Artisans,Machines,and Descartes's Organon

Quotations from Descartes are taken from Œuvres de Descartes, ed. by Adam Charles Tannery Paul , new edn (11 vols, Paris, 1996), and are cited in the form: AT vi, 33–45. English translations are taken from The philosophical writings of Descartes, transl. by Cottingham John Stoothoff Robert Murdoch Dugald (3 vols, Cambridge and New York, 1984–1991), and are cited in the form: CSM i, 123–35.

Descartes , Discours de la méthode, AT vi, 75; CSM i, 149.

On the role of observations and experiments, see Garber Daniel , “Descartes and experiment in the Discourse and Essays”, in his Descartes embodied: Reading Cartesian philosophy through Cartesian science (Cambridge, 2001), 85–110; Blake Ralph M. , “The rôle of experience in Descartes' theory of method (I)”, The philosophical review, xxxviii (1929), 125–43; Blake , “The rôle of experience in Descartes' theory of method (II)”, The philosophical review, xxxviii (1929), 201–18; Gewirtz Alan , “Experience and the non-mathematical in the Cartesian method”, Journal of the history of ideas, ii (1941), 183–210; Clarke Desmond M. , Descartes's philosophy of science (Manchester, c. 1982); Sakellariadis Spyros , “Descartes's use of empirical data to test hypotheses”, Isis, lxxiii (1982), 68–76.

Descartes , Discours de la méthode, AT vi, 72–73; CSM i, 148.

Money sometimes was not a good enough incentive to hold artisans in check. When the time came, for instance, to engrave the plates for the Discours and Essais, Descartes and his printer made sure the engraver would not leave without giving an address or procrastinate for too long. The only way to enforce their wish was to keep this engraver (Franz Schooten the younger) “under house arrest”: “Celui qui les taille [the plates] me contente assez, et le libraire le tient en son logis, de peur qu'il ne lui échappe”, Descartes to Constantijn Huygens, 30 October 1636, AT i, 614.

Shapin Steven , A social history of truth: Civility and science in seventeenth-century England (Chicago and London, 1994). I have contended elsewhere that volontaires, although unhelpful in producing knowledge per se, were Descartes's vectors of knowledge dissemination; they were the ones who Descartes trusted would make his philosophy known. Gauvin J.-F. , “Volontaires and artisans in Descartes's natural philosophy”, unpublished manuscript presented at the History of Science Society annual meeting, Cambridge, MA, 21 November 2003.

Shapin , A social history of truth (ref. 5), chap. 8.

Bennett J. A. , “The mechanic's philosophy and the mechanical philosophy”, History of science, xxiv (1986), 1–28. Long Pamela O. , “Power, patronage, and the authorship of ars: From mechanical know-how to mechanical knowledge in the last scribal age”, Isis, lxxxviii (1997), 1–41; Long , Openness, secrecy, authorship: Technical arts and the culture of knowledge from Antiquity to the Renaissance (Baltimore, 2001), esp. chaps. 6–7; Findlen Paula , Possessing nature: Museums, collecting, and scientific culture in early modern Italy (Berkeley, 1994); Daston Lorraine Park Katharine , Wonders and the order of nature, 1150–1750 (New York, 1998); Harkness Deborah , Neighborhoods of science: Knowledge and practice in Francis Bacon's London, 1560–1620 (forthcoming); Smith Pamela H. , The body of the artisan: Art and experience in the Scientific Revolution (Chicago and London, 2004). On the latter see the essay review by Moran Bruce T. , “Knowing how and knowing that: Artisans, bodies, and natural knowledge in the Scientific Revolution”, Studies in the history and philosophy of science, xxxvi (2005), 577–85.

As Descartes explains, “for one man cannot turn his hand to both farming and harp-playing [cithara], or to several different tasks of this kind, as easily as he can to just one of them”. Descartes, Regulæ ad directionem ingenii, AT x, 359–60; CSM i, 9.

“Habituum autem varia sunt genera, alii enim sunt animi, alii vero corporis.” Eustachius a Paulo Sancto , Summa philosophica quadripartita (2 vols, Lyons, 1609), ii, 121. See Gilson Etienne , Index scolastico-cartésien (Paris, 1912), s.v. habitus. Descartes, Règles utiles et claires pour la direction de l'esprit en la recherche de la vérité, ed. and transl. by Marion Jean-Luc (The Hague, 1977), 90–91.

“Arithmetical demonstration and the other sciences likewise possess, each of them, their own genera; so that if the demonstration is to pass from one sphere to another, the genus must be either absolutely or to some extent the same. If this is not so, transference is clearly impossible, because the extreme and the middle terms must be drawn from the same genus: Otherwise, as predicated, they will not be essential and will thus be accidents.” Aristotle, Posterior analytics 1.7. The Internet Classics Archives (classics.mit.edu, accessed on 3 August 2005). A very good discussion is found in Dear Peter , Discipline and experience: The mathematical way in the Scientific Revolution (Chicago and London, 1995), 36–46.

On the interconnectedness of knowledge as one of the central components of Descartes's project, Garber Daniel , Descartes's metaphysical physics (Chicago and London, 1992).

Descartes, Regulæ, AT x, 359–61; CSM i, 9–10 for the quotes.

Descartes, Regulæ, AT x, 361; CSM i, 10.

On the uniqueness of ars and unity of scientia, Marion Jean-Luc , Sur l'ontologie grise de Descartes: Science cartésienne et savoir aristotélicien dans les Regulæ, 2nd edn (Paris, 1981), 25–30.

Marion suggests that the Regulæ contain the seeds of the Cartesian metaphysics as found in the Meditations, but it does not then unfold because Descartes was unable properly to order the intellectual simple natures with the common simple natures. Marion Jean-Luc , “Cartesian metaphysics and the role of the simple natures”, in The Cambridge companion to Descartes, ed. by Cottingham John (Cambridge, 1992), 115–39.

