Descartes and Sunspots: Matters of Fact and Systematizing Strategies in the Principia Philosophiae

Summary

Descartes' two treatises of corpuscular-mechanical natural philosophy—Le Monde (1633) and the Principia philosophiae (1644/1647)—differ in many respects. Some historians of science have studied their significantly different theories of matter and elements. Others have routinely noted that the Principia cites much evidence regarding magnetism, sunspots, novae and variable stars which is absent from Le Monde. We argue that far from being unrelated or even opposed intellectual practices inside the Principles, Descartes' moves in matter and element theory and his adoption of wide swathes of novel matters of fact, were two sides of the same coin—that coin being his strategies for improving the systematic power, scope and consistency of the natural philosophy presented in the Principia. We find that Descartes' systematising strategy centred upon weaving ranges of novel matters of fact into explanatory and descriptive narratives with cosmic sweep and radical realist Copernican intent. Gambits of this type have recently been labelled as ‘cosmographical’ (the natural philosophical relating of heavens and earth in contemporary usage). Realist Copernican natural philosophers, from Copernicus himself, through Bruno, Gilbert and Galileo did this to varying degrees; but, we suggest, Descartes presented in Books III and IV of the Principia the most elaborate and strategically planned version of it, underneath the ostensible textbook style of the work.

Acknowledgements

Early versions of this paper were presented to the Annual Conference of the Australasian Association for the History, Philosophy and Social Studies of Science, University of Sydney, July 2010 and to the Descartes New Studies Workshop, Unit for History and Philosophy of Science, University of Sydney, April 2011. For substantive comments and criticisms on those occasions, we thank Stephen Gaukroger, Keith Hutchison, Ofer Gal, Gideon Manning and Alan Chalmers. David Oldroyd, Simon Schaffer, Paul Lodge and Peter Pesic each made pertinent strategic suggestions about this project.

Notes

¹ Le Monde was first published in Paris in 1664. In this paper standard works of Descartes, and their translations, are abbreviated as follows:

AT =Oeuvres de Descartes (revised edition, 12 vols.), edited by C. Adam and P. Tannery (Paris, 1964-76). References are by volume number (in roman) and page number (in Arabic).

SG=The World and Other Writings, edited and translated by Stephen Gaukroger (Cambridge,1998).

MM=René Descartes, The Principles of Philosophy, translated by V. R. Miller and R. P. Miller, (Dordrecht, 1991)

MSM=Rene Descartes, Le Monde, ou Traité de la lumière, translated by Michael S. Mahoney (New York, 1979).

CSM(K)=The Philosophical Writings Of Descartes, 3 vols., translated by John Cottingham, Robert Stoothoff, and Dugald Murdoch, and (for vol. 3) Anthony Kenny, (Cambridge, 1988) References are by volume number (in roman) and page number (in Arabic).

²Rosaleen Love, ‘Revisions of Descartes' Matter Theory in Le Monde’, British Journal for the History of Science, 8 (1975), 127-37; John W. Lynes, ‘Descartes' Theory of Elements from Le Monde to the Principles’, Journal of the History of Ideas, 43 (1982), 55–72. Love does not directly compare the matter theories of Le Monde and the Principles, but rather juxtaposes Descartes' implied matter theory in his Essais of 1637 to that of the Principles, as it were imputing the former to Le Monde, often in an erroneous sense it must be said. The particular problems raised by Love's manner of interpreting Le Monde are not the topic of the current paper, but further comment on Love, and Lynes, appears below at note 44. By ‘matter theory’ we shall mean Descartes' theories of the elements, or genres of micro-particles into which his matter-extension is taken to be divided in Le Monde and later in the Principia Philosophiae. Strictly, and most abstractly speaking, Descartes' theory of matter consists in his doctrine of matter-extension. However, that concept, taken in isolation, plays almost no role in the descriptions and explanations he offers in the working machinery of his natural philosophy, and it is these, rather than abstract doctrines on the metaphysical level with which we are concerned. (See note 32 below.) Accordingly, throughout this paper as we discuss Descartes' accounts of cosmology, cosmogony, magnetism, sunspots, variable stars, novae and the generation of planets, we indifferently label our object of study the ‘matter theory’ or ‘element theory’ of Descartes—or sometimes his ‘matter and element theory’. It is worth recalling, in this regard, the sage words of T.S. Kuhn, discussing the inner workings of Cartesian natural philosophy: ‘…Descartes introduced a concept which since the seventeenth century has greatly obscured the corpuscular basis of his science and cosmology. He made the universe full. But the matter that filled Cartesian space was everywhere particulate in structure.’ T.S. Kuhn The Copernican Revolution (New York, 1959, 1^st ed. 1957), 240.

³For example, the expositions of such leading commentators as Stephen Gaukroger, Descartes' System of Natural Philosophy (Cambridge, 2002) and William Shea, The Magic of Numbers and Motion: The Scientific Career of Rene Descartes (Canton, Mass.,1991).

⁴‘Novel’ in this context does not necessarily mean newly adduced by the author in question. In the natural philosophical contest of the generation of Descartes, novel factual claims by others were routinely co-opted and reframed within one's own philosophy of nature. To be up to date in this style of work did not demand production of fresh claims about matters of fact. These rules of the game were to change considerably amongst the next generation of natural philosophers. Descartes does not mention magnetism or sunspots in Le Monde. However, he alludes to novae ever so briefly (see note 55 below).

⁵Some historians of science seem to take natural philosophical systematizing and a thirst for novel matters of fact as opposed or mutually exclusive seventeenth–century practices. Just as it is currently fashionable to talk about the origin of ‘experimental science’ later in the century as some sort of revolutionary outbreak of truly modern protocols for getting, handling and communicating miraculously atheoretical matters of fact, whilst conveniently forgetting almost everything that post-Kuhnian history and sociology of scientific knowledge taught us about theory-loading of facts, and of experimental hardware, let alone the continued existence of a rapidly changing but still living field of natural philosophical contention. J. A. Schuster and A. B. H. Taylor, ‘Blind Trust: The Gentlemanly Origins of Experimental Science’, Social Studies of Science 27 (1997), 503–536; L. Boschiero, Experiment and Natural Philosophy in Seventeenth Century Tuscany (Dordrecht, 2007). (Cf. note 44 below.)

⁶As we shall see in Section 3, this statement is not quite correct in the case of the Principles, where the third element does not appear during the cosmogony, but only during the actual cosmological steady state.

⁷J. A. Schuster, ‘L'Aristotelismo e le sue Alternative’, in La Rivoluzione Scientifica, edited by Daniel Garber (Rome, 2002), 337–57 (337–8); J. A. Schuster, ‘Descartes—Philosopher of the Scientific Revolution; Or Natural Philosopher in the Scientific Revolution’, Journal of Historical Biography 5 (2009), 48–83 (57–9, 64–5).

⁸In Section 10 we shall see that the formation of planetary (Earth-like) structures is a necessary result of natural processes, given the contingent death of a star and its migration into/capture by a neighbouring vortex. That the planet forming process is necessary has tended to lead commentators to conflate Descartes' Earth theory with his cosmogony. But his history of the Earth (or any planet) is not cosmogonical, rather a necessary process triggered by random events inside his dynamic, steady state cosmos. Indeed it may be said that Descartes' dynamic steady state cosmology resides entirely outside the purview, or implications, of his little cosmogonical story.

⁹In an unusually prescient comment R. F. McRae [‘Cartesian Matter and the Concept of a World’, in Descartes, Critical Assessments, 4 vols, edited by Georges J. D. Moyal (New York, 1991), IV, 153–62 (159)], noted that in Descartes' natural philosophy, ‘If it is the relation of the fixed stars to one another which constitutes the form of the world, then…the universe does, according to Descartes, have a history of change from one world to another world as a result of the growth of sunspots and the death of stars’. This remark foreshadows the entire thrust of our argument in this paper, although, as indicated in note 8, we do not quite attribute ‘world-making and world-breaking’ significance to the behaviour of variable stars or births of planets as treated by Descartes in the Principles.

¹⁰Jacqueline Biro, On Earth as in Heaven: Cosmography and the Shape of the Earth from Copernicus to Descartes (Saarbrücken, 2009) pp. 8–9. Cosmography is defined by Biro, extrapolating from definitions by John Dee, Thomas Blundeville, Nathanial Carpenter and William Barlow, as ‘that part of natural philosophy that provided within one explanatory framework the relationship between the heavens and earth’, or as John Dee said, ‘matcheth Heaven and the Earth in one frame’. Such early modern definitions usually say that cosmography requires the use of astronomy, geography and other disciplines. This demands some clarification. First of all, references to astronomy in this connection clearly are mistaken, if we are considering astronomy to be the mixed mathematical discipline devoted to construction of geometrical models of planetary motions. Cosmography was a domain within the field of natural philosophy, hence it is not astronomy that is being related to theorising about the Earth but rather that dimension of natural philosophy dealing with structure, matter and cause in the cosmos, to wit, cosmology as we have termed it above. As to the other term in the relation, loosely called geography above, one has to recognise that geography had many acceptations in the period, mirrored today by historians of the field (Biro, ibid., 12, note 19, discussing the views of Lesley Cormack and David Livingstone). The portion of geography considered to be part of cosmography might be taken to be mathematical geography. But there are difficulties here, as part of what was meant by mathematical geography was just that, a mixed or practical mathematical field with at best highly debatable relevances for natural philosophy and cosmology. In addition, the other parts of mathematical geography—such as the study of terrestrial gravity and magnetism, the study of exact locations, and deep articulations to cartography—constituted a diffuse and only partially natural philosophically relevant suite of concerns. Given all this, Biro adopted a contemporary term ‘geognosy’ in order to construct an historian's category of ‘geognosic opinion’ to serve as the ‘Earthly’ partner to cosmology in the cosmography pairing. Geognosic opinion would then be ‘ideas and knowledge about the Earth's structure’; that is, geognosic knowledge claims concerned issues of structure, matter and cause in regard to the Earth. (Biro, ibid., 16 and note 27 thereto) Within natural philosophical discourse, this is to be paired, cosmographically, with cosmology as claims about structure, matter and cause in the cosmos. (In this paper we simply denote the ‘Earth’ part of the heavens/Earth pairing as ‘theory of the structure and nature of the earth’. Hence, for us, cosmography is that dimension of natural philosophising in which cosmological and Earth theory claims were placed in relation to each other.)

