Abstract
In this paper, I examine the manner in which Descartes defends his Vortex Hypothesis in Part III of the Principles of Philosophy (1644), and expand on Ernan McMullin’s characterization of the methodology that Descartes uses to support his planetary system. McMullin illuminates the connection between the deductive method of Part III and the method Descartes uses in earlier portions of the Principles, and he brings needed light to the role that imaginative constructions play in Descartes’s explanations of the phenomena. I develop McMullin’s reading by bringing further attention to the constraints that Descartes places on the imagination in Part III. I focus in particular on the way in which Descartes uses metaphysical truths concerning God’s nature to support his general description of the planetary system, and on the way he relies on a mathematical standard of intelligibility to defend his proposals about the configuration of matter. Attending to the role of metaphysics and mathematics in Part III shows that Descartes’s arguments for the explanatory power of the Vortex Hypothesis are more effective than McMullin suggests. The reading I forward also offers important perspective on how Descartes’s hypotheses in Part III can be seen as both metaphysically and mathematically well-grounded.
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Notes
Unless otherwise noted, all references to the Principles are to the Miller and Miller (1984) translation. Following standard citation format, I supply page numbers for references to the Preface, and I supply the part and section number for references to the main body of the text. As per Miller and Miller’s convention, squiggly brackets signal text that was added to the 1647 French edition of the Principles. For citations to other works by Descartes, I use ‘AT’ to refer to Descartes (1996), ‘CSMK’ to refer to Descartes (1991) and ‘CSM’ to refer to Descartes (1985).
In a letter from 11 November 1640, for instance, as the Meditations are nearing publication, Descartes reports to Mersenne that this “little metaphysics contains all the principles of my physics” (CSMK, p. 157; AT III, p. 233). A couple of months later, Descartes says in a similar vein “that these six Meditations contain all the foundations of my physics” (28 January 1641; CSMK, p. 173; AT III, pp. 297–298).
There is good evidence that, prior to the 1640s, Descartes subscribed to the view that physics ought to be founded on some more fundamental discipline. For instance, in the unpublished and incomplete Regulae (ca. 1628), he claims that our study of the natural world develops out of the more universal science that he describes in the text. Also, the belief that physics could be demonstrated from metaphysics is expressed in the letter to Mersenne from late November 1633 that is included immediately below. The significance of the post-1633 “metaphysical turn” that I stress above is that it prompted Descartes to publically present his natural philosophy as a metaphysics-first project. My thanks to Zvi Biener for urging me to clarify this point.
The historical details surrounding the Galileo Affair are certainly much more complicated than Descartes interprets. Source material linked with the dispute between Galileo and the Church can be found in Finocchiaro (1989). See Friedman (2008) for discussion of how the philosophical debates central to the Galileo Affair help illuminate the concerns that motivated Descartes’s “metaphysical turn.”
The Vortex Hypothesis is first made public in Part Five of the anonymously published Discourse on Method (1637). However, in the Discourse, Descartes provides a very brief overview of the system and offers no specific arguments in favor of his position. He also makes no specific mention of the Sun being at the center of the system, and the only motions to which he refers are the motions of the heavens and the stars (CSM I, pp. 132–133; AT VI, pp. 42–44).
In accepting that the arguments of Part III are meant to be genuinely convincing to a reader of the Principles, I am in agreement with Des Chene (2000), Garber (1992) and Gaukroger (2002), all of whom part ways with commentators who claim that Descartes’s primary goal in Part III is to disguise his Copernican commitments, not to provide well-grounded or sophisticated arguments for his planetary system. On this alternative reading, which can be found in Gaukroger (1995), there is something disingenuous about this portion of the text, and the best we can allegedly say is that Descartes relies on his relativist account of true motion to provide an unconvincing argument that, properly speaking, the Earth is at rest relative to the ether in which it is situated. Gaukroger abandons this view, and argues in Gaukroger (2002) that his earlier reading is inconsistent with the development of Descartes’s mechanics from 1633 to 1644, and also inconsistent with what is presented in Part III (Gaukroger 2002, pp. 142–146). Hatfield (1993) tackles the broader “dissimulation thesis” and challenges the claim that the metaphysical foundationalism Descartes describes as characteristic of his mature physics is merely a ploy to appease the Church. Hatfield argues, in particular, that the discovery of a pure intellect was a key development in Descartes’s philosophy, which allowed him to fashion proofs of God and the soul that could serve as the metaphysical foundations for the program of natural philosophy he publishes in the 1640s.