Descartes to Marin Mersenne, March 1637?, AT i, 349. Descartes, Discours de la méthode, AT vi, 61; CSM i, 142. In a very insightful analysis of Descartes's famous anaclastic line, Daniel Garber shows how the programmatic statement of the method can be reconciled with a theory of practice. Following this example closely, Garber explains that what the method gives is a “workable procedure for discovering an appropriate path” between the reductive steps the knower has to take from a question asked to the actual intuitus, in this case, of a potentia naturalis. From there, the constructive steps (deductions) take us back to the question asked, for which we are now in possession of certain knowledge. Garber , Descartes's metaphysical physics (ref. 11), 35–36 (emphasis in original). For a very helpful diagram, see Garber , “Descartes and experiment in the Discourse and Essays”, in Descartes embodied (ref. 2), 85–110, p. 100.

Descartes , Discours de la méthode, AT vi, 22; CSM i, 122. Descartes emphasizes the same point a few pages later: “Moreover, I continued practising the method I had prescribed for myself. Besides taking care in general to conduct all my thoughts according to its rules, I set aside some hours now and again to apply it more particularly to mathematical problems” (AT vi, 29; CSM i, 125). See also Descartes , Règles utiles et claires pour la direction de l'esprit (ref. 9), 208. A more detailed and somewhat similar analysis is given in Schouls Peter A. , Descartes and the possibility of science (Ithaca and London, 2000), 63–91.

Descartes , Discours de la méthode, AT vi, 61–62; CSM i, 142–3.

Descartes , Regulæ, AT x, 400; CSM i, 33.

Descartes , Regulæ, AT x, 400–2; CSM i, 33–34.

Descartes , Regulæ, AT x, 371; CSM i, 16. Descartes maintains that “the power of judging well and of distinguishing the true from the false — Which is what we properly call ‘good sense’ or ‘reason’ — Is naturally equal in all men”. Descartes , Discours de la méthode, AT vi, 2; CSM i, 111.

The classic reference remains Rossi Paolo , Philosophy, technology, and the arts in the early modern era, transl. by Attanasio Salvator (New York, 1970). A more sophisticated analysis has recently been published by Smith , The body of the artisan (ref. 7).

Descartes , Regulæ, AT x, 404; CSM i, 35.

Descartes , Regulæ, AT x, 382; CSM i, 22.

Descartes , Regulæ, AT x, 384; CSM i, 23.

According to Jean-Luc Marion, Descartes would have used in French the word ‘adresse’ — And not ‘sagacité’, which is close to ‘perspicacité’ — To designate this mental faculty, a word the natural philosopher happily applied to both mechanical and mental skills. For instance, “il faut de l'adresse et de l'habitude pour faire et pour ajuster les machines que j'ai décrites”, and “savoir joindre l'adresse de la main à celle de l'esprit”, Descartes , Discours de la méthode, AT vi, 77 and Descartes to Huygens, 1 November 1635, AT i, 330, respectively. Descartes , Règles utiles et claires pour la direction de l'esprit (ref. 9), 208–9.

Descartes , Regulæ, AT x, 362–4; CSM i, 10–11. In the Discours Descartes mentions that he did not “cease to value the exercises done in the Schools”. Descartes , Discours de la méthode, AT vi, 5; CSM i, 113.

Descartes , Regulæ, AT x, 372; CSM i, 16.

Descartes , Regulæ, AT x, 397; CSM i, 31.

The “continuous and wholly uninterrupted sweep of thought” refers to Rule VII and is part of Descartes's theory of order. On the mechanical thinking process, this could explain some of Descartes's strange assertions like: “Ce qui cadre beaucoup avec ma manière de philosopher, et qui revient merveilleusement à toutes les expériences mécaniques que j'ai faites de la nature à ce sujet”, Descartes to Villebressieu, summer 1631, AT i, 217. See also Descartes to Froidmont , 3 October 1637, AT i, 420–1. Descartes , Règles utiles et claires pour la direction de l'esprit (ref. 9), 204.

Descartes , Regulæ, AT x, 379; CSM i, 20.

Descartes , Regulæ, AT x, 404; CSM i, 35, where it is translated as “to invent an order”. For a complete discussion see Marion , Sur l'ontologie grise de Descartes (ref. 14), 71–78.

Weber Jean-Paul , La constitution du texte des Regulæ (Paris, 1964). See also Schuster John , “Descartes' mathesis universalis, 1619–1628”, in Descartes, philosophy, mathematics and physics, ed. by Gaukroger Stephen (Brighton, 1980), 41–96.

Descartes , Regulæ, AT x, 377–8; CSM i, 19. Marion , Sur l'ontologie grise de Descartes (ref. 14), 55–69, is by far the most sophisticated and persuasive analysis of the mathesis universalis.

This point is made in Rule XIV of the Regulæ: “For the Rules which I am about to expound are much more readily employed in the study of these sciences [arithmetic and geometry] (where they are all that is needed) than in any other sort of problem. Moreover, these Rules are so useful in the pursuit of deeper wisdom that I have no hesitation in saying that this part of our method was designed not for the sake of mathematical problems; our intention was, rather, that the mathematical problems should be studied almost exclusively for the sake of the excellent practice which they give us in the method”, Descartes , Regulæ, AT x, 442; CSM i, 58–59. The science of order produced by the mathesis universalis represents Michel Foucault's seventeenth-century shift of épistémè. Foucault acknowledges that order does not necessarily mean an all-out mathematization of knowledge. Foucault , Les mots et les choses: Une archéologie des sciences humaines (Paris, 1966, 2001), 71.