¹¹In other words, What is the nature of the Earth as a planet? What can be gathered about the Earth, for example, about its structure, its magnetism (Gilbert), its tides (Galileo and Descartes), the nature of local fall, that would support its construal as a planet amongst planets and allow for the motions realist Copernicanism required of it? For realist Copernicans the relation of ‘the Earth’ to everything else, that is, ‘the heavens’, changed, becoming the relation of any and all planets, their structures and geneses, to any and all stars, their nature and developmental patterns. Biro (note 10) has shown that claims about the structure of the Earth could now be exploited cosmographically, for realist Copernican ends: Early to mid sixteenth century technical developments in geography, consequent upon the re-discovery of Ptolemy's Geography and leavened by the findings of the voyages of discovery, were at first only grudgingly granted by the Scholastic Aristotelians, but were eagerly seized as a resource by natural philosophers advocating Copernican cosmology, with Galileo and Descartes offering late examples of such cosmographically focused tactics in a sequence of varied yet uniformly anti-Aristotelian natural philosophical gambits stretching from Copernicus himself, through Bruno, Gilbert and others. We further articulate Biro's initiative in our discussion below in Section 11 of the nature of Descartes' ‘grand cosmographical gambit’ in the Principles.

¹²An example of the presence of a definite cosmographical orientation in Le Monde occurs when Descartes offers his first account of the elements, in Chapter 5, a text we shall discuss in detail immediately below in Section 3. In these passages (AT XI 24–6; MSM 37–9; SG 17–18), Descartes identifies his three elements with Aristotelian traditional ones: first element with fire; second element with air and third element with earth. It is a commentators’ commonplace that Descartes was attempting here to preserve some continuity with (at least part of) traditional element theory. In Le Monde, as some suggest, he may have viewed his ‘naming’ his elements as yet another rhetorical ploy to keep the intended francophone honnête homme reader on side. But, his gambit would have arguably been quite unconvincing to just about any natural philosophically literate reader. Moreover, if that was part of Descartes' aim, it certainly seems he did not stick with it, dropping the pretence in the Principles. Not previously noticed, however, is a deeper motive, one grounded in systematizing tactics: This naming of the elements seems to have cosmographical significance in the sense we have given to the term. In this new system, neither air nor fire are elements found on and about a unique Earth. In the light of his radical Copernican realism, envisioning effectively an infinite number of star and planetary vortical systems, Descartes was saying to the aware reader that ‘air’ had been misconstrued by Aristotelians as the essential constituent of the local terrestrial atmosphere only. No, ‘air’ is ubiquitous in the cosmos, constituted of the spherical boules of second element that make up each and every stellar vortex. What natural philosophers have termed air is just a mixture of various kinds of earthy particles of third element, with the usual unavoidable interstitial ‘filler’ material of fugitive second and first element particles. Similarly ‘fire’ is not the Aristotelian element at home in some peculiar sense just below the Earth's moon. Again, no, for fire is the first element, the very stuff of every star, including our sun. Renaming the elements was less an unconvincing bow to traditional teaching than it was—as we have foreshadowed—a hint and sign of a new cosmography; that is, a new relation between all planets, in any vortex whatsoever, including our Earth, and all the stars and stellar vortices of the universe. If we are correct about this, we have here a nice example of Descartes' well known proclivities toward both elusiveness and allusiveness, in his simultaneous (and contradictory) appeal to the old element names and new cosmographical tactics. In any case, as this paper argues, the Principles will display a much greater attention to cosmographical strategies and content.

¹³AT XI 24–6; MSM 37–9; SG 17–18. We should note Descartes' continual interjection of phrases such as ‘I conceive’, ‘I accept’ or ‘I judge’. An epistemological constraint is involved, implicitly harking back to the doctrine of his Regulae ad directionem ingenii (left incomplete in 1628), in that nothing is conceived or imagined of these elements which is not clearly intuitable. [J. A. Schuster, ‘Descartes' mathesis universalis: 1618–1628', in Descartes: Philosophy, Mathematics and Physics, edited by Stephen Gaukroger (Brighton, Sussex, 1980), 41–96] The description involves only considerations of motion, size, shape and arrangement. (Nevertheless, the behaviour of the first element is quite inexplicable. How can it continually change shape and adapt itself to the ever shifting interstices of the second element without experiencing a change in density?) Although it cannot be proved that elements exactly like these exist, the discussion moves within the discursive limits set out in the Regulae on the basis of a theory of perception, and further employed in Chapters 1 to 4 of Le Monde.

¹⁴Cf. J. A. Schuster, 'Descartes Opticien: The Construction of the Law of Refraction and the Manufacture of its Physical and Methodological Rationales 1618-1629' in Descartes' Natural Philosophy: Optics, Mechanics and Cosmology, edited by S. Gaukroger, J. A. Schuster and J. Sutton (London, 2000), 258–312 (286–95).

¹⁵AT XI 29–30; SG 19-20; MSM 45–47

¹⁶Here we ourselves offer at first a simple reading. In Le Monde the third element actually predates the other two, being in a sense present from the moment God injects motion into the block of matter-extension. In the Principia the third matter is produced only in the dynamic steady state cosmos, out of portions of first element. So, ‘sooner or later’ applied to both texts means that in the end, somewhere in the steady state cosmos following the cosmogony, we have three and only three matter formats for micro-particles.

¹⁷J. Lynes (note 2), 55.

¹⁸It has not always been the case that the matter theoretical contrasts between Le Monde and the Principia have been glossed over. Gabriel Daniel (1649–1728) for instance, who was a strong critic of Descartes, was not sure which of the two versions to accept: ‘whether the third element be contemporary with the other two, as M. Descartes seems in some measure to suppose in his Treatise of Light: or, whether it be form'd by the Conjunction of several Parts of the first element hook'd to one another, as he seems to teach in the Book of Principles’. Gabriel Daniel, A Voyage to the World of Cartesius (London, 1692), 261.

¹⁹These three accounts of the elements are foreshadowed at the end of Chapter 4 of Le Monde, which deals with the nature of the terrestrial atmosphere and arguments about the void, continuity of matter and phenomena of pumps. Descartes suggests it is reasonable to view the air to be a material plenum. This forces one to postulate the existence of other genres of unobservable particles completely filling the interstices which must exist amongst the grosser, but also unobservable, particles of air. Thus, Descartes hints at the later unveiling of his third matter, and other interstitial genres of matter.

²⁰AT XI 33; MSM 53–5; SG 22–3. ‘Let us rather conceive of it [‘our matter’] as a true, perfectly solid body, which uniformly fills the entire length, breadth, and depth of the great space at the centre of which we have halted our thought. Thus, each of its parts always occupies a part of that space and is so proportioned to its size that it could not fill a larger one nor squeeze itself into a smaller one, nor (while it remains there) suffer to find a place there.’

²¹AT XI 34; SG 23; MSM 53–5 ‘Let us add further that this matter can be divided into any parts and according to any shapes that we can imagine, and that each of its parts is capable of receiving in itself any motions that we can also conceive. Let us suppose in addition that God truly divides it into many such parts, some larger and some smaller, some of one shape and some of another, as it pleases us to imagine them. It is not that He thereby separates them from one another, so that there is some void in between them; rather, let us think that the entire distinction that He makes there consists in the diversity of the motions He gives to them. From the first instant that they are created, He makes some begin to move in one direction and others in another, some faster and others slower (or indeed, if you wish, not at all): thereafter, He makes them continue their motion according to the ordinary laws of nature.’ [emphasis added]

²²AT XI 49; SG 32–3; MSM 79–81. ‘… to consider this matter in the state in which it could have been before God began to move it, one should imagine it as the hardest and most solid body in the world. And, since one could not push any part of such a body without pushing or pulling all the other parts by the same means, so one must imagine that the action or the force of moving or dividing, which had first been placed in some of the parts of matter, spread out and distributed itself in all the others in the same instant, as equally as it could.

