjecture and unobservable causes fill the Renaissance commentary tradition on Aristotle’s Meteorology. 21 Morin is best remembered for these disputes and for disputes he has with Gassendi, but Morin was an important seventeenth-century astrologer and the likely author of the second set of objections to Descartes’ Meditations (Garber, 1995). 22 For more on color and the rainbow, see Shea (1991) and especially Buchwald (2007). 23 It may be helpful to imagine the observable phenomenon Descartes is appealing to as an unequal pinch. On entering a prism subtle matter can be pinched by surrounding matter moving at a different speed. Just as pinching a marble with our fingers will cause the marble to spin because of the unequal force that we apply, refracting light can be pinched by ‘‘neighboring balls’’. 20

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already present in the mediums though which the beam of light travels, the periphery of the beam of light will gain or lose speed, with any change diminishing toward the center of the beam. We could go on at some length in analyzing Descartes’ remarks about prisms and refraction, but what is most important for us in Descartes’ account is that his analogical reasoning leads him to assign the production of color to the variable motion of subtle matter. For his part, Morin has considerable difficulty with Descartes’ reference to spinning balls. He cannot understand, for example, why Descartes allows balls of the subtle matter to ‘‘roll . . . in air’’ prior to entering a refracting surface even though everything presented in the Meteors concerning refraction implied to Morin that the balls begin to spin ‘‘only when they encounter a more solid [refracting] surface’’ (1996, I 547). Morin’s failure to appreciate Descartes’ use of analogy as well as Descartes’ unwillingness to abandon analogies characterizes the rest of the correspondence between the two. Descartes’ initially defends himself in a letter sent five months after Morin’s initial correspondence. First Descartes describes a broad-minded conception of analogy: you have wonderfully shrunk the meaning of the word ‘like’. . . and you would like for it to be used only to join the terms of a comparison [comparaison], which is between different things. But if this were true, then when one said that someone did something like a learned person, then that would mean that he wasn’t learned. (Ibid., II 204–5) There is no doubt that Morin commits himself to an impoverished view of analogy and Descartes is right to reject Morin’s proposal. Nevertheless, the context of Morin’s remarks is the discovery of Descartes’ Stage 2 hypothesis about light and the subsequent analogies used to illustrate light’s effects in keeping with the initial hypothesis. Just as Descartes advances his position in the Dioptrics by hypothesis and analogy, however, his defense of the Meteors uses the same strategy: I do not speak at all about the subtle matter, but about wood balls, or other visible matter [matiere visible], which are pushed towards water; as is evident from my making them turn completely contrary to the parts of the subtle matter, and compare [compare] the turning which they acquire in leaving air and entering water, to that which the parts of the subtle matter acquire in leaving water or glass and entering air. (Ibid., II 208) This is the first mention of ‘‘wood balls’’ in Descartes’ discussion of light but the point he is trying to make is clear enough. In the Meteors he uses an analogy to illustrate how his Stage 2 hypotheis about light might explain the production of color. This is how Morin should understand the claim from the Meteors that light’s action ‘‘must be imagined’’ in terms of spinning balls. Put another way, Descartes is telling Morin that the majority of the discussion in the Meteors concerns the Known Effect1: Known Cause of spinning balls, and Morin has taken the analogy too literally. Morin is no more convinced by this new analogy than he had been by the Meteors. The tone of Morin’s reply one month later even has an air of exasperation. He was simply unwilling to allow analogies with observable phenomena to guide a discussion about the nature of light and the manner in which it produced its effects. As he writes, ‘‘difficulties in physics are rarely put to rest by comparisons; there is nearly always some difference, or some ambiguity, or the [substitution of] the obscure by the more obscure’’ (Ibid., II 291). Morin reiterates the difficulties he finds in Descartes’ appeal to analogy later in the same letter. Given that ‘‘you [Descartes] respond only through comparisons [comparaisons], I have already warned you that [comparisons] rarely are appropriate for resolving