Rule IV should be understood as Descartes's response to the intellectual clash between the Jesuits Benito Pereira and Christopher Clavius regarding the epistemology of mathematics. Descartes's mathesis universalis is neither Pereira's philosophia prima nor Clavius's attempt at defending the philosophical status of mathematics. The mathesis is a highly developed philosophical blend between two traditions found within the Society of Jesus. Mehl Edouard , Descartes en Allemagne, 1619–1620: Le contexte allemand de l'élaboration de la science cartésienne (Strasbourg, 2001), 243–61. Dear , Discipline and experience (ref. 10), 32–46.

Descartes , Regulæ, AT x, 366; CSM i, 12–13. Marion , Sur l'ontologie grise de Descartes (ref. 14), 42: “L'apparente contradiction … du privilège préalablement reconnu aux seules mathématiques, plus qu'une incohérence, traduit le coup de force et l'intention profonde des Regulæ: mettre au jour, à l'encontre de la constante aristotélicienne, où certitude et ‘physique’ restent inversement proportionnelles, des objets non-mathématiques (et donc ‘physique’) propres à fournir le même degré (voire un plus grand) de certitude, que n'en fournit l'objet des mathématiques; considérer comme certain un objet non-mathématique: Telle est la tâche que se fixent les Regulæ, au terme de la seconde [règle].”.

I follow here the theoretical idea of structures structurées et structurantes of Bourdieu Pierre , Le sens pratique (Paris, 1980), 88–89.

Bourdieu , Le sens pratique (ref. 38), 92. Regarding weaving and other simple arts, “they present us in the most distinct way with innumerable instances of order, each one different from the other, yet all regular”, Descartes , Regulæ, AT x, 404; CSM i, 35.

On exercices structuraux Bourdieu , Le sens pratique (ref. 38), 126. Interestingly enough, perspicacitas and sagacitas as exercices structuraux for the mind find a correspondence in the mechanical arts that not even Francis Bacon dared contemplate. To him “The human mind is misled by looking at what is done in the mechanical arts, in which bodies are entirely changed by composition and separation, into supposing that something similar also happens in the universal nature of things”, Bacon Francis , The new organon, ed. by Jardine Lisa Silverthorne Michael (Cambridge, 2000), aphorism LXVI, 53.

Descartes , La recherche de la verité, AT x, 500; CSM ii, 402.

Descartes , La recherche de la verité, AT x, 502–3; CSM ii, 403–41.

The literature on this topic is rich. See, for instance, Mauss Marcel , “Body techniques”, in Sociology and psychology: Essays, ed. by Brewster Ben (London, 1979), 97–135, and Sibum Otto , “Reworking the mechanical value of heat: Instruments of precision and gestures of accuracy in early Victorian England”, Studies in history and philosophy of science, xxvi (1995), 73–106.

Loyseau Charles , A treatise of orders and plain dignities, ed. and transl. by Lloyd Howell A. (Cambridge, 1994 [1610]), 179–81. Some tradesmen such as “apothecaries, goldsmiths, jewellers, haberdashers, wholesalers, drapers, hosiers, and others like them”, gained some prominence because their crafts involved commerce. The latter artisans, who called themselves “honourable men” and “bourgeois”, were morally superior to other tradesmen whose métiers “consist[ed] rather in physical labour than in commercial activity or in shrewdness of mind”. Mere manual labourers were almost by definition the basest artisans of them all since “there is no worse occupation than to have no occupation”. To qualify as a honnête homme an artisan had to leave the manual labour almost entirely to others, thus transforming himself into a merchant.

See Nicot Jean , Thresor de la langue française (1606), where one can read under artisan: “Artisan, ou Artiste, Artifex, Opifex”. L'Académie Française made the distinction we are accustomed to use today only in 1762: “artiste, celui qui travaille dans un art où le génie et la main doivent concourir (un peintre, un architecte sont des artistes); l'artisan est un ouvrier dans un art mécanique, un homme de métier”, Le Grand Robert de la langue française, ed. by Rey Alain , s.v. artisan. For an historical analysis of this significant shift, Larry Shiner, The invention of art: A cultural history (Chicago and London, 2001), 99–120. de La Fontaine Jean , for instance, in one of his fables — Le lion abattu par l'homme — Used ‘artisan’ to describe a painter.

Descartes , Discours de la méthode, AT vi, 9; CSM i, 115. In the Furetière and Académie Française dictionaries, ‘artiste’ is used especially to portray alchemists. In the Middle Ages, it became common to name “artistes” (or sometimes artiens) those who studied the liberal arts — Scholars en devenir — And “artifex” those who practised the mechanical arts. Shiner , The invention of art (ref. 46), 30.

“Ce que l'on pourroit desirer d'eux [Peripateticiens] (au cas qu'ils voulussent ayder à establir la vraye Philosophie) consiste seulement à dresser des memoires fidelies des leurs obseruations, & de leurs experiences: Ce qu'il ne faut pas esperer iusqu'à ce que les honnestes hommes s'employent à cet art, & iusques à ce que les Artistes & Operateurs ayent quitté l'imagination de la poudre de projection, de la Magnesie des sages, & de la pierre Philosophique”, Mersenne , Qvestions inovyes, ov recreation des sçavans (Paris, 1634; facsimile Stuttgart, 1972), Question xxviii, 126–7.

Eamon William , Science and the secrets of nature: Books of secrets in medieval and early modern culture (Princeton, 1994), 281.

Eamon , Science and the secrets of nature (ref. 48), 284. On the concept of mêtis more generally, Detienne Marcel Vernant Jean-Pierre , Les ruses de l'intelligence: La mètis des Grecs (Paris, 1974).

Solmsen Friedrich , “Nature as craftsman in Greek thought”, Journal of the history of ideas, xxiv (1963), 473–96 ( Plato , Gorgias, 503e, quoted on p. 484). See also Gille Bertrand , Les mécaniciens grecs: La naissance de la technologie (Paris, 1980). On Aristotle and his legacy, Smith , The body of the artisan (ref. 7).