‘It is true that this equality could not be totally perfect. First, because there is no void at all in the new world, it was impossible for all the parts of matter to move in a straight line; rather, all of them being just about equal and as easily divertible, they all had to come together in some circular motions. And yet, because we suppose that God first moved them diversely, we should not imagine that they all come together to turn about a single centre, but about many different ones, which we may imagine as diversely situated with respect to one another.’ [emphasis added]

Notice that this passage, contrasted to the one cited in the note 21, seems to presume that there is some time interval between God's creation of matter extension and his injection into it of particle-producing motion. Alternatively, to preserve a unified and total creation by God, one might suggest that the gap between creation of matter-extension and insertion of motion to shatter it is merely logical, there being no temporality in God's creative act. The consequences for the matter-theoretical cosmogonical narrative, as considered by us here, are irrelevant; but the consequences for articulating Descartes' natural philosophy to one theological position or another might be considerable.

²⁵AT XI 49–50; SG 33; MSM 81.

²³AT XI 49; SG 33; MSM 81.

²⁴Gaukroger (note 3), 152, note 19, where he cites Eric Aiton, The Vortex theory of Planetary Motion (London, 1972), 63 note 78.

²⁶The dynamical concepts in play here in Le Monde and their origins are clarified in S. Gaukroger and J. A. Schuster, ‘The Hydrostatic Paradox and the Origins of Cartesian Dynamics’, Studies in the History and Philosophy of Science, 33 (2002), 535-572; Schuster (note 14); and J.A. Schuster, “‘Waterworld’: Descartes' Vortical Celestial Mechanics and Cosmological Optics—A Gambit in the Natural Philosophical Agon of the Early 17^th Century’, in The Science of Nature in the 17 ^th Century: Patterns of Change in Early Modern Natural Philosophy, edited by Peter Anstey and J.A.Schuster (Dordrecht, 2005), 35-79.

²⁷AT XI 50-1; SG 33; MSM 81–3: ‘Thus, in a short time all the parts were arranged in order, so that each was more or less distant from the centre about which it had taken its course, according as it was more or less large and agitated in comparison with the others. Indeed in as much as size always resists speed of motion, one must imagine that the parts more distant from each centre were those which, being a bit smaller than the ones nearer the centre were thereby much more agitated.’

²⁸Force of motion is a function of size (quantity of matter) and speed (or instantaneous tendency to motion), so, as the size of particles in a vortex decreases, their speed must increase in order for the ‘stability condition’ to be maintained.

²⁹Remembering that Descartes has introduced his element theory in Chapter 5 in a ‘non-cosmogonical’ context, shaped by his didactic strategy at that point.

³⁰AT XI 53; SG 34; MSM 85.

³¹AT XI 56–7; SG 37; MSM 93: ‘In order for me to begin to tell you about the planets and comets, consider that, given the diversity in the parts of matter that I have supposed [at the creation] even though most of them have—through breaking up and dividing as a result of collision with one another—taken the form of the first and second element, there nevertheless remains to be found among them two kinds [as described in the text above] that had to retain the form of the third element.’ And, two pages later (AT XI 60; SG 39; MSM 99), describing the formation of comets and planets out of third matter, he opens with ‘…no matter where the parts of matter that could not take the form of the second or the first element may have been initially…’ [emphasis added] Thus Descartes reiterates the existence of third matter particles before the initial formation of the first and second element.

³²Nowhere in Le Monde does Descartes state the element theoretical unity of heaven and Earth; that is stars and vortices and planets (plus comets and moons). The sun (and the other stars) differ from the Earth (and all other planets and comets). Descartes attributes to stars a nature ‘totally contrary to that of the Earth because the action of their light is enough for me to recognise that their bodies are of a very subtle and very agitated matter.’ (AT XI 29–30; SG 20; MSM 45–7) Here, again, we have an indication of the way the element theory in Le Monde is largely driven by the theory of light. Hence the needs of Descartes' theory of light tend to run against the most radical implications of embracing an infinite universe realist Copernicanism, where such a strong ‘bar’ between ‘planetary’ and ‘heavenly’ types of matter would seem otiose and counterproductive. All this will change in the Principia.

It is, however, true that if by matter theory in Descartes, we mean solely the theory of matter-extension, then, of course, a unity of heavens and Earth was achieved from the start, and in principle Descartes could have gone on to assert the transmutability of the elements into which this matter-extension happened initially to be sorted. In fact, however, natural philosophising was about producing detailed explanations of ranges of new and old facts, and ‘systematisation’ of the resulting suite of explanations. To ‘do’ natural philosophy, Descartes could not simply devote himself ad infinitum to ‘analysis’ of the doctrine of matter-extension and its possible implications. (Cf. note 2.) We see this already in the simple fact that the purpose of the cosmogonical story is to produce the elements and the types of structures—stars, vortices, planets—they constitute. In Cartesian natural philosophy, matter-extension as such lasts an instant (the instant of creation). While it exists in its pure state, no ‘nature’ or cosmos yet exists, so there is not yet any subject matter for natural philosophy. Similarly, although Descartes ‘could’ have had transmuting elements in Le Monde, based on his matter-extension doctrine, in articulating his natural philosophy in Le Monde, he specifically denied that possibility. Therefore, historians need to look to Descartes' aims and tactics in natural philosophising for reasons for his insistence in 1633 on what became unnecessary to assert in 1644.

³³‘Confusion seems less in accordance with the supreme perfection of God the creator of things than proportion or order’ so he was ‘supposing at this point that all the particles of matter were, initially equal in respect both of their size and their motion’. This point and the other textual references in this paragraph are located at: Principles III articles 46–7; AT VIII-1 102–3; CSM I 257; MM 106–7.

³⁴John Heilbron, Electricity in the 17 ^th and 18 ^th Centuries: A Study of Early Modern Physics (Berkeley, 1979), 31–33.

³⁵Two versions of star formation are offered in the Principles, III, articles 54 and 72; AT VIII-1 107–8, 125; MM 111, 122–3. The former version corresponds to our text above; the latter gives an explanation more dependent on diametrically opposite axial inflows of first element from the equatorial areas of neighbouring vortices toward the centre of the vortex the creation of whose central star is being discussed. Alternatively the second story might be interpreted as Descartes' detailed account of the movement of first element particles into and out of an already formed star. This latter account does map completely onto his explanation of the formation of oppositely handed rimmed particles of first element which cause magnetic phenomena, given later in Book III Articles 87 through 93.

³⁶The process of production of this sub-species of first element particles is related at Principles III articles 87–93; AT VIII-1 142–7; MM 132–6.

³⁷Cf. Gaukroger (note 3), 150. Principles, III, articles 65-67; AT VIII-1, 116–19; MM 118–19.

³⁸We put the matter this way because there is some ambiguity in Descartes' text on the issue of where and how the right and left handed rimmed particles are formed. There is no doubt he intended that the larger particles of first element, being pressed through the interstices of the spherical boules, can become rimmed and handed; but, on the other hand it is also clear that it is their passage along the axis of vortical rotation into the polar regions of a central star that gives the oppositely directed particles their opposite twists. We defer to the excellent hermeneutics of Gaukroger on this point, noting his reading at two places in his analysis of the Principles: [1] At Gaukroger (note 3), 152 the production of the rimming is elided with the twisting into handedness during the axial transit. ‘The larger parts of the first element have to pass around the tightly packed globules of the second element, and they become twisted into grooved threads, those coming from opposite poles being twisted in opposite directions, that is, having left- and right-handed screws (article. 91)’. [2] But, at pp.175-6 discussing Descartes' treatment of terrestrial magnetism in Book IV of the Principles, Gaukroger seems to interpret the twisting into handedness to be a generic result of forcing through interstices of boules, and not necessarily (though perhaps sufficiently) a result of the cosmic transit along vortical axes of rotation: ‘The generation of these grooved particles had been set out in Part III (articles. 87–93). Their grooves derive from the fact that they are squeezed through the interstices of contiguous spherical globules. As a result of this squeezing they end up as cylinders having three or four concave sides joined by rims….Moreover, because they rotate on being squeezed through these interstices, the channels or grooves are rotated, forming a stream of diagonally grooved, cylindrical fragments, some of which have a left-hand screw, some a right-hand screw, according to the direction of the twist’.

³⁹ Principles III articles 94–95; AT VIII-1 147–8; MM 136.

⁴⁰ Principles III article 94; AT VIII-1 147–8; MM 136. Gaukroger (note 3), 153 comments: ‘These grooved particles…move to the centre of the vortex. On account of their relatively small degree of agitation and their irregular surfaces, they easily lock together to form large masses at the surface of the star from which they emerge. Because of their size and small degree of agitation, they “resist that action in which we said earlier that the force of light consists” and as a result they appear as a spot on the surface of the Sun. Descartes compares the process by which they are formed to the boiling of water which contains some substance which resists motion more than the water: it rises to the surface on boiling to form a scum, which, by a process of agglutination, comes to acquire the character of the third element’.

⁴¹ Principles III article 96; AT VIII-1 148. MM 136.

⁴² Principles II article 23; AT VIII-1 52; CSM I 232. Descartes states explicitly ‘celestial matter is no different from terrestrial matter’.

⁴³AT XI 28; SG 19; MSM 43-5. But by January 1639 he must have begun to change his theory of matter, because in a letter to Mersenne Descartes says: ‘some terrestrial particles continually take on the form of subtle matter when you crush them up; and some particles of this subtle matter attach themselves to terrestrial bodies, so there is no matter in the universe which could not take on all the forms’. (AT II 485; CSMK 133) See also above, note 32.

