Le règne des mathématiques n’est plus. Le goût a changé. C’est celui de l’histoire
naturelle et des lettres qui domine.
Diderot to Voltaire, 19 February 1758
Abstract
Intellectual history still quite commonly distinguishes between the episode we know as the Scientific Revolution, and its successor era, the Enlightenment, in terms of the calculatory and quantifying zeal of the former—the age of mechanics—and the rather scientifically lackadaisical mood of the latter, more concerned with freedom, public space and aesthetics. It is possible to challenge this distinction in a variety of ways, but the approach I examine here, in which the focus on an emerging scientific field or cluster of disciplines—the ‘life sciences’, particularly natural history, medicine, and physiology (for ‘biology’ does not make an appearance at least under this name or definition until the late 1790s)—is, not Romantically anti-scientific, but resolutely anti-mathematical. Diderot bluntly states, in his Thoughts on the interpretation of nature (1753), that “We are on the verge of a great revolution in the sciences. Given the taste people seem to have for morals, belles-lettres, the history of nature and experimental physics, I dare say that before a hundred years, there will not be more than three great geometricians remaining in Europe. The science will stop short where the Bernoullis, the Eulers, the Maupertuis, the Clairauts, the Fontaines and the D’Alemberts will have left it.... We will not go beyond.” Similarly, Buffon in the first discourse of his Histoire naturelle (1749) speaks of the “over-reliance on mathematical sciences,” given that mathematical truths are merely “definitional” and “demonstrative,” and thereby “abstract, intellectual and arbitrary.” Earlier in the Thoughts, Diderot judges “the thing of the mathematician” to have “as little existence in nature as that of the gambler.” Significantly, this attitude—taken by great scientists who also translated Newton (Buffon) or wrote careful papers on probability theory (Diderot), as well as by others such as Mandeville—participates in the effort to conceptualize what we might call a new ontology for the emerging life sciences, very different from both the ‘iatromechanism’ and the ‘animism’ of earlier generations, which either failed to account for specifically living, goal-directed features of organisms, or accounted for them in supernaturalistic terms by appealing to an ‘anima’ as explanatory principle. Anti-mathematicism here is then a key component of a naturalistic, open-ended project to give a successful reductionist model of explanation in ‘natural history’ (one is tempted to say ‘biology’), a model which is no more vitalist than it is materialist—but which is fairly far removed from early modern mechanism.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
Mayr seems to be recycling an old intuition of Foucault’s, according to which the eighteenth century was essentially concerned with discipline, automatization and social control, in an obsessive extension of a mathesis universalis, with La Mettrie’s ‘man-machines’ serving as an image of infinitely reproducible automata under the orders of Frederick the Great (Foucault 1975, p. 138). Minsoo Kang endorses Foucault’s view in his otherwise superlative study of automata across the centuries, which I learned a great deal from (Kang 2011, p. 133f.). For an overview of the theme of automatization in the Enlightenment, see Schaffer (1999).
McLaughlin (2002); see in addition Bognon-Küss and Wolfe (Eds.), forthcoming. I have made the preliminary case elsewhere for why a considerable part of the (broad) domain of ‘natural history’ as used by authors such as Diderot and Buffon corresponds to what we would call ‘biology’: not just a ‘geological’-type history of Life but also a comprehensive, comparative study (Wolfe 2009).
On iatromechanism see Grmek (1972); on Stahlian animism see Duchesneau (2000). The idea of a ‘neither-nor’ position will also be familiar to those who have studied eighteenth-century medical vitalism, which is not the topic of the present article, although I touch on authors like Bordeu and Venel who belong to that story.
Of course there were traditions of ‘Romantic science’ (as discussed in Cunningham and Jardine (Eds.), 1990; Poggi and Bossi (Eds.). 1994), but the strands of anti-mathematicism I describe here were not attempts at erecting ‘parallel’ or ‘rival’ scientific programs; in addition, an author like Diderot is a committed determinist, quite willing to allow for natural ‘modelling’ of human behavior, including in the sense of social regularities.
Sydenham/Locke, Anatomia (1668), Locke ms., National Archives PRO 30/24/72/2 ff. 36v–37r., transcribed in Dewhurst (1963), pp. 85–93, here, p. 85. The manuscript is attributed variously to each or both authors, different parts being in the handwriting of one or the other.
Philopirio clearly seems to be a kind of avatar of Mandeville—a foreign-trained physician with radical materialist leanings when he waxes theoretical or metaphysical (stated first in the Preface (Mandeville 1730, p. xiii) and more explicitly with reference to the ‘Low Countries’ (3)). Later in the book (p. 126) Philopirio notes he studied in Leyden (like Mandeville, who had defended a thesis on animal automatism at Leyden in 1689), and adds (p. 132) that he defended a thesis “Chylosi vitiata” in 1691.