Descartes , Regulæ, AT x, 375–7; CSM i, 18–19.

Smith , The body of the artisan (ref. 7), esp. chaps 4 and 5 (quote on p. 142).

Goubert Pierre , Beauvais et le Beauvaisis de 1600 à 1730: Contribution à l'histoire sociale de la France du XVIIe siècle (Paris, 1960), 281–2, 585. Deyon Pierre , “Variations de la production textile aux XVIe et XVIIe siècles”, Annales: Economies, sociétés, civilisations, xviii (1963), 921–55. Farr James R. , Hand of honor: Artisans and their world in Dijon, 1550–1650 (Ithaca and London, 1988). Heller Henri , Labour, science and technology in France, 1500–1620 (Cambridge, 1996), chap. 6.

Baron Roger , Science et sagesse chez Hugues de Saint-Victor (Paris, 1957), 60–87.

Cardon Dominique , La draperie au Moyen Âge: Essor d'une grande industrie européenne (Paris, 1999), 416–17, 539–63. See also Israel Giorgio , “Des Regulæ à la Géométrie”, Revue d'histoire des sciences, li (1998), 183–236, where he discusses the role of weaving in Descartes's thinking.

According to Adrien Baillet, if Descartes had been raised in a condition allowing him to become an artisan, he would have been a skilful one because, we learn, he had in his youth a particular inclination for the arts. Like so many other such claims made by Baillet this one could be utterly wrong, or at best a misinterpretation. Baillet Adrien , La vie de Monsieur Des-Cartes (2 vols, Paris, 1691), i, 35. Geneviève Rodis-Lewis believes Baillet has his chronology wrong here, and that this remark should be associated to a much later phase in Descartes's life: Rodis-Lewis , “Descartes' life and the development of his philosophy”, in The Cambridge companion to Descartes (ref. 15), 21–57, p. 26. Descartes himself often contradicts Baillet's assertion. He said, for instance, that he was born without any manual abilities: “pour moy … i'estois venu au monde sans mains.” Descartes to, [Nov.-Dec. 1638?], AT ii, 452.

Descartes , Discours de la méthode, AT vi, 9; CSM i, 115. On the role of travel during the early modern period, see the remarkable opus by Roche Daniel , Humeurs vagabondes: De la circulation des hommes et de l'utilité des voyages (Paris, 2003).

Schama Simon , The embarrassment of riches: An interpretation of Dutch culture in the Golden Age (New York, 1997). On Dutch Baconianism, Alpers Svetlana , The art of describing: Dutch art in the seventeenth century (Chicago, 1983), esp. chap. 1. Smith , The body of the artisan (ref. 7), esp. chaps. 5 and 6.

This is first thing Beeckman writes down in his Journal:“Quæritur cur artes inter se non sint subordinatæ….” On the importance of both scientia and ars, he also writes down on the first page of the Journal: “Ad excitandum artium studium illud maximè faceret, si immunitates alicujus vectigalis etc. ijs qui Euclidis Elementa intelligerent, promitterentur. Quibus bene intellectis, pauci cætera studia negligerent, etiam in medijs occupationibus mechanicis.” Beeckman Isaac , Journal tenu par Isaac Beeckman de 1604 à 1634, ed. by de Waard Cornélis (4 vols, The Hague, 1939–53), i, 1.

Gaukroger Stephen Schuster John , “The hydrodynamic paradox and the origins of Cartesian dynamics”, Studies in the history and philosophy of science, xxiii (2002), 535–72, p. 552. For a general appraisal of the Beeckman—Descartes relationship, Gaukroger Stephen , Descartes: An intellectual biography (Oxford, 1995), chap. 3; van Berkel Klaas , “Descartes' debt to Beeckman: Inspiration, cooperation, conflict”, in Descartes' natural philosophy, ed. by Gaukroger Stephen Schuster John Sutton John (London, 2000), 46–59. The classic work on Beeckman remains Van Berkel Klaas , Isaac Beeckman (1588–1637) en de mechanisering van het wereldbeeld (Amsterdam, 1983), see pp. 217–35 for the role of technology in Beeckman's thinking.

Gaukroger , Descartes (ref. 60), 92–103. Schuster John A. , “Descartes and the scientific revolution, 1618–1634: An interpretation”, Ph.D. Dissertation, Princeton University, 1977, i, 117–27. Bos Henk J. M. , “On the representation of curves in Descartes' Géométrie”, Archives for the history of exact sciences, xxiv (1981), 295–338. Serfati Michel , “Les compas cartésiens”, Archives de philosophic lvi (1993), 197–230.

Baillet , La vie de M. Des-cartes (ref. 56), i, 67–70 on meeting the two mathematicians. On Bramer and his instruments, Descartes , Cogitationes privatæ, AT x, 241–2. The best analysis of Descartes in Germany and the significance of this sojourn is Mehl, Descartes en Allemagne (ref. 36). See also Shea William R. , The magic of numbers and motion: The scientific career of René Descartes (Canton, MA, 1991), 103–7.

Bennett , “The mechanics' philosophy and the mechanical philosophy” (ref. 7); Bennett J. A. , “Geometry in context in the sixteenth century: The view from the museum”, Early science and medicine, vii (2002), 214–30, pp. 229–30. On epistemic culture see Knorr-Cetina Karin , Epistemic cultures: How the sciences make knowledge (Cambridge, MA, and London, 1999).

The best accounts are Gaukroger , Descartes (ref. 60), 135–86; Schuster John A. , “Descartes opticien: The construction of the law of refraction and the manufacture of its physical rationales”, in Gaukroger Schuster Sutton (eds), Descartes's natural philosophy (ref. 60), 258–312; Shea , The magic of numbers and motion (ref. 62), 149–63. See Sabra A. I. , Theories of light from Descartes to Newton (Cambridge, 1981), 93–135 for Fermat's criticisms.