⁴⁴As we have noted, leading interpreters, such as Lynes (note 2) and Love (note 2), approached the problem of the differences between Le Monde and the Principles as centrally concerning matter and element theory. Additionally they looked for external triggers or motives for Descartes making the changes. For example Lynes (note 2), 72 placed emphasis on religious motivations, with Descartes striving to overcome the possibly heretical implications of his early supposedly atomistic-looking matter theory in Le Monde by means of his putatively better ability later to demonstrate the absence of any void in nature in the Principles. (In fact Descartes has a robust plenist account in both treatises.) Similarly Love's explanation for the changes in matter theory boils down to Descartes' increasing commitment to a plenist physics in the Principles: She maintained that Descartes must have revised his theory of matter between 1637 and 1644, basing her claim on the fact that in the Discourse, published in 1637, there is only one subtle element, while in the Principles there are two. Love suggested that the change from one subtle element to two could have been triggered by Morin's criticism of Descartes' theory of light, in particular the need of some matter to fill in the void between globules that transmit light. This for Love meant in all probability that the unpublished 1633 version of Le Monde only had one subtle element and thus is not identical to the one eventually published in 1664. Hence, Love (note 2), 127, claimed that the differences between the two works ‘follow from Descartes' well-known identification of substance with spatial extension, and his consequent rejection of the void’. We leave aside here the overwhelming evidence that a close analysis of the text of Le Monde and its course of construction undermine all this, since it is virtually certain that Descartes had the three elements in the original conception, and simply note that Love's explanation is based on a metaphysical driver, Lynes’ on a theological one. In response to these and other guesses at circumstantial external drivers of Descartes' strategies and inscriptions, we suggest that the casting about for such putative causes is beside the point and actually rather ahistorical. When an actor is playing a competitive game in a field of contestation, the best initial explanation for the actor's moves resides in the best picture the historian can devise of the actor's assessment of the state of play, his resources and goals. (Cf. the seminal works on the socio-political dynamics of claim construction and negotiation in mature sciences by Pierre Bourdieu, ‘The Specificity of the Scientific Field and the Social Conditions of the Progress of Reason’, Social Science Information, 14 (1971), 19–47; and Steven Shapin, ‘History of science and its sociological reconstructions’, History of Science, 20 (1982), 157–210, especially his discussion of actors’ vested interests in their own field and discipline's state of play and likely directions of development, pp.164–69.) That is why this paper stresses Descartes' systematizing goals inside the game of natural philosophising. It is also why we have related those goals to Descartes' healthy respect for facts. Like any good, competitive natural philosopher (or later modern scientist) he knew facts need to be assessed, interpreted, selected for use, reframed in terms of the theory and claims under discussion, and argumentatively deployed for persuasion. His appetite for facts, their theoretical reframing and leveraging for further explanatory uses were intimately linked to his goals and strategies for building a winning system of natural philosophy, proclivities that will be display below, especially in Sections 6 through 9.

⁴⁵Aiton (note 24), 3.

⁴⁶Hence, the exposition of the vortex theory in Le Monde can be heuristically aided by careful comparison with the later presentation in the Principles, a technique followed in Schuster (note 26).

⁴⁷In fact Descartes manages to invoke boats in a current as models for both planets and comets, quite different types of celestial objects which behave in vortices in contrasting ways, as we shall see. The ‘boat in a current model’ is far from trivial, because the detailed theory of celestial mechanics that it represents is quite sophisticated.

⁴⁸Schuster (note 26), 46. Figures 2, 3 and 4 derive from Schuster's study, where their interpretative basis is also discussed. In these figures straight lines are used to represent the functional relations amongst boules’ sizes, speeds and distances from the central star gathered from the verbal expressions in Descartes' texts. It is not intended that Descartes entertained such linear relations. What is important is the general representation of the force-stability principle and how that relates to Descartes' claims about the size and speed distributions with distance.

⁴⁹Descartes quite clearly says it is the rotation of a central star that adds this extra agitation to vortical boules up to a certain distance from the star. (AT XI 53; SG 34–5) It would seem reasonable, however, to attribute this effect in part to the simple fact of the high agitation of the particles of first element making up the star. After all, in other contexts in these treatises Descartes attributes important consequences to the activity of agitated first element particles on stellar surfaces. (See below notes 85 and 101 for other examples) It may be that Descartes wished to emphasize the rotation of the central star and not introduce a factor that, arguably, could have effect even if rotation did not occur. Since in Le Monde Descartes was not mobilizing sunspots as stellar surface phenomena demonstrating the rotation, he certainly seems to have believed in rotation quite apart from the issue of sunspots. This tends to support the idea that the genealogy of his celestial mechanical thinking back goes back to encountering Kepler, who initially asserted solar rotation in his celestial physics. On Descartes' engagement with Beeckman's work on Kepler in 1628–29, just prior to starting to write Le Monde, and its influence on the shape of his vortical mechanics, see Schuster (note 26), 70–2.

⁵⁰ Le Monde, AT XI 54-6; SG 35-7; Principles, III articles 84, 148; AT VIII-1 138–40; 196–7; Schuster (note 26), 48. In regard to our exposition here the following should be noted: Descartes' final cosmological model of the distribution of size, speed and force of motion of vortical spherical particles, and the dynamical role of the sun and other stars, are identical in the two treatises. The cosmogonical origins of the cosmological steady state, including the dynamics of pre-element vortices, are set out in more detail in Le Monde. In the Principles Descartes gives us his cosmogony of nearly identical Ur-particles which from the moment of creation rotate around their own centres and move at ‘average’ speed around numerous proto–vortical centres. He explains how second and first element particles evolve in this situation, but makes no explicit statement about vortex dynamics and distributions of size, speed and force of vortical particles in relation to the cosmogony. These details are supplied only for the cosmological dynamical steady state of the Principles after the formation of first element, spherical second element, and most importantly, stars. This difference is unimportant for our exposition here, which aims to bring out the nature of the vortex mechanics and the importance in it of the theory of rotating first element stars.

⁵¹Descartes is characteristically more clear about the concept of massiveness or solidity in the Principles than in Le Monde. For discussion of this concept and of the interpretive principles involved in its extraction from the two texts, see Schuster (note 26), 41–3, 52–3.

⁵²Schuster (note 26), 49

⁵³This is a very simplified, ‘headline’ version of Descartes' theory. The technicalities of Descartes' argument are more complicated than our short exposition here allows. For full details on the Cartesian locking and extruding mechanism see Schuster (note 26), 44–55, including especially note 32 to p. 53. For our purposes, dealing with the strategic, cosmographical structure of the Principles, these further dynamical details need not concern us, notwithstanding their high significance for the understanding of Cartesian physics in the larger sense.

⁵⁴As Descartes argues clearly in the Principles (Book III, article 140, cf. articles 121, 122, 147) and less clearly in Le Monde (AT XI 57-69; Schuster (note 26), 52–3), a planet too close to the central star for its given solidity will be translated to a higher orbit; a planet too far away from the central star for its given solidity will be translated (a form of fall, by the way) to a lower orbit. As for comets, they are planets of such high solidity that they overcome the resistance of boules at all distances up to and including K. Such an object will pass beyond the K level, where it will meet boules with decreasing volume to surface ratios, hence less resistance, and be extruded out of the vortex into a neighbouring one. But, flung into the neighbouring vortex, the comet meets increasing resistance from its boules above that vortex's K distance. Picking up increments of orbital speed, the comet starts to generate centrifugal tendency again, eventually being flung back out of the second vortex. [Schuster (note 26), 54] Descartes' vortex mechanics thus makes some interesting predictions about comets: they do not come closer to any star than the layer K of that star's vortex; they are ‘more massive’ than any and all planets, they move in spiral paths oscillating out of and into solar systems.

⁵⁵In Le Monde (AT.XI. 104–9; SG 67–70; MSM 183–97.) Descartes briefly alludes to the novae of 1572 and 1604, explaining them as due to the shifting and bending of intervortical boundaries, which can produce multiple images of a single star, or, so he claims, a star's sudden appearance or disappearance. As we shall see, his explanation of novae in the Principles is quite different and is an integral part of his overall cosmographical strategy for dealing with magnetism, sunspots, novae, variable stars and planet formation and structure. His discussion of novae, variables and vortex jostling in the Principia focuses on Book III, articles 111–16 and includes the key figure to which the entire discussion is referred [introduced below as Figure 5 in Section 9]. At one point (article 114) Descartes interestingly likens the movement back and forth of a vortical boundary and the accompanying formation/destruction of stellar crusts of sunspots to the behaviour of a pendulum. Cf. note 108 below.

⁵⁶As Richard Westfall, The Construction of Modern Science: Mechanisms and Mechanics (New York, 1971), 36–7, describes the encounter over lab based manipulations: ‘…the mechanical philosophy had to explain away magnetic attraction by inventing some mechanism that would account for it without recourse to the occult. Descartes' was particularly ingenious. In considerable detail, he described how the turning of the vortex generates screw-shaped particles which fit similarly shaped pores in iron. Magnetic attraction is caused by the motion of the particles, which in passing through the pores in magnets and iron, drive the air from between the two and cause them to move together. What about the fact of two magnetic poles? Very simple, Descartes replied; there are left handed screws and there are right handed screws’.