My thanks to an anonymous reviewer for urging me to clarify the sense in which the argument strategy that Descartes uses in the Treatise in Light is different from the one he uses in the Principles.
These observed phenomena include: the “ratios of distance and magnitude between the Sun, the Earth, and the Moon” (III.5); the “distance between the other Planets and the Sun” (III.6); the relative distance between the Earth and the fixed Stars (III.7); and the position of the fixed Stars relative to each other (III.14).
As suggested by the imagery of Descartes’s Tree of Philosophy, there is a broader goal that is directing the project of Part III: His explanation of the heavens is meant to contribute to our knowledge of the natural order. In Sect. 5 below, I discuss the sense in which the claims of Part III count as knowledge claims for Descartes. For the moment, I narrow my focus on Descartes’s more specific goal in Part III, namely, to explain observed phenomena by means of the Vortex Hypothesis, so that I can illuminate his strategy for arguing in favor of his planetary model and also the role of truth in this area of Descartes’s natural philosophy. My thanks to an anonymous reviewer for encouraging me to clarify my approach to Part III of the Principles.
As Descartes puts it, just as a man at sea has difficulty determining whether the changing position he observes is caused by the motion of his vessel, or by the motion of the vessels he sees in the distance, so too “when, from our situation [on Earth], we observe the course of the Planets and their various positions, even careful observation does not always bring sufficient understanding to enable us to determine {from what we see}, to which bodies we ought properly to attribute {the causes of} these changes” (III.15).
As helpfully emphasized by an anonymous reviewer, Descartes’s characterization of the main difference between Tycho’s and Copernicus’s systems diverges from our contemporary understanding of how they differ. From our current vantage point, we would say that Tycho’s system attributes less motion to the Earth than Copernicus’s, but Descartes claims the opposite, because he is relying on his definition of true motion as relative motion. See Sect. 3 below for further discussion of the relevance of Descartes’s account of true motion in Part III of the Principles.
See, for instance, Descartes’s characterization, in the 1647 Preface, of the method that he uses in the Principles to identify the true principles of natural philosophy (Descartes 1984, pp. xxi–xxii).
We find Descartes repeating this sentiment in I.75, where he states that “from a consideration of [God’s] attributes we can investigate the truth of the remaining things, since He is their cause” (I.75). As emphasized by McGuire (2007), these claims from Descartes about the best method for natural philosophy are informed by his commitment to the Neo-Platonic principle that our human “order of knowing” ought to correspond to the metaphysical “order of being.” Namely, our inquiries into creation should commence with our knowledge of God, because, for Descartes, such an epistemic progression is faithful to a metaphysical picture according to which God the Creator is prior to the things He has created.
Much has been written about how Descartes connects God’s role as the primary cause of motion with the causation seemingly found in created bodies. For recent discussion, see Hattab (2000), Ott (2009) and Schmaltz (2008). See also Domski (2018) for a reading of how our limited though certain knowledge of God’s nature informs what Descartes’s laws of nature communicate about the workings of the natural world.
To support reading the enumerations of Part III as “deductions,” McMullin refers to remarks from the earlier Regluae (ca. 1628), where Descartes explicitly acknowledges that there are two types of “deduction.” One type begins from what is intuitively known and is “simple and transparent.” The other type, which begins from a claim that is not intuitively known, “is complex and involved [and] we call it ‘enumeration’ or ‘induction,’ since the intellect cannot simultaneously grasp it as a whole” (CSM I, pp. 37; AT X, p. 408). In further support of his reading, McMullin also refers to the ambiguous use of the French term deduire during the early seventeenth century, as noted by Clarke (1982).
McMullin provides slightly different translations of these two passages. See McMullin (2008, p. 97).
On McMullin’s account, the essential difference between intuitive and imagined representations in the Principles is that the former compel our assent, but the latter do not. Put differently, intuitively known perceptions indicate what is true, whereas imagined representations indicate what is possible. In Sect. 5 below, I discuss the significance of this distinction for the notion of natural knowledge that’s at play in Part III of the Principles. The question of whether Descartes’s use of the imagination in 1644 is faithful to the characterization of the imagination that’s presented in the Meditations I leave for another time.