Drawing accurate parabolic mirrors held no secrets for Mydorge, judging from a letter sent by Robert Cornier to Mersenne, one of the Minim's early correspondents: “I do not know of any other means of making parabolic mirrors beyond those with which you are acquainted, especially since you have the paper of Mr. Mydorge who knows all that can be known on the matter. I can only tell you that Mr. [Guillaume] Le Vasseur says that he has found an absolutely certain way by the sines. But I cannot say more since I do not yet know how he goes about it.” Cornier to Mersenne, 18 August [1625], in Correspondance du Père Marin Mersenne, religieux minime, ed. by de Waard Cornélis (17 vols, Paris, 1933–88), i, 260–1; quoted in Shea, The magic of numbers and motion (ref. 62), 150. This Le Vasseur was an instrument-maker from Rouen, well-known in the region for his work in navigation and map-making. Cornier to Mersenne, 16 January 1626: “Je vous envoie le billet tel que Le Vasseur me l'a envoyé pour responce à ce que vous me demandiés des longitudes et latitudes”, Correspondance du Père Marin Mersenne, i, 332; see also ibid., 242–3. His method of drawing parabolic shapes “by the sines” most likely has nothing to do with Descartes's (and Mydorge's) later determination of the sine law for the refraction of light. Snel (in the 1620s) and Harriot (c. 1598) found the same law of refraction, but both were unknown to Descartes.

Melchior-Bonnet Sabine , Histoire du miroir (Paris, 1994), 31–39. At the end of the century mirrors became common objects of consumption for the noblesse and bourgeoisie alike. On Mydorge's disbursement, Baillet , La vie de Monsieur Des-Cartes (ref. 56), ii, 326.

Cornier to Mersenne, 16 January 1626: “Ce que vous me mandés de l'excellence des miroirs de M' Midorge, me faict souvenir de vous prier de me mander si c'est de sa façon et, si ainsi est, quelle en est la matiere et la dose.” Cornier to Mersenne, 27 Jauary 1626: “Je vous remercie de toute mon affection de la peone que vous prenés à m'expliquer les miroirs de M'Midorge et ses opinions. J'euse bien desiré scavoir son poli, mais puisqu'il se le reserve, il n'en fault point parler. J'en scay quelques uns qui sont bons et dont j'ay veu l'effect qui, je croy, se peut conduire à une grande perfection.” Correspondance du Père Marin Mersenne (ref. 65), i, 331, 354.

On Mydorge's importance for Descartes as an instrument maker cum natural philosopher, Baillet writes: “Rien au monde ne luy fut plus utile que ces verres pour connoître & pour expliquer, comme il a fait depuis dans sa Dioptrique, la nature de la lumiére, de la vision, & de la réfraction. M. Mydorge luy en fit faire de paraboliques & d'hyperboliques, d'ovales & d'élliptiques. Et comme il avoit la main aussi sûre & aussi délicate que l'esprit subtil, il voulut décrire luy-même les hyperboles & les éllipses. C'est ce qui fut d'un secours merveilleux à M. Descartes non seulement pour mieux comprendre qu'il n'avoit fait jusqu'alors la nature de l'éllipse & de l'hyperbole, leur propriété touchant les réfractions, la maniére dont on doit les décrire; mais encore pour se confirmer dans plusieurs belles découvertes qu'il avoit déja faites auparavant touchant la lumiére, & les moyens de perfectionner la vision.” Baillet , La vie de Monsieur Des-Cartes (ref. 56), i, 149–50.

When Aleaume passed away late in 1627, Peiresc feared for his manuscripts (some of which written by Viète) and instruments. Peiresc thus suggested on 8 January 1628 that “l'instrument [the compass] que luy avoit faict Ferrier pour descrire la ligne necessaire à la convexité desdictes lunettes et miroirs convexes, et les verres et miroirs qu'il en avoit essayez … il faudroit que cela passast par les mains de M'Midorge, tresorier de France … lequel seul je cognois en ce pais le plus approchant de la curiosité de feu M'Alleaume et de sa doctrine et prattique aux mathematiques et mechaniques.” Quoted in Mersenne , Correspondance du Père Marin Mersenne (ref. 65), i, 617. See also Cornier to Mersenne , 24 December [1627]: “Je croy que M' Midorge ne se sera pas oublié dans la venduë de M'Alleaume”, ibid., 613.

Ferrier's first name is sometimes questioned. Daumas Maurice (Les instruments scientifiques aux XVII^e et XVIII^e siècles (Paris, 1953), 98) suggests it is Guillaume, basing his assertion on the nineteenth-century French instrument maker Camille Sébastien Nachet. Yet Jean-Baptiste Morin in a 1634 publication refers to Ferrier as “D. Ioannes Ferrier, instrumentorum mathematicorum sollertissimus et accuratissimus fabrefactor”. I use this latter information in naming Ferrier. Morin is quoted in Correspondance du Père Marin Mersenne (ref. 65), i, 516.

Baillet , La vie de Monsieur Des-Cartes (ref. 56), i, 151.

Cornier to Mersenne, 16 March 1626, in Mersenne , Correspondance du Père Marin Mersenne (ref. 65), i, 420. This part of the letter refers, according to the editors of the Correspondance, to a letter sent by Mydorge to Mersenne regarding the hyperbolic or elliptical shape of the anaclastic line. Mydorge to Mersenne, [February-March 1626?], in ibid., i, 404–15. For a discussion of the dating of this letter, Gaukroger , Descartes (ref. 60), 438–39 (note 26). Regarding Ferrier and parabolic mirrors, Cornier continues: “Il [Ferrier] dict une chose merveilleuse, qu'une si petite partie de parabole brusle avec effect si loing. Car d'ordinaire, pour brusler de loing, estant necessaire d'avoir une portion d'une grande circonference, cela est si plat en petit volume qu'il demeure avec très peu de force”, Correspondance du Père Marin Mersenne (ref. 65), i, 420. Descartes will later say that it is impossible for a miroir ardent to burn at a distance of one league (lieue) unless the mirror is over twelve metres (“plus de six toises”) across, even if it had been the work of an Angel. Descartes to Mersenne, January 1630, AT i, 109–10. Mersenne discusses this topic in Qvestions inovyes (ref. 47), Question xxxv. On the history (legend) of Archimedes's great burning mirrors, Simms D. L. , “Archimedes and the burning mirrors of Syracuse”, Technology and culture, xviii (1977), 1–24.