⁵⁷On the points about the nature of the natural philosophical field in the critical phase of the scientific revolution c.1630–1660 in the this and previous two sentences: J. A. Schuster, 'The Scientific Revolution' in The Companion to the History of Modern Science, edited by R. Olby et al (London, 1990), 217–42 (224–7, 232–8); Schuster (2002, note 7), 339–41, 344–8; and Schuster, ‘What was the Relation of Baroque Culture to the Trajectory of Early Modern Natural Philosophy’, forthcoming in Archives internationales d'histoire des idées, 2012.

⁵⁸Similarly, Gilbert insisted that his knowledge was built on assiduous attention to experiments and to facts reported by craftsmen and artisans, and that it was productive of useful results, most notably improving the use of the magnetic compass in navigation.

⁵⁹It might be asked whether we are maintaining that this strategy was deliberate on Descartes' part or whether it exists merely as an analyst's construct. We answer that it arguably was deliberate and part of his way of contesting for hegemony in natural philosophy. This is based on our reading the text of the Principia for its underlying goals and strategies, which we hold to be better than imputing motives based on circumstantial events or evidence. (Cf. above note 44 on Lynes and Love, and below Section 12, especially note 135.)

⁶⁰See our comments on this point above at note 38.

⁶¹Galileo Galilei, Letters on Sunspots, in Discoveries and Opinions of Galileo, translated and edited by Stillman Drake (Garden City, 1957), 87–144 (102). Compare Galileo twenty years later in Galileo Galilei, Dialogue Concerning the Two Chief World Systems, translated by Stillman Drake (Berkeley, 1953), 54, ‘[many spots] dissolve and vanish far from the edge of the sun, a necessary argument that they must be generated and dissolved’.

⁶²There are four contenders for the discovery of sunspots: Within about 18 months in 1611/2 Johann Fabricius [De Maculis in sole observatis, et apparente earum cum sole conversione, narratio. (Witebergae, 1611)], Christopher Scheiner [Tres epistolae de maculis solaribus (Augustae Vindelicorum, 1612)] {under the pseudonym of Apelles and published by Marcus Welser}, and Galileo [Istoria e dimostrazioni intorno alle macchie solari e loro accidenti. (Roma, 1613)], appeared and claimed discovery. Fabricius probably saw them as early as March 1611, Scheiner in spring 1611 and Galileo, who in 1613 responded to Scheiner's published claims of 1612, claimed observations eighteen months earlier (this was in the published version of his first letter, to Welser, on sunspots, May 14, 1612, hence he was claiming observations as early as 1610). [In the Dialogue Concerning the Two Chief World Systems, Galileo (note 61), 345, he again claimed observations as early as 1610.] Harriot, whose observations exist only in manuscript form, has notes on sunspots dating from December 1610, but began regular observations only about year later, following Fabricius’ publication [Judit Brody, The Enigma of Sunspots: A Story of Discovery and Scientific Revolution (Edinburgh, 2002), 68]. It should also be noted that the painter and poet Raffael Gualterotti [Discorso sopra l'apparizione de la nuova stella (Firenze, 1605)] claimed to have followed for several days movements of spots on the sun. He explained them as resulting from a conjunction of Mars and Saturn which attracted exhalations and vapours which were drawn to the sun, purified and rarefied to become sunspots. Galileo knew Gualterotti and had corresponded with him. (Brody, op. cit, 25–6, 55)

⁶³Descartes to Mersenne, 8 October 1629, AT I 23; CSMK 6.

⁶⁴Parhelia or mock suns or sun dogs are 'two concentrations of light on the small halo at the same altitude as the sun' [Marcel Minnaert, Light and Color in the Outdoors, translated and revised by L Seymour (New York,1993), 214].

⁶⁵On the process of emergence of the project of Le Monde, see SG, x-xiii.

⁶⁶AT I, 248 note referring back to p.23 l.25–29.

⁶⁷Eventually he dealt with parhelia in the Météores and with sunspots in the Principia.

⁶⁸Descartes to Mersenne, 18 December 1630, AT I, 102–3.

⁶⁹Descartes to Mersenne, January 1630, AT I 112–13; CSMK 18; Descartes to Mersenne, 4 March 1630, AT I 125. Gassendi observed spots between 1618 and 1638. Descartes was seeking information by correspondence regarding as yet unpublished material. Gassendi's detailed reports on the 1626 observations and others only appeared in his Opera Omnia (1658) in the following locations: Vol.1 Syntagmatis philosophici pt 2 of pt 2 De rebus caelestibus pp.553–4 on spots; Vol.4 Observationes Coelestes ab anno 1618 in annum 1655 (repr.1658). Maculares solares [observations in 1626 p. 99–100, in 1638 pp.411–12]; Mercurius in Sole visus et Venus invisa… 1631 (1632) pp. 499-505 (letters to W. Schickard). Mercury was so small that at first Gassendi thought it was a sunspot.

⁷⁰To Mersenne, 4 March 1630, AT I 125, Descartes writes, ‘Vous ne me dites pas de quel cofté font les pôles de cette bande, où fe remarquent les taches du Soleil, encore que ie ne doute point qu'ils ne correfpondent aucunement à ceux du monde, & leur ecliptique à la noftre’. This concerns the band to which sunspots seem confined, in particular, taking that band to be revolving around the sun, where the poles of its axis of rotation would be located. He doubts these poles correspond to the celestial poles and that the band's inclination to the celestial equator would equal that of our ecliptic. All of which seems to imply that at this time his view was that the sunspots are not planets, or at least are not like the known planets (and so might well be on the surface of the sun on this argument). Scheiner's original views had been supported by others, such as Jean Tarde [Borbonia Sydera (1620), French trans. (1623)] and C. Malapertuis [Austriaca sidera (Duaci, 1633)], whilst Fortunius Licetus [De novis astris et cometis. (1623), 124) held the interesting view, intermediate between theories of sunspots and orbiting planets, that spots cannot be solar exhalations because those would be more rarefied, not darker. He added that some falsely claim that there are craters on the sun. He thought they are parts of the aether condensing/rarefying in turn.

⁷¹For example: Leaving aside Gualterotti, mentioned above, note 62; Galileo likened ‘sunspots to clouds or smoke’ [Galileo 1957 (note 61), 140); Kepler in 1612 suggested to Simon Marius that spots might be like clouds originating from the fire of the sun and that perhaps cometary material also originates from the sun [Johannes Keplers Gesammelte Werke, edited by M. Caspar (München, 1938), vol. 17 p. 36]; J.R. Quietanus told Kepler, August 13, 1619 [ibid. vol 17 pp.371–4 at 372], that he thought comets ‘ex maculis solis colligitur et coacervatur’ and Kepler told him in reply, August 31, 1619 [ibid. vol 17, pp. 375–86 at 376], that Marius agreed with this; Marius himself in 1619 argued that comets might come from the sun because for the last year and half [covering the period of the comet of 1618] there had been few spots on the sun [Astronomische und astrologische Beschreibung des Cometen…1618 (Nürnberg, 1619)]. He also stated that he had seen spots on the sun with tails; and generally held that the surface of the sun is like molten gold, the spots being like slag; Willebrord Snell, also discussing the comet of 1618 explained comets as ‘maculae istae exhalationes…solis flagrantis atque ista ex recessu & interiore corpore per sua crateras eructantis quemadmodum in terris Aetna’. [Descriptione cometae anni… 1618. (Lugduni Batavorum, 1619)]

⁷² Le Monde, AT XI 29; SG 20; MSM 45. Also: ‘we shall take one of those round bodies composed of nothing but the matter of the first element to be the sun, and the others to be the fixed stars’, Le Monde, AT XI 53; SG 35; MSM 87. Cf. above note 32 and text to which it refers.

⁷³Moreover in that case Descartes probably would have had to have taken some account of the strong claims for their appearance and disappearance, as mentioned above (note 61), often on the middle of the sun, a difficult challenge if they are planets (compared to their appearance and disappearance near the edges of the solar disk, which could be explained as visibility effects concerning continuously existing small planets). It should also be noted that when Descartes in the Principles accepts that the spots exist and form on the surface of the sun, there are celestial mechanical consequences with which he must deal: Observations of the spots indicate that the sun does not spin as quickly on its axis (in terms of linear velocity, not radial velocity) as the vortex theory would imply—that is, faster than any planet in its orbit. [Gaukroger (note 3), 153 and Principles, III article 32, AT VIII-1 93; MM 97] where the rotational period for sunspots is given as twenty-six days.) For this and other reasons Descartes introduces the conception of stellar aether, an earthy atmosphere near a star, and extending out as far as its nearest planet, largely constituted by dissolved sunspots, which slows the rotational speed of the star. [Principles III article 148, AT VIII-1, 196-7; MM 172] On other functions of the aether see below, note 87 and text thereto. Finally, the detection and description of transits of Venus or Mercury across the sun, posed many difficulties at the time, not to mention the complications introduced if one took sunspots actually to be conjunctions of small planets orbiting near the sun. For example, Scheiner had failed to observe a transit of Venus which he could have used early on to argue for the visibility of the other smaller planets whose conjunctions he claimed produced the appearances of sunspots [Brody (note 62), 49] Gassendi in 1631 after hesitation, thinking he was observing a sunspot, claimed he had observed a transit of Mercury; while earlier, in 1607, Kepler had taken a sunspot for Mercury seen against the sun's disk [Brody (note 62), 27]. After Gassendi's observation there was more clarity about distinguishing a sunspot from a transiting planet. Hence by the time the transit of Venus was first observed in 1639 by Jeremiah Horrocks, as Brody (note 62), 78, writes, ‘the argument had already turned around. Previously the emphasis was on proving that the spots were not planets, now it had to be shown that a planet was not a spot’.