McMullin acknowledges that true metaphysical and physical principles underwrite the natural philosophy of Part III, and claims that it is precisely because Descartes accepts such truths that his method should not be interpreted as a hypothetico-deductive one (McMullin 2008, p. 98). However, McMullin does not consider the specific ways that these truths inform Descartes’s imaginative constructions, or the way that they might serve as standards for evaluating the explanatory quality of his hypotheses.
The reason, Descartes explains, is because of the laws of nature. With the laws of nature stemming from God’s immutable conservation of nature, and thus known to be timelessly true principles of created things, we are assured that these laws have governed material bodies, and all their changes in form, from the moment of creation up to the present. Consequently, Descartes explains, “it is almost impossible to imagine any [initial] arrangement from which we could not deduce...the same effect,” that is, from which we could not “reach the form which is {at present} that of this world” (III.47).
See for instance the creation story described in the Treatise on Light, where Descartes proposes that originally, the pieces of matter had varying speeds and sizes, and where he explicitly refers to the original state of matter as “chaos.” (Descartes 1998, pp. 23–24; AT XI, p. 35) See also Part Five of the Discourse, where, in describing the project of the Treatise on Light, Descartes claims that he “supposed that God now created, somewhere in imaginary spaces, enough matter to compose such a world; that he variously and randomly agitated the different parts of this matter so as to form a chaos as confused as any the poets could invent” (CSM I, p. 132; AT VI, p. 42).
The Geometry was included as one of the appendices to the anonymously Discourse, along with the Opticks and Metereology. All three together are described by Descartes as examples of the method that he forwards in the main body of the text.
I certainly do not mean to suggest that all of the claims in the Geometry concerning mathematical intelligibility map on to what we find in the Principles. Indeed, in the Principles there are cases where Descartes refers to constructions that are not considered “geometrical” by the standards of the Geometry. In III.59, for instance, he considers a path that is produced from the combination of a circular motion and a rectilinear motion—the very type of construction procedure that renders a curve “mechanical,” or non-geometrical, in the Geometry. The more restricted claim that I am making is that from 1637 to 1644, Descartes subscribes to the same ideal of mathematical simplicity and intelligibility, namely, one that rests on a notion of equality. See Domski (2009) for how Descartes incorporates the intelligibility of mathematically simple motions into the arguments of The World.
My characterization of how to connect the method of Part III with the process of mathematical deduction is reinforced by Descartes’s claim in the final article of Part II that he does not “accept or desire in Physics any other principles than in Geometry or abstract Mathematics; because all the phenomena of nature are explained thereby, and certain demonstrations concerning them can be given” (II.46). In the discussion above, I rely on remarks from the Discourse, because these provide a picture of Descartes’s understanding of mathematical demonstrations that’s more fine-grained than that offered in III.46.
In claiming that the mathematical ideals for simplicity and for deductive reasoning play a regulative role in the project of Part III, we gain a more nuanced sense of how Descartes’s physics could be read as a mathematical physics. Of course, this is not meant to discount the important work of scholars who have explored why there is no mathematical formalism in Descartes’s physics. For more on this question, see Gabbey (1993) and Garber (2000), who examine why Descartes does not include the mathematical science of mechanics in the Principles, and Slowik (1996), who discusses the difficulty of quantifying the speeds and motions of the bodies that are included in Descartes’s vortex model.
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During the past few years, several people generously offered feedback on different versions of this paper. Audience members at Macalester College and the University of Notre Dame provided very helpful suggestions, and the constructive advice I received from Kelly Becker, Katherine Brading, Mary Kathryn Karafonda, Gideon Manning, and three anonymous reviewers helped me fine-tune the aims and scope of this project. I am especially grateful to Zvi Biener for commenting on the penultimate version of the paper. Whatever murkiness and confusions might remain, my presentation is clearer and more focused because of his recommendations.
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Domski, M. Imagination, metaphysics, mathematics: Descartes’s arguments for the Vortex Hypothesis. Synthese 196, 3505–3526 (2019). https://doi.org/10.1007/s11229-017-1533-6
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DOI: https://doi.org/10.1007/s11229-017-1533-6