Descartes to Huygens , [December 1635], AT i, 335–7.

“Quid ita, nunquid hujuscemodi operibus utilissimis caremus, quia multi, qui has lineas repererunt, eas aeterno silentio involvunt, ne quando alicui proficiant.” Quoted in Correspondance du Père Marin Mersenne (ref. 65), i, 299.

“[Descartes] devint luy-même en trés peu de têms un grand maître dans l'art de tailler les verres: & comme l'industrie des Mathématiciens se trouve souvent inutile par la faute des Ouvriers dont l'adresse ne répond pas toûjours à l'esprit des Auteurs qui les font travailler, il s'appliqua particuliérement à former la main de quelques Tourneurs qu'il trouva les plus experts, & les mieux disposez à ce travail. En quoy il eut la satisfaction de voir le succez de ses soins avant que de sortir de la France pour se retirer en Hollande”, Baillet , La vie de Monsieur Des-Cartes (ref. 56), i, 150.

Burnett D. Graham , Descartes and the hyperbolic quest: Lens making machines and their significance in the seventeenth century (Philadelphia, 2005), 36. On Descartes, Ferrier and artisans, see also Shea , The magic of numbers and motion (ref. 62), 151–8, 191–201; Belgioioso Giulia , “Descartes e gli artigiani”, in La biografia intellettuale di René Descartes attraverso la Correspondance, ed. by Armogathe Jean-Robert Belgioioso Giulia Vinti Carlo (Naples, 1999), 113–65.

Descartes is not insensitive to Ferrier's problems, which he associates with some sort of psychological unrest: “Aprés tout, ie plains fort M^r. Ferrier & voudrais bien pouuoir, sans trop d'incommodité, soulager sa mauuaise fortune; car il la merite meilleure, & je ne connois en luy de deffaut, sinon qu'il ne fait jamais son conte sur le pié des choses présentes, mais seulement de celles qu'il espere ou qui sont passées, & qu'il a vne certaine irresolution qui l'empesche d'executer ce qu'il entreprend. Ie lui ay rebattu presque la mesme chose en toutes les lettres que ie luy ai écrittes; mais vous auez plus de prudence que moy, pour sçauoir ce qu'il faut dire & conseiller”, Descartes to Mersenne, [18 March 1630], AT i, 132. Ferrier's lack of mechanical skills may have been caused by a too strong inclination towards pure mathematics: “[L]a douceur qu'il [Ferrier] avoit trouvée dans la méditation, & dans les entretiens des Mathématiciens, avoit beaucoup diminué en luy l'habitude du travail [manuel]”, Baillet , La vie de Monsieur Des-Cartes (ref. 56), i, 186. In a letter Ferrier sent to Descartes, he mentions indeed how much he wants to “taste” and “comprehend” the “true foundations of science” from scholars such as Descartes “tant i'ay d'ambition de me faire connoistre par quelque chose au delà du commun”, Ferrier to Descartes, 26 October 1629, AT i, 51.

Burnett , Descartes and the hyperbolic quest (ref. 76), 36.

Descartes to Golius , [January 1632], AT i, 234–5, where Descartes mentions he will send the first part of his Dioptrique that deals with refraction, without the philosophy.

Hamou Philippe , La mutation du visible: Essai sur la portée épistémologique des instruments d'optique au XVII^e siècle (2 vols, Villeneuve D'Ascq (Nord), 1999), i, 239–88.

Eastwood Bruce Stansfield , “Descartes on refraction: Scientific versus rhetorical method”, Isis, lxxv (1984), 481–502.

“Au surplus je ne croy pas que vostre mathematicien [Descartes], quelqu'habile homme qu'il soit, puisse bien donner des raisons des refractions jusques à ce qu'il ait enseigné de faire des lunetes de Hollande par raison et reglement en telle longueur que l'on vouldra. Car en cela git un des plus grands secrets des refractions à mon advis…”, Cornier to Mersenne , 16 March 1626, in Correspondance du Père Marin Mersenne (ref. 65), i, 420.

It is interesting to note that the theoretical portion of Besson's Jacques Theatrum instrumentorum machinarum (Orleans, 1569) was never published, yet is developed in the manuscript version (British Library) of the work. Keller Alex , “A manuscript version of Jacques Besson's book of machines, with his unpublished principles of mechanics”, in On the pre-modern technology and science: Studies in honour of Lynn White, Jr., ed. by Hall B. S. West D. C. (Malibu, 1976), 75–95.

Descartes to Ferrier , [2 December 1630], AT i, 185. Descartes , Discours de la méthode, AT vi, 77; CSM i, 150. Descartes to Mersenne , [25 January 1638?], AT i, 500–1; Daumas , Les instruments scientifiques aux XVII^e et XVIII' siècles (ref. 70), 99; Baillet , La vie de Monsieur Des-Cartes (ref. 56), i, 320–1.

Descartes is fully aware that precise instrument making is of the utmost importance to natural philosophy. Instruments can be used, for instance, to ascertain the number, velocity, and shape of sunspots and to know how the air refracts the light from the stars, and whether it also affects the light from the Moon. Descartes to Mersenne , January 1630, AT i, 113: “Mais ces choses là requierent des instrumens si iustes ….”.