⁷⁴Scheiner, Rosa Ursina (Bracciano, 1630), 537, ‘maculae & faculae in ipso sole sunt’. Scheiner also stated that the spots grow, change, diminish, darken, lighten, disappear in the middle of the sun. Ibid. p. 490.

⁷⁵ Principles, III article 35; AT IX-2, 118; MM 98-99.

⁷⁶Descartes to Mersenne, February 1634, AT I 281.

⁷⁷ Principles, Mais d'ailleurs les obferuations qui font dans ce liure, fournissent tant de preuues, pour oster au Soleil les mouuemens qu'on luy attribuë, que ie ne sçaurois croire que le P. Scheiner mesme en fon ame ne croye l'opinion de Copernic; ce qui m'étonne de telle forte que ie n'en ose écrire mon fentiment..[Also see MM 99, note 29]

⁷⁸Arguably neither theory was fully acceptable to Descartes at the time of composing Le Monde: To decide that sunspots are generated and destroyed on the surface of the sun would violate the matter theory of Le Monde; but, to accept sunspots as small planets orbiting very near the sun would require first overcoming the scepticism he had expressed to Mersenne in 1630 about this claim (see note 70), and second, significant further articulation of his vortex celestial mechanics.

⁷⁹Additionally, let us also recall that, thanks to Beeckman, Descartes first saw Galileo's Dialogo in 1634 and so was potentially exposed to Galileo's persuasive deployment of his claims about sunspots, which in turn served as powerful arguments for the (Copernican) unity of heaven and Earth. Of course, Descartes saw the book for a short time only, for thirty hours, but he made some reasonable use of it for his own purposes, as in his later reported critique of the natural philosophical relevance of Galileo's abstract and idealized account of fall and projectile motion. (To Mersenne, 11 October 1638, AT II 385).

⁸⁰ Principles, III article 35, AT VIII-1 95; MM 98.

⁸¹ Principles, III article 74, AT VIII-1 129; MM 124.

⁸²In addition, let us not forget that sunspots supplied observational evidence for the first time that the sun rotates. Although he does not say so, Descartes could not have wished for a better validation for his theory of vortices, notwithstanding the celestial mechanical issues requiring further adjustment, mentioned above at note 73. At the time of writing Le Monde he had passed up this advantage, which had been obvious to, and valued by Galileo and Kepler a generation earlier, when sunspots had first been observed.

⁸³Descartes' thoughts were later echoed by the Swiss astronomer Rudolf Wolf (1816–1893). 'I compared the whole appearance of the sunspots to currents which proceed periodically from the two poles of the sun towards its equator.' (Authors’ translation.) Rudolf Wolf, Die Sonne und ihre Flecken (Zürich,1861), 27.

⁸⁴ Principles, III article 97, AT VIII-1 149; MM 137. Descartes' explanation appeals to his explanation of prismatic colours in the Météores of 1637.

⁸⁵ Principles, III article 98, AT VIII-1, 149–50; MM 137–8; The explanation follows directly from Descartes' theory of light. The first matter surging around the edges of a spot not only contributes to a tendency to motion propagated out through the boules of the vortex, but also produces a more than normal intensity of that tendency, a set of stronger than normal rays. (It is crucial to understand that in Descartes' theory of light the propagation of the tendency to motion through the boules that constitutes light is always instantaneous, but the intensity or force of that tendency can vary. There can be weak or strong rays, albeit always instantaneously propagated. [This point is made clear in Schuster (note 14), 261, and applied to reconstructing the development of Descartes' physical optics.] Returning to Descartes' explanation of faculae, strictly speaking he claims that a facula can form following the existence of a spot, and, by extension of the process described, a spot can turn into a facula; and vice versa, meaning that he claims that dark spots can turn into bright regions and vice versa.

⁸⁶ Principles, III article 96, AT VIII-1 148 MM 137.

⁸⁷ Principles, III article 100, AT VIII-1 150; MM 138-39. The central thread of Descartes' narrative of the formation of the Earth in Part IV of the Principles involves the formation of all the third matter on Earth that exists above the inner, unreachable, crust that suffocated the original star. This new planetary third matter is formed largely from material derived from the aether of the dead star (Principles, IV articles 1–7, AT VIII-1 203–6; MM 181–4).

⁸⁸By modern definitions these of course were supernovae. The contemporary search for other novae included David Fabricius’ claim regarding Mira Ceti in 1596 (which we discuss immediately below in the context of the later claims that it is in fact a variable); and Kepler and others’ identification of a supposed nova in 1600 (Kepler acknowledged that it was first seen by W.J. Blaeu who put it on his celestial globe.) Cf. Michael A. Hoskin, ‘Novae and Variables from Tycho to Bullialdus’, Sudhoffs Archiv für Geschichte der Medizin und der Naturwissenschaften, 61 (1977), 195–204. The star of 1600 is now regarded as a LBV (luminous blue variable), hence it is neither a nova nor a supernova.

⁸⁹Explanations invoking divine action could include the following: the star has been around since the creation but it was hidden and brought to the fore by God as a sign of his omnipotence; or, it had actually been newly created by God. A miracle could be carried out directly by God or through natural causes at the fiat of God. The latter might well violate the sense of ‘natural’ that previously held in a given natural philosophy. For example a Christian Aristotelian could take a new star as the result of God's decision to use (hitherto unknown but) natural causes in the heavens to generate a new star. Problems would be created for the natural philosophy as previously expounded.

⁹⁰The latter possibility was discussed by Tycho Brahe, Tychonis Brahe Dani Opera omnia, edited by J.L.E. Dreyer (Hauniae, 1916), III, Astronomiae instauratae progymnasmatum pars tertia, 204. This reports the opinions of John Dee and Gemma Cornelius that the new star moves away in a straight line. However there is also evidence that both Gemma Cornelius [De peregrina stella (Antwerp, 1573)], and Michael Maestlin had thought the 1572 nova was newly created. Maestlin thought there were not enough exhalations and that the star was newly created by God. This was published in his Demonstratio astronomica loci stellae novae, tum respectu centri mundi … appearing pp. 27–32 in N. Frischlin, Consideratio nouae stellae …(Tubingen, 1573). The key passage was recently cited by M. A. Granada, ‘Michael Maestlin and the new star of 1572’, Journal for the History of Astronomy, 38 (2007), 99–124 (104). Maestlin's ‘edificatory poem’ (Granada, op. cit., p.101) states that the star announces the second coming. Maestlin deals mainly with the location of the star, except for the key passage in question, which was also quoted by Tycho, op. cit., 60, as part of his reproduction of the entire document with commentary (Progymnasmatum, Opera omnia, III, 58–62, with commentary, 62–67.) Tycho himself said that the new star was formed of matter from the Milky Way, but not of such perfection or solid composition as other stars, in the Conclusio to Tycho Brahe his Astronomicall coniectur of the new and much admired [star] which appeared in the year 1572 (Amsterdam, Theatrum Orbis Terrarum; reprinted New York, 1969); Fortunius Licetus, De novis astris et cometis (1623), held that the phenomena are created and then annihilated. He also writes that there are also some people who think a nova is an old star, neglected, not observed by the ancients. Reisacher and Valesius (or Vallesius) thought an old faint star got brighter through sudden transformation of the air between it and us, so it was not a new creation [J.L.E. Dreyer, Tycho Brahe (Edinburgh,1890) p. 64] [Vallesius is quoted in J. Tacke, (1653) Coeli anomalon (Gissae Hassorum, 1653) and by B. Reisacher, De mirabili novae ac splendidissimae stellae (Vienna, 1573)]. Kepler, De stella nova in pede Serpentarii (Pragae, 1606), in Johannes Keplers Gesammelte Werke, edited by M. Caspar (München, 1938), I, Chapter 20, 248–51 reports discussions with David Fabricius about where the material for the new star of 1596 (Mira Ceti) came from: whether the star had been around since the creation but hidden and then brought to the fore by God as a sign; or newly created either by God or by physical processes from existing material which must be all over the universe, since (Ibid., Chapter 22, 259) the ‘star in the whale’, was not close to the Milky Way.

⁹¹In 1612 David Fabricius, (Prognosticon astrologicum auff das Jahr 1615, Nürnberg, J Lauer) wrote that novae, like comets, do not dissipate but can remain unseen, then reappear. Little note was taken of this claim, let alone any possible natural philosophical significances. Hence, in accord with modern understandings of the construction and attribution of discoveries in science, it would be quite wrong to credit Fabricius with the discovery of variable stars. See Arjen Dijkstra, ‘A Wonderful Little Book. The Dissertatio Astronomica by Johannes Phocylides Holwarda (1618–1651)’, in Centres and Cycles of Accumulation in and Around the Netherlands during the Early Modern Period, edited by Lissa Roberts (London, 2011), 73–100 (77).

⁹²Dijkstra (note 91) pp. 86–87.