a difficulty’’ (Ibid., II 297). And so, Morin ignores Descartes’ new analogy of spinning wooden balls and askes again about the subtle matter that continued to elude him. To the modern reader Morin may appear to have the better argument. After all, part of the reason we turn to analogy is because we cannot provide deductive arguments. This bias against analogical reasoning can be traced to the Ancient world and is manifest in Aristotle and the commentary tradition on the Posterior Analytics (Allen 2001). Descartes’ own vacillation over the truth of his hypotheses, coupled with his insistence that he could provide a demonstration if he wanted to, looks to be further evidence that analogical reasoning is a second-rate option even for him. Thus, we might hear Morin as saying: if you can demonstrate these claims demonstrate them, do not give us partial analogies that must be abandoned whenever a question arises about the subtle matter that is the effect’s true cause. In other words, explain the nature of light and its effects without analogies or accept that you have no coherent view of the nature of light. Using comparisons to make claims specifically about the natural world was not new to Descartes. At least since Epicurus, whose letter to Herodotus was again available in the late sixteenth century, atomists had been arguing for the existence of the subvisible void by drawing a comparison to the motion of observable objects into empty space. Gassendi commented explicitly on Epicurus’ letter and showed considerable interest in analogical reasoning himself (e.g., 1684, 14; 1981 [1658], p. 160). Descartes also refers to the atomists’ use of analogical reasoning near the end of the Principles (1996, VIII 325). Yet, he does not refer to the precedent from atomists in response to Morin. Instead, in his next letter Descartes concedes the point that he uses analogy to answer difficult questions in physics and then offers a theory of falsification, or what I have been calling his ‘‘philosophy of analogy’’: True, the comparisons [comparaisons] that are usually employed in the Schools explain intellectual matters by means of physical ones, substances by means of accidents, or at any rate, one quality by means of a quality of a different kind, and they are not very instructive [n’instruisent que fort peu]. But in the comparisons [pource qu’en celles] which I employ, I compare motions only with other motions, or shapes with other shapes; that is, I compare things that are too small to be perceived by the senses with other things that can be so perceived, the latter differing from the former simply as a large circle differs from a small one. I maintain, therefore, that comparisons of this sort are the most appropriate means [ells sont le moyen le plus propre] available to the human mind for laying bare the truth in problems of physics [questions Physiques]. I would go so far as to say that, when someone makes an assertion concerning nature which cannot be explained by any such comparison [qui ne peut ester expliquée par aucune telle comparaison], I think I have demonstrative knowledge that the point is false [je pense sçauoir par demonstration qu’elle est fausse]. (1991, 122) There are two distinct claims being made here. One is a defense of his earlier practice. The other is a new claim, consistent with his earlier practice, but of considerable interest in its own right. In the remainder of this section I will first discuss Descartes’ defense and then his philosophy of analogy. Whereas the scholastics ‘‘explain intellectual matters by means of physical ones, substances by means of accidents, or at any rate, one quality by means of a quality of a different kind’’, Descartes’ analogies can inform us about the world ‘‘too small to be perceived’’. More than this even, and against Morin’s position, analo-

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gies are the ‘‘most appropriate’’ means for supporting or making a claim in physics.24 Unlike the scholastic’s analogies, as Descartes describes them, which commit what we would now call a ‘‘category mistake’’. Descartes’ analogies are informative and relevant because they confine themselves to the same ontological category. Descartes clearly believes this last constraint precludes comparisons like those offered by scholastics, but it is worth noting that without an additional premise this is not so. Seeing what this premise is is not easy, however, because Descartes does not specify which specific analogies he finds objectionable. Consider, however, a passage from the Rules, where Descartes distinguishes his use of a particular analogy: Let us then conceive of the matter in the following way. First, in so far as our external senses are all parts of the body, sense-perception . . . is merely passive . . . sense-perception occurs in the same way in which wax takes on an impression from a seal. It should not be thought that I have a mere analogy [analogiam] in mind here: we must think of the external shape of the sentient body as being really changed by the object in exactly the same way as the shape of the surface of the wax is altered by the seal. (1985, 40). In the Rules, Descartes is rejecting the scholastic description of how sense-perception takes place. I think it is plausible to believe that Descartes has the scholastics in mind as the ones who use the example of the wax and seal as a ‘‘mere analogy [analogiam]’’. Yet, they could legitimately use the comparison of wax receiving a seal without violating Descartes’ stipulation that we only use analogies within the same ontological category. For the scholastic, both senseperception and the wax and seal involve the transfer of form from an object impressing itself upon formable matter. In slightly more technical terms, for the scholastic the perception to be explained and the transfer of a ‘‘real quality’’ from the object both belong to the category of quality. The same goes for the seal and wax. Thus, by the scholastic’s lights, comparing the two satisfies Descartes’ strict standard for a good analogy: avoid category mistakes. Descartes understands his ontological constraint as limiting comparisons to ‘‘things that are too small to be perceived by the senses with other things that can be so perceived, the latter differing from the former simply as a large circle differs from a small one.’’ But how does Descartes know that things too small to be perceived do not differ in kind from sensible objects? This question brings us back again to Descartes’ Stage 1 hypothesis and the additional premise that rules out the scholastic’s use of the seal and wax analogy. What is unstated in the letter to Morin, just as it was unstated in the Dioptrics as we saw in the last section, is Descartes’ conception of matter as extension. The analogy Descartes draws between his activity in physics and the geometer’s work with circles brings out nicely the role played by his Stage 1 hypothesis. A circle, whether large or small, may be defined as a figure generated by describing all points equidistant from a given center. This is what it is to be a circle and even if particular circles will vary in their accidents of color or size, they remain essentially the same. From their definition, further truths can be known to apply to circles, such as the fact that each circle’s radius is half its diameter or that p is equal to every circle’s circumference divided by its diameter. In the latter case, geometers can legitimately compare a large circle to a small circle by comparing

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the circumference divided by the diameter of the one to the circumference divided by the diameter of the other to find an unknown quantity. Put into a ratio-like form where the unknown quantity is a diameter of one of the circles we get: Known Circumferance1 : Known Diameter1 :: Known Circumferance2 : Unknown Diameter. This is a legitimate comparison given the essential similarity of all circles. When Descartes uses analogies that belong to the same ontological category, his Stage 1 hypothesis his hypothesis serves exactly the same role as the definition of the circle for the geometer. Recall the ratio-like form of Descartes’ analogies: Known Effect1 : Known Cause :: Known Effect2 : Unknown Cause. Descartes’ analogies are informative and legitimate because they are limited to the same ontological category where everything is essentially the same—the physicist is just dealing with matter in motion.25 The difficulty the scholastic encounters is that he has too many ontological categories informing his analogies. Besides clarifying his use of analogy to Morin and the role played by his Stage 1 hypotheis, Descartes also says that analogies are a necessary part of physics. Lacking an analogy of the sort he advocates, Descartes claims that we have definitive reason to believe a proposed explanation is false; i.e., the effect or the cause is either non-existent or outside of nature. This suggestion is unacceptable to Morin and his very deep disagreement is evident in the last letter between the two: I am amazed that you think so highly of comparisons to prove things in physics, to the point of saying that ‘when someone makes an assertion concerning nature which cannot be explained by any such analogy, I think I have demonstrative knowledge that the point is false,’ since one can find many effects in nature which have nothing resembling them. (1996, II 411; emphasis added). As before, Morin has a point. It is one thing to use an analogy to aid in discovery or to make a hypothesis more intelligible, but something else entirely to claim that analogies between motions or analogies between shapes are the only acceptable way to use analogies in physics. It is something even more to say that without an analogy an explanation is lacking. Again, what Morin does not appreciate is Descartes’ Stage 1 hypothesis that all matter is just extension. This point is made in Garber (Unpublished) and it is the assumption about matter’s essence that makes all the difference to Descartes’ philosophy of analogy.26 For Descartes’ view is not simply, where there is a cause there is an analogy. Rather, his view is that where there is just extension there will always be some analogy to aid in discovery or illustration. And, of course, by a Stage 1 hypothesis extension is everywhere. Descartes makes this explicit in the Principles: I . . . acknowledge that I recognize no matter in corporeal things apart from that which the geometers call quantity . . . i.e. that to which every kind of division, shape and motion is applicable. Moreover, my consideration of such matter involves absolutely nothing apart from these divisions, shapes and motions. . .. And

24 In a contemporaneous letter, Descartes writes to Plempius that it ‘‘is perfectly reasonable to judge of things which are too small for the senses to perceive by the example and similarity of those we see’’ (1991, p. 65; modified). 25 This also helps explain why Descartes nowhere shows any hesitance about problems generated by scale-variance. The laws of nature are scale-invariant because they owe the existence to God’s immutability and the nature of his creation, namely extension. There is no more scale-variance in a physics of extension as there is in a geometry of extension. 26 An alternative assumption is Descartes’ commitment to a unified science (Statile, 1999). Yet a third alternative, though it is not Descartes’ own, is simplicity. I discuss simplicity in the conclusion below.