Descartes to Golius , [2 February 1632], AT i, 236–40. “Ie ne doute point que vous ne puissiés trouuer plusieurs autres inuentions meilleures que celle cy pour faire la mesme experience, si vous prenés la peine d'en chercher; mais pource que ie scay que vous aués beaucoup d'autres occupations, I'ay creu que si vous n'y auiés pas encore pensé, ie vous soulagerais peut-estre d'autant …” (ibid., 240).

Schrynemakers Arthur H. , “Descartes and the weight-driven chain-clock”, Isis, lx (1969), 233–6. On the Archimedean screw, Descartes to Huygens , 15 November 1643, AT iv, 761–6. According to Leucheron, the experiment was done many times with the same result. Descartes does not doubt the outcome per se, but still believes it is worth exploring further. Mersenne asked someone to do the experiment with an arquebuze, giving again the same result as in the Récréations mathématiques. Descartes, however, is not convinced and does not judge it sufficient to draw certain knowledge from it (quelque chose de certain). He therefore suggests doing the experiment again with an instrument of his own design, using a cannon always kept in the upright position by a system of pulleys. Descartes to Mersenne , [April 1634], AT i, 287; Descartes to Mersenne , 15 May 1634, AT i, 293–94. The choice of a cannon that could support a cannonball of 30 to 40 pounds is better because the iron from which it is made does not melt as easily as the lead ball from the arquebus; and moreover such a big ball would be found more easily if it came back to earth.

Descartes uses these fashionable machines to investigate the phenomenon, as well as to relocate wonder from garden engineers to natural philosophers, thus displacing a “science of miracles” from simple technical achievements to the knowledge of mathematics and mechanical philosophy. Werrett Simon , “Wonders never cease: Descartes's Météores and the rainbow fountain”, The British journal for the history of science, xxxiv (2001), 129–47.

Baird Davis , Thing knowledge: A philosophy of scientific instruments (Berkeley, 2004). Burnett , Descartes and the hyperbolic quest (ref. 76), 132, for the association of the lens-grinding machine to an “epistemological instrument”. On the philosophy of instrumentation, Radder Hans (ed.), The philosophy of scientific experimentation (Pittsburgh, 2003).

Descartes to Burman , AT v, 174. English translation in Cottingham John (ed.), Descartes'conversation with Burman (Oxford, 1976), 44, §73.

Burnett , Descartes and the hyperbolic quest (ref. 76), 125–32.

Galilei Galileo , Sidereus nuncius, in Le opere di Galileo Galilei, ed. by Favaro Antonio (20 vols, Florence, 1890–1909), iii, 53–96, p. 59. For the English translation, Galileo , Sidereus nuncius or The sidereal messenger, transl. by van Helden Albert (Chicago and London, 1989), 35.

A very good analysis of organon qua instrument is given by Bates Don , “Machina ex Deo: William Harvey and the meaning of instrument”, Journal of the history of ideas, lxi (2000), 577–93. See also Des Chene Dennis , Spirits and clocks: Machine and organism in Descartes (Ithaca and London, 2001), 89–95 for an analysis of Suárez's notion of instrument.

“Si bien qu'il ne nous reste a considerer que les organes exterieurs, entre lesquels ie comprens toutes les parties transparentes de l'œil, aussy bien que tous les autres cors qu'on peut mettre entre luy & l'obiet”, Descartes , Dioptrique, AT vi, 148.

Descartes , Dioptrique, AT vi, 114–17.

Jones Matthew L. argues somewhat similarly when he writes that Descartes's compasses “offered the crucial heuristic, a material propaedeutic, for Descartes' [s] revised account of mathematics freed from memory and subject to a criterion of graspable unity. A simple mathematical instrument became the model and exemplar of the knowledge of Descartes's new subject, the one supposedly so removed from the material”, Jones , “Descartes's geometry as spiritual exercise”, Critical inquiry, xxviii (2001), 40–71, p. 61.

Paré Ambroise , Les œuvres de M. Ambroise Paré conseiller, et premier chirurgien du roy (Paris, 1598), chap. 22, “Des moyens & artifices d'adiouster ce qui defaut naturellement ou par accident”.

Huygens to Descartes , 8 September 1637, AT i, 395–96: “Mais comme il [le tourneur d'Amsterdam] est homme industrieux en matiere de mouuemens mechaniques, il presume de venir a bout de vostre inuention a beaucoup moins de façon. En effect, il produit des choses si estranges par des petites machines de deux liards, que si ce n'estoit vous, Monsieur, i'espererois qu'il abregeroit de quelque chose ce que vous auez desseigné pour arriuer a la perfection de ces verres; nous verrons ce qui arriuera, & vous en rendrons compte.” Descartes to Huygens , 5 October 1637, AT i, 433: “Mais puisqu'il vous plaist en sçauoir mon opinion, ie vous diray franchement que tant s'en faut que i'espere qu'il en viene a bout, auec des machines qui ayent moins de façon que la miene, qu'au contraire ie me persuade qu'on y doit encore adiouster diuerses choses, que i'ay omises, mais que ie croy n'estre point si difficiles a inuenter que l'vsage ne les enseigne.” 99. “[M]ais pour reuenir à ceux qui ont eu cognoissance des Machines mouuantes & Hidrauliques, peu en ont escrit de nostre temps, bien est vray, que Jacob Besson, Augustin Ramelly, & quelques autres ont mis en lumiere quelques Machines par eux inventees sur le papier, mais peu d'icelles peuuent auoir aucun effect, & ont creu, que par vne multiplication de roües dentelees, lesdites machines auroient effect, selon leur pensee, & n'ont pas consideré, que ladite multiplication est liee auec le temps, comme il sera monstré en son lieu …”, de Caus Salomon , Les Raisons des forces movvantes Auec diuerses Machines tant vtilles que plaisantes Aus quelles sont adioints plusieurs debeings de grotes et fontaines (Frankfurt, 1615), n.p., Epistre au Lecteur. De Caus gives an example (Theoresme XVI) of a machine to raise weights made of six geared wheels of increasing size. Although, theoretically, multiplying the number of wheels can expand infinitely the load a machine can lift, in this theorem de Caus calculates that a worker would have to turn the crank 2,985,984 times to cause the sixth and biggest wheel to make a single revolution. Assuming this worker could turn the crank 10,000 times a day, it would still take 298 days for the sixth wheel to complete one revolution!.