⁹³Johannes Phocylides Holwardus, Panselenos, …id est dissertatio astronomica (Franekerae, 1640) pars secunda de novis phaenomenis, sive stellis, 185–288. The ‘new star’ disappeared after he first observed it, and Holwarda failed to observe it all through the summer of 1639 (‘frustra omnia’, p.285) But Holwarda saw it again about eleven months later, on Nov 7, 1639. By that time his book was being printed, so he added an appendix (pp. 277–88) about the reappearance. Here he pointed out that he had already suggested the phenomenon might disappear and reappear, and now identified the observations with a star in Cetus. (Dijkstra, note 91, 86–87, see also 89ff on the design and aim of Holwarda's book). A slightly different account of the timing of Holwarda's observations, making use of the work of Michael Hoskin (note 88), is offered by William Donahue, ‘Astronomy’ in the Cambridge History of Science, III, Early Modern Science, edited by Katherine Park and Lorraine Daston (Cambridge, 2006), 590–1, according to which Holwarda re-observed Mira Ceti in 1640 while his book reporting the initial discovery was in press, the appendix being added to report that reappearance. Note that, given Mira Ceti's eleven month cycle the 1640 observation by Holwarda must have been no earlier than October of that year.

⁹⁴Ismael Bullialdus [Boulliau], Ad Astronomos Monita Duo (Paris, 1667) established Mira Ceti's period as about 333 days, allowing him successfully to predict future appearances. He proposed that the star rotates, periodically showing a more luminous region to earthly observers. So, as Dijkstra, note 91, pp. 92–97, convincingly shows, and as we might expect based on modern studies of the negotiation and attribution of discovery, the historical process of recognizing that a periodically disappearing and reappearing star had been found was long and hotly contested.

⁹⁵R. Vermij, The Calvinist Copernicans (Amsterdam, 2002) says Descartes was in contact with many Dutch scholars (as is well known in any case), but offers no evidence concerning Holwarda. H Terpstra, Friesche Sterrekonst (Franeker, 1981) says there is no proof that Descartes knew Holwarda, but also claims, p.67 that there is no doubt of Descartes' influence on natural philosophy in Franeker; that Descartes certainly influenced Holwarda; but, that there is no proof they met in person. This question is not definitively resolved. The authors are currently exploring it further. Mersenne was quickly made well aware of Holwarda's work and the ensuing debate (Dijkstra, note 91, 94–5), and so he may have been Descartes' main or initial informant on the matter.

⁹⁶Desmond Clarke, Descartes: A Biography (Cambridge, 2006), Appendix 1 on ‘Descartes' Principal Works’. Descartes was working on the Principles all during his controversy with Voetius and the University of Utrecht, the publication of the Meditations in 1641 and various entanglements with some Jesuits. It was only in January 1643 that he told Constantijn Huygens that he was currently working on the sections about magnetism. Ibid. 233. Clarke (p. 233 note 30) assumes this applies to the explanation of Gilbert's lab manipulations in Book IV of the Principles, but it might just as well apply to the cosmic magnetism prominent in Book III.

⁹⁷ Principles, III articles 102, 104; AT VIII-1 151–2; MM 139–40, 140–1.

⁹⁸ Principles, III article 111; AT VIII-1, 158–60; MM 144–5.

⁹⁹Descartes refers explicitly only to novae, but here the reappearance at the same place is an important feature, as we shall see. Principles, III article 104; AT VIII-1 152; MM 140–1

¹⁰⁰ Principles, III article 111; AT VIII-1 158–60; MM 144–5.

¹⁰¹This is yet another of many examples in the Principles of the outward thrust of stellar first element from the surface of a star. Compare our remarks above at notes 49 and 85.

¹⁰² Principles, III articles 105–8; AT VIII-1 153–6; MM 141–3.

¹⁰³One should recall that first element particles are constantly flowing into the central star from the north and south along its axis of rotation.

¹⁰⁴ Principles, III article 111; AT VIII-1 158–60; MM 144–5.

¹⁰⁵ Principles, III articles 112, 114; AT VIII-1 160–2; MM 145, 146–7.

¹⁰⁶ Principles, III article 104; AT VIII-1 152; MM 140–1. Descartes cites the 1572 nova in Cassiopeia, ‘a star not previously seen’. He also mentions, more controversially: [1] the possibility of the disappearance of one of the Pleiades in ancient times, seven stars being mentioned in myth but only six reported by later Greek writers (MM 140 note 105)—such a star, if it once was visible, has obviously been occluded for over two thousand years; and [2] the presumed fact that, ‘We also notice other [more enduring] stars in the sky which formerly were unknown [to the ancients]’, a claim which MM otherwise explain in their note 107 to p. 141.

¹⁰⁷ Principles, III articles 112, 114, AT VIII-1 160–2; MM 145, 146–7. In contrast to the 1572 nova which he does report, Descartes does not name Mira Ceti, Fabricius, Fullenius or Holwarda. It is almost as though he is happier to offer the explanation in principle for a phenomenon of which he surely is aware in general, but without giving any firm citation of dates, discoverers or objects, thus revealing a still neo-Scholastic approach to the description and explanation of phenomena as ‘generally well known’. Cf. Peter Dear, Discipline and Experience: The Mathematical Way in the Scientific Revolution (Chicago, 1995).

¹⁰⁸See for example: Principles, III article 104, AT VIII-1 152; MM 140. Speaking of novae, in particular the 1572 nova, Descartes says that such a star ‘may continue to show this brilliant light for a long time afterwards, or may lose it gradually’. Cf. Principles, III article 111, AT VIII-1 159; MM 145: the ‘almost instantaneous’ appearance of a star; Principles, III article 112, AT VIII-1 160–1; MM 145: a star ‘slowly disappearing’; and, Principles, III article 114, AT VIII-1 162; MM 146–7, the same star can alternately appear and disappear, which phenomenon Descartes elucidates with the analogy of pendulum motion (see note 55 above). An excellent exposition of Descartes' theories of comets, variable stars and novae (as a sub-species thereof) may be found in Tofigh Heidarzadeh, A History of Physical Theories of Comets from Aristotle to Whipple (Dordrecht, 2008), 67–81. Very helpful and well conceived diagrams accompany the discussion of the key points.

¹⁰⁹ Principles III article 101, AT VIII-1 151; MM 139: ‘That the production and disintegration of spots depend upon causes which are very uncertain’, a remark to be taken in conjunction with his explanations offered in the next twenty or so articles of the Principles, dealing with novae, variables and sunspots.

¹¹⁰The ‘re’ is in brackets, because causally the star may be reappearing, but humans may only be noticing a star in that position for the first time; it is what European natural philosophers and astronomers had since 1572 called a new star.

¹¹¹ Principia III, arts, 118–19; AT VIII-1, 166–8; MM 149-50. On the orbital behaviours of planets, and comets, see above Section 4, especially note 54 and related text.

¹¹²The narration/explanation of Earth formation and structure occurs at Principia, IV, arts 1–44, AT VIII-1, 203-31; MM 181–203. Most of the attention paid to this material has been devoted to seeing Descartes as a founder of the early modern and enlightenment tradition of speculative theorizing about the Earth. (Cf. Jacques Roger, ‘La Théorie de la Terre au XVII Siècle’, Révue d'Histoire des Sciences, 26 (1973), 23–48.) The unfolding of this tradition, particularly in its English Protestant context, has been most perspicaciously analysed by Peter Harrison, who correctly argues that the issue was not the substitution of a natural philosophical cosmogony for the account in Genesis, but rather the nuanced issue of which natural philosophical account best explicated or shed light on Genesis, a matter about which Descartes' account arguably had already displayed some sensitivity. P. Harrison, ‘The Influence of Cartesian Cosmology in England’ in Descartes' Natural Philosophy, edited by S. Gaukroger, J. A. Schuster and J. Sutton (London, 2000), 168–92.

¹¹³As analysed in Schuster (note 26) and above, Section 4.

¹¹⁴Satellites are also planetary in nature, cf. Schuster (note 26), 75. Also see Le Monde AT X 69–70; SG 45; where the moon is termed a planet: ‘…if two planets meet that are unequal in size but disposed to take their course in the heavens at the same distance from the sun…’. In the Principles, of course, Descartes can rely on his genealogy of planets from encrusted stars — for example, at Book III article 146; AT VIII-1 195–6; MM 171: ‘Concerning the creation of all the Planets’ where it is clear that the planets of our solar system, along with the Earth's moon, the four satellites of Jupiter and the two Descartes attributes to Saturn all derive from encrusted stars in now defunct vortices, and are ‘planetary’ in nature.

¹¹⁵For Galileo and Descartes the tides provide a prime example of a phenomenon on Earth which, if well theorised, provides strong evidence for the motion of the Earth. Biro (note 10, 73–110) devotes two chapters to their cosmographical use of theories of the tides. For Descartes in the Principles, tides are implied to be a feature of all planets, just as their magnetism is. Both sets of phenomena would be present on any and every planet, since their genealogies are identical to that of our Earth: Every planet carries with it the axial orientation of pores to accept the two species of screw shaped particles of first matter which it had as a star. Exactly how this is retained in the now third matter crustal layer[s] of the planet is detailed in Descartes' story of the Earth in Part IV of the Principles. Similarly the process of formation of oceans, mountains, valleys and atmosphere would be the same for all planets evolved from dead stars.

¹¹⁶The crust in question is not the primordial crust formed of sunspots which initially strangled the star. That crust remains deep in the planet, untouched by this process of creation of oceans, seas, landforms and atmosphere. Cf. note 87.