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since all natural phenomena can be explained in this way . . . I do not think that any other principles are either admissible or desirable in physics. (1985, 247). If something is entirely unlike shape, size or motion, it will not enter into Descartes’ physics.27 Whereas Morin, like the scholastics, accepts a plurality of ontological categories, Descartes does not. For him, explanations without analogy run afoul of an immediate consequence of his ontology. Thus, Descartes’ method in physics looks something like this: we know the general principles that define the material world; e.g. matter is just extension, there are certain laws of nature. We observe a given effect. To explain what we observe we need to proceed to the sub-visible world. This world cannot be observed. Given my principles, however, the subvisible world is essentially the material world I sense, but on a much smaller scale. To explain what we observe we should look for some combination of sizes, shapes and motions of sensible bodies that produce effects similar to the ones we are looking to explain. Once we find such a combination, we have an analogy with one missing term. We next infer the missing term, the Unknown Cause, on the basis of the observable analogue—Known Effect1: Known Cause. Or, as Descartes himself puts it in the Principles: ‘‘Later on, when 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., 288). The procedure Descartes advocates requires us to find analogues whose behavior mimics the behavior that we are trying to explain. Only then can we infer to the extended causes we cannot see. 5. Conclusion In this paper, I have sought to elucidate Descartes’ use of analogy, and in particular to show how we should understand the differences between the roles of analogies and hypotheses in his physics. I also claimed that Descartes’ view holds considerable appeal. But given how frequently his Stage 1 hypothesis about the essence of matter entered into the last two sections, this may seem a bizarre claim. For how can Descartes’ philosophy of analogy look appealing unless we accept his Stage 1 hypothesis? A response can be found in the value we assign to simplicity when choosing among competing theories and explanations. Descartes promotes simplicity in physics by embracing his Stage 1 hypothesis that matter is extension. As we have seen, this is the fundamental principle of his physics and it is this principle that allows him to reject explanations for which an analogy cannot be given. In hindsight, Descartes’ physics gains its simplicity at the cost of embracing a dubiously austere ontology. If we are willing to see Descartes’ claims to Morin as part of an effort to insist that we preserve simplicity, however, the absence of an analogy may just be a sign that simplicity, at the level of our fundamental principles, is being compromised.28 Should we accept an explanation to which no analogy applies and add complexity to our principles? This is the question Descartes’ philosophy of analogy and its theory of falsification is asking. His answer was an emphatic no—too emphatic because of how conservative such a strong emphasis on simplicity turns out to be—but Descartes’ question is one we all face regardless of what our fundamental principles turn out to be. To accept that no analogies exist is to accept Morin’s belief that ‘‘one can find many effects