Chene Des , Spirits and clocks (ref. 93), 101–2.

Descartes , Discours de la méthode, AT vi, 57; CSM i, 140. See also Descartes , Règles utiles et claires pour la direction de l'esprit (ref. 9), 89–91.

On the representation of bodily parts in Descartes's first two posthumous editions of the treatise on man, Wilkin Rebecca M. , “Figuring the dead Descartes: Claude Clerselier's Homme de René Descartes (1664)”, Representations, lxxxiii (2003), 38–66.

Descartes , L'homme, AT xi, 120; CSM i, 99.

Descartes , Le monde, AT xi, 34–35, 46–47; quotation, CSM i, 97.

Gaukroger , Descartes (ref. 60), 63–64. Werrett , “Wonders never cease” (ref. 88). On clocks see Mayr Otto , Authority, liberty & automatic machinery in early modern Europe (Baltimore and London, 1986), and Rossum Gerhard Dohrn-Van , The history of the hour: Clocks and modern temporal orders, transl. by Dunlap Thomas (Chicago and London, 1996), esp. chap. 8.

Loyseau , A treatise of orders and plain dignities (ref. 44), 5.

Muchembled Robert , Culture populaire et culture des élites dans la France moderne (XV–XVIII^e siècle), 2nd edn (Paris, 1991), 225–85. Foucault Michel , Surveiller et punir: Naissance de la prison (Paris, 1975), esp. 159–227. Elias Norbert , The civilizing process: Sociogenetic and psychogenetic investigations, rev. edn (Oxford and Malden, MA, 2000). An interesting criticism of Elias's thesis is found in Duerr Hans Peter , Nudité et pudeur: Le mythe du processus de civilisation, transl. by Véronique Bodin and Jacqueline Pincemin (Paris, 1998). Such a radical rationalization of the state and social life can only be understood in the light of the disorders created by the Wars of Religion. See, for instance, Crouzet Denis , Les Guerriers de Dieu: La violence au temps des troubles de religion, vers 1525-vers 1610 (2 vols, Seyssel, 1990), ii, 624, and Holt Mack P. , The French wars of religion, 1562–1629 (Cambridge, 1995), 210–16. One of the most interesting sociological studies on this topic is Bourdieu Pierre , Méditations pascaliennes, rev. edn (Paris, 2003), 185–234: “Les injonctions sociales les plus sérieuses s'adressent non à l'intellect mais au corps” (p. 204).

de Laffemas Barthélemy , Reiglement genéral pour dresser les manufactures en ce royaulme (Paris, 1603), where he wrote: “Le defaut de nos polices a perverti l'ordre qui s'observoit, tant a la fabrique des manufactures qu'à l'effet de tout ce qui en dépend ….” Hence the King had to reestablish the “manufactures de draperie et de teintures en leur légalité, bonté et perfection anciennes”. Quoted in Levasseur Emile , Histoire des classes ouvrières et de l'industrie en France avant 1789 (2 vols, Paris, 1900–1), ii, 155. Contemporary to Laffemas, Antoine de Monchrestien comes to an identical conclusion in 1615 when he says that “Le plus Royal exercice que peuvent prendre Vos Majestés c'est de ramener à l'ordre ce qui est détraqué. De régler et distinguer les Arts tombez en une monstrueuse confusion”, Monchrestien , Traicté de l'æconomie politique, ed. by Billacois François (Geneva, 1999), 66.

Farr James R. , “Cultural analysis and early modern artisans”, in The artisan and the European town, 1500–1900, ed. by Crossick Geoffrey (Aldershot, 1997), 56–74, p. 67.

For “masters of letters”, Loyseau , A treatise of orders and plain dignities (ref. 44), 226. For how “unfair” was the production of masterpieces, Levasseur , Histoire des classes ouvrières et de l'industrie en France avant 1789 (ref. 108), ii, 141.

Ribe Neil M. pointedly argues that nature in the end “is not a source of standards but is itself subject to the higher standard of Cartesian rationality”, Ribe , “Cartesian optics and the mastery of nature”, Isis, lxxxviii (1997), 42–61, p. 53.

Jones Matthew L. , “Descartes's geometry as spiritual exercise” (ref. 96). Mersenne , Qvestions inovyes (ref. 47), Question xii, 45–46.

Descartes's universal bon sens is the very first assertion he makes in the Discours de la méthode. On Descartes's philosophy of education in general, Garber Daniel , “Descartes, or the cultivation of the intellect”, in Descartes embodied (ref. 2), 277–95.

Dear Peter , “A mechanical microcosm: Bodily passions, good manners, and Cartesian mechanism”, in Science incarnate: Historical embodiments of natural knowledge, ed. by Lawrence Christopher Shapin Steven (Chicago and London, 1998), 51–82.

Bacon , The new organon (ref. 40), Aphorism CXXII, 95.

On Descartes's audience generally, Cavaillé Jean-Pierre , “Descartes stratège de la destination”, XVII^e siècle, clxxvii (1992), 551–9; Cavaillé , ‘“Le plus éloquent philosophe des derniers temps’: Les stratégies d'auteur de René Descartes”, Annales: Histoire, sciences sociales, 1994, 349–67.