¹¹⁷The historiographical view point behind this remark is the common, if often only tacit view that that ideas have causal power; that earlier ideas (texts, books, core concepts) can ‘influence’ later thinkers. The loci classici for debunking this view in the history of ideas are John Dunn, ‘The Identity of the History of Ideas’, Philosophy, 43 (1968), 85–104 and Quentin Skinner, ‘Meaning and Understanding in the History of Ideas’, History and Theory, 8 (1969), 3–53. Later, post-Kuhnian sociologists of scientific knowledge, notably Barry Barnes and Stephen Shapin, widened this critique and applied it to the difficult terrain of scientific traditions. [Barry Barnes, T.S.Kuhn and Social Science (London, 1982) and Steven Shapin, ‘Discipline and Bounding: The History and Sociology of Science As Seen Through the Externalism-Internalism Debate’, History of Science 30 (1992), 333–369.] They insisted that articulation of concepts within a tradition cannot occur via influence, but rather through later actors’ access to, and appropriation, reinterpretation and redeployment of earlier intellectual or ‘cultural’ resources. This applies to ‘facts’ as well: it cannot be a question of how the past of the tradition—including claims about matters of fact previously accepted within it—forces or ‘influences’ present moves; but, of how later players mobilise and deploy resources for their present moves, subserving goals and tactics they have also chosen and framed.

¹¹⁸T. Goldstein, ‘The Renaissance Concept of the Earth in its Influence Upon Copernicus’, Terrae Incognitae 4 (1972), 19–51; E. Grant, ‘In Defense of the Earth's Centrality and Immobility: Scholastic Reaction to Copernicanism in the seventeenth century’, Transactions of the American Philosophical Society, 74 (1984), 20–32; W. G. L. Randles, ‘Classical models of world geography and their transformation following the discovery of America’ in Geography. Cartography and Nautical Science in the Renaissance. The Impact of the Great Discoveries (Aldershot, 2000), 5–76. Grant cites an article in French by Randles dated 1980. This suggests that the concepts in the English version of the work by Randles appeared in the earlier French article and therefore Randles’ work predates that of Grant.

¹¹⁹In the thirteenth century, Aristotelians such as Sacrobosco and Michael Scot tried to reconcile the ideal picture of concentric spheres of the elements with the indubitable existence of dry land by proposing that the earth emerged slightly from the sphere of water. In the fourteenth century, Jean Buridan and Albert of Saxony articulated the ‘floating apple’ model of the Earth to square theory of the Earth with the additional belief, ascribed to Aristotle in some circles, that the sphere of water is ten times larger than that of earth. Biro (note 10), 17–21, 23–25, following GGR.

¹²⁰In the late fifteenth and sixteenth century, controversy erupted with thinkers like Vadianus, Fernal, Nunes and Peucer rejecting the floating apple model of the Earth on the basis of knowledge gained from the voyages of discovery, and campaigning for the notion of a spherical, terraqueous globe derived from Ptolemy's Geography. It appears that the terraqueous globe entered university curricula only in the late sixteenth century through the efforts of Clavius. Biro (note 10), 17–21, 30–6.

¹²¹Biro (note 10), 28–30, 36–9, synthesizing the important claims by GGR on this little appreciated point.

¹²²Biro (note 10) on Gilbert, 57–64; on Galileo, 73–94.

¹²³We have of course seen important cosmographical elements in Le Monde: for example, the fundamental assertion that the Earth is just another planet, in a realist Copernican framework of infinitely many stellar systems; the overtones of the new element theory, discussed above in note 12, and the theory of the tides, as we have mentioned.

¹²⁴We gratefully acknowledge that a number of the foregoing points in this paragraph emerged in the course of extensive discussions between Biro and Schuster, during the course of his supervision of her MA dissertation, which was later revised to produce Biro (note 10). There was an evolution from Copernicus’ own concentration on the shape of planet Earth, through Gilbert's detailed natural philosophising about the inner structure and make up of the Earth, down to Descartes' invocation of a process of heavenly generation to cement his cosmography and provide a developmental story for what Biro (note 10) terms his ‘geognosic’ claims about Earth's structure and formation. For realist Copernicans the exploitation of strategic space in cosmography was a continuing theme in their corners of the natural philosophical field, and so Descartes' ‘theory of the Earth’ is not so much the stark novelty that some historians of geology sometimes make it out to be, but a radical turn embedded in a longer running strategic campaign by the supporters of realist Copernicanism. This approach allows Biro to compare and contrast the cosmographical strategies of various actors. For example, she points out the interesting differences in geognosic modelling of oceans in Galileo's and Descartes' theories of the tides: For Galileo it is the containment of particular seas and oceans in their basins that allows the combined orbital movement and diurnal spin of the Earth mechanically to cause the tides. For Descartes, as Biro shows, the theory of tides depends on stressing the fluid continuity of all the Earth's seas and oceans, a theme he over–stated in Le Monde and corrected for in the Principles. Biro (note 10), 106–7.

¹²⁵Early in Book II of the Principia, at article 25, Descartes defines motion as ‘the transfer of one piece of matter or of one body, from the neighbourhood of those bodies immediately contiguous to it and considered at rest, into the neighbourhood of [some] others’ (AT VIII-1 53–4; MM 51). This is the philosophical definition of motion contrasted with vulgar or common understandings (Cf. Book II, article 24 ‘What movement is in the ordinary sense’)

¹²⁶ Principia, III article 28, AT VIII-1 90; MM 94–5: ‘…no movement, in the strict sense, is found in the Earth or even in the other Planets; because they are not transported from the vicinity of the parts of the heaven immediately contiguous to them, inasmuch as we consider these parts of the heaven to be at rest. For, to be thus transported, they would have to be simultaneously separated from all the contiguous parts of the heaven, which does not happen’.

¹²⁷Daniel Garber, Descartes' Metaphysical Physics (Chicago, 1992), 181–8, discusses the matter with his usual care and perspicacity. In the end, p. 188, Garber rejects the view that Descartes' theory of motion and its laws is an ‘elaborate mask’, a ‘contrived stratagem’ to allow him to deny motion to the Earth.

¹²⁸Peter Dear, Revolutionizing the Sciences: European Knowledge and its Ambitions, 1500–1700 (Princeton, 2001), 96, ‘Descartes was not worried about the potential heresy inherent in his ideas about the extent of the universe or the nature of the stars. He major concern…was the unorthodoxy (as defined by Galileo's trial) of holding that the earth is in motion. Descartes published the Principles, with its more elaborate version of the same world–picture as that of Le Monde, only once he had thought of a way to deny the movement of the earth without compromising any of his cosmology. The trick (and that is what is really was) involved emphasizing the relativity of motion’. And, p. 98, ‘The subtlety of Descartes' theology was matched by the subtlety of his physics. As far as he could help it, no one would be able to accuse him of teaching that the earth moves’.

¹²⁹Readers familiar with legal proceedings, then or now, would recognise the strength of Descartes' position, if threatened in a legal context. He could have quoted, verbatim, extensive and connected published passages about the true, ‘philosophical’ definition of motion and the non-motion of the Earth, and read those passages with pointed literalness.

¹³⁰Innumerable instances of Descartes' habitually secretive, reclusive, publicly masked and overtly tricky persona are captured with great panache in Desmond Clarke (note 96).

¹³¹Although we might make an exception for Christiaan Huygens, who mocks exactly the interweaving of cosmographical claims into what we termed the explanatory and descriptive narrative in the Principles. Huygens wondered how Descartes. ‘an ingenious man, could spend all that pains in making such fancies hang together’ [Cosmotheoros (The Hague, 1698), cited in Brody (note 62), 84] This mirrors a change in natural philosophical temper and rules in the next generation, leading to exactly the dissipation of the Cartesian system and piecemeal use and criticism of it that we discuss immediately below. However, Huygens (no modern historian!) misses the point about what the game of natural philosophising was about in the preceding Baroque age, and how well Descartes had played.

¹³²Cf. note 112.

¹³³In the telling remark that ends Book III (AT VIII-1 202; MM 177), Descartes asserts that all inequalities of planetary motion can be sufficiently explained using the framework he has provided. Clearly, he in no way intends that explanations will proceed by deductions from laws of motion, plus boundary conditions, leading to the exposure and study of various levels and types of perturbations. So, for example, it is not elliptical orbits, and their deviations that he wishes to study, leading to refinement of the relevant laws. Rather, he offers a ‘sufficient’ (verbal and qualitative) explanation of orbital phenomena and the general facts that no orbit is perfectly circular, and that all orbits display variations over time.

¹³⁴Cf. above notes 107, 108 and 109 and texts thereto.

¹³⁵Cf. above notes 44, 59. By this point it is perhaps appropriate to point out that there was nothing defensive or reactive about Descartes' novel moves in the Principles which we have discussed in this paper. Love (note 2) and Lynes (note 2) might each be read as depicting Descartes as motivated, even forced, to make matter theoretical changes by defensive consideration of real or possible theological or metaphysical criticism. But merely defensive gambits arguably would have taken quite different shapes, as we have hinted. Natural philosophical contestation may be decoded in part as like a game; its rules of utterance are in part determinable; and, as in other games, when master players make well considered, complex attacking moves, that is obvious to attentive spectators.