in nature which have nothing resembling them.’’ Even today there are very few of these. Acknowledgments I have benefited from the advice and constructive suggestions of many friends and colleagues in writing this paper. I wish to thank Mordechai Feingold, Daniel Garber, Kristine Haugen, Chris Hitchcock, Mac Pigman and Jim Woodward, all of whom discussed issues related to analogy with me. I also wish to thank Roger Ariew, Paul Bartha, Mary Domski, Melissa Pastrana and two anonymous referees for this journal, all of whom provided me with significant feedback on the manuscript. I am very grateful to all the people mentioned here. References Allen, J. (2001). Inference from signs: Ancient debates about the nature of evidence. Oxford: Clarendon Press. Anstey, P. (2005). Experimental versus speculative natural philosophy. In P. Anstey & J. Shuster (Eds.), The science of nature in the seventeenth century: Patters of change in early modern natural philosophy (pp. 215–242). Dordrecht: Springer. Ariew, R. (2010). The new matter theory and its epistemology: Descartes (and late Scholastics) on hypotheses and moral certainty. In P. Anstey & D. Jalobeanu (Eds.), Vanishing matter and the laws of motion: Descartes and beyond (pp. 31–48). London: Routledge. Bartha, P. (2010). By parallel reasoning: The construction and evaluation of analogical arguments. Oxford: Oxford University Press. Bellis, D. (2010). Le visible et l’invisible dans la pensée Cartésienne: Figuration, imagination et vision dans la philosophie naturelle de René Descartes (2 vols., PhD diss.). Université Paris-Sorbonne. Buchwald, J. (2007). Descartes’s experimental journey past the prism and through the invisible world to the rainbow. Annals of Science, 65, 1–46. Clarke, D. (1982). Descartes’ philosophy of science. University Park: Penn State University Press. Clarke, D. (1989). Occult powers and qualities: Cartesian natural philosophy under Louis XVth. Oxford: Clarendon Press. Clarke, D. (1990). The Discours and Hypotheses. In G. Belgioioso, G. Cimino, P. Costabel, & G. Papuli (Eds.), Descartes: Il Methodo E I Saggi (pp. 201–209). Rome: Enciclopedia Italiana. Clarke, D. (2010). Hypotheses. In D. Clarke & C. Wilson (Eds.), The Oxford handbook of philosophy in Early modern Europe (pp. 249–271). Oxford: Oxford University Press. Des Chene, D. (2001). Spirits and clocks: Machine and organism in Descartes. Ithaca: Cornell University Press. Descartes, R. (1985). The philosophical writings of Descartes, (J. Cottingham, R. Stoothoff & D. Murdoch, Eds.) (Vol. 2). Cambridge: Cambridge University Press. Descartes, R. (1991). The philosophical writings of Descartes, (J. Cottingham, R. Stoothoff, D. Murdoch, & A. Kenny, Eds.) (Vol. 3). Cambridge: Cambridge University Press. Descartes, R. (1996). Oeuvres de Descartes (C. Adam & P. Tannery, Eds.) (11 vols.). Paris: J. Vrin. Gabbey, A. (1990). Explanatory Structures and Models in Descartes’ Physics. In G. Belgioioso, G. Cimino, P. Costabel, & G. Papuli (Eds.), Descartes: Il Methodo E I Saggi (pp. 273–286). Rome: Enciclopedia Italiana. Galison, P. (1984). Descartes’s comparisons. Isis, 75, 311–326. Garber, D. (1995). J.-B. Morin and the Second Objections. In R. Ariew & M. Grene (Eds.), Descartes and His Contemporaries: Meditations, Objections and Replies (pp. 63–82). Chicago: University of Chicago Press. Garber, D. (1978). Science and certainty in Descartes. In M. Hooker (Ed.), Descartes: Critical and interpretative essays (pp. 114–151). Baltimore: Johns Hopkins Press. Garber, D. (Unpublished). Early Modern Analogies and Models: Descartes and Galileo. Gassendi, P. (1684). Syntagma Philosophiae Epicuri cum Refutationibus Dogmatum. Amsterdam: Janssonio-Waesbergios. Gassendi, P. (1981). Pierre Gassendi’s Institutio Logica (H. Jones, Trans.). Assen: Van Gorcum. (First published 1658). Hatfield, G. (1988). Science, Certainty, and Descartes. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association, 2, 249–262. Hatfield, G. (2000). Descartes naturalism about the mental. In S. Gaukroger, J. Schuster, & J. Sutton (Eds.), Descartes’ natural philosophy (pp. 630–658). London: Routledge.

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