Elementa Medicinae (1717), translated as The Philosophical and Mathematical Elements of Physick (1718), §§ LXXVII and LXXXVIII, in Pitcairne (1718), pp. 353, 354. That Pitcairne’s arguments in favour of mathematics, contra philosophy may have a political subtext (promoting the ‘certainty’ of mathematics against the danger of dissent, enthusiasm and theological ferment, as discussed in Schaffer 1989) lies beyond the scope of the present paper.
The prominent iatromechanical physician Giorgio Baglivi insisted in the early 1700s that static medicine be considered a legitimate part of the medicine of solids, and recommended to this end the reading of both Harvey and Sanctorius (Dacome 2012, p. 385), a connection reiterated in the scholarly literature, e.g. “Harvey was to some extent applying the mental habits of the dietetic physician” (Bylebyl 1977, p. 383). Similar considerations were involved, not in the study of digestion but of circulation (before and after Harvey), for instance with regard to how much blood it was suitable to eliminate in bloodletting.
See Salter and Wolfe (2009) for more discussion of this point. Massey (1995) critically evaluates various charges against Harvey’s experiments for not being ‘quantitative enough’ (pp. 43–45), in a way which complements my ‘qualitative’ point here (and what is termed “embodied empiricism” in Salter and Wolfe (2009)). The same point can be made by focusing on the term (and the notion) of a law (thinking of e.g. Galilean laws, like the law of falling bodies): Harvey doesn’t speak about his account of circulation as a law, while the Scottish Newtonians in the 1690s and thereafter explicitly use the language of laws.
Cf. Roux’s “historically situated and empirical definition of mathematics”: “what should be called ‘mathematics’ is the activities of those who called themselves or were called by others ‘mathematicians”’ (Roux 2010, p. 325).
Bordeu, Recherches sur le pouls par rapport aux crises (1754), in Bordeu (1818), vol. I, pp. 257–258 (All translations are mine unless otherwise indicated); see also Terada (2006). Bordeu’s discussion of the history of medical theories of the pulse is actually more complicated than this, as he criticizes both Galenic and more ancient (e.g. Chinese) theories for their vagueness, and proposes what we might call more “functional” descriptions, referring to the activity of other organ systems such as the arteries, but also to rhythm and pace.
Bordeu, Recherches sur les maladies chroniques (1775), § XVI, in Bordeu (1818), vol. II, pp. 831–832. However, there is no monolithic anti-mathematical position in the Montpellier vitalist context. The Stahlian Boissier de Sauvages, a professor in Montpellier during the study years of figures such as Bordeu and Venel, was explicitly dismissive of anti-mathematical trends, bluntly asserting that “I attribute the errors committed in Medicine to a lack of knowledge of Mathematics,” describing mathematics as the “foundation of physics and philosophy,” and warning against those who seek to “banish it from medical schools” (de Sauvages 1772, vol. I, p. 77). Sauvages acknowledges that some parts of mathematics, like “astronomy and trigonometry,” are not useful to medicine, but contrasts these with fluid dynamics (for understanding blood vessels), acoustics and optics (for understanding hearing and vision) (pp. 77–78). Similarly, Robert Whytt, a member of the same medical tradition (animism) in the Scottish context, also privileges the soul as an explanatory term while at the same time conducting extensive quantitative experiments in life science, notably repeating the ‘hydrostatic’ experiments of Stephen Hales, and using quantitative arguments to address cases like the treatment of gallstones (Whytt 1755).
Thanks to Sebastián Molina for this point. One could add that the distinction between ontologically founded and strictly skeptical forms of anti-mathematicism matches the diversity of iatromathematical projects, some which genuinely seek to reduce bodily organs to mathematical entities (an ‘ontological’ reduction, then), others which view mathematization as a kind of heuristics.
Fibra enim physiologo id est, quod linea geometræ (von Haller 1757, I, p. 2).
Edward Eizat, Apollo Mathematicus: or the Art of Curing Diseases by the Mathematicks, 1695, cit. Stigler (1992), p. 114.
Enc. I, p. vi, emphasis mine (thanks to Iulia Mihai for calling my attention to this passage).
Éléments de physiologie, ch. VI, “Volonté,“ in Diderot (1975), XVII, p. 485.
It is indeed the case that the program of natural history had something to do with a rejection of Cartesianism, definitely with an anti-mathematical attitude. Similarly, it is possible, or even probable, that a different intellectual strand, more Baconian, more Lockean, leads through natural history to ‘biology’. Yet Bacon would not have approved of the anti-mathematical impulse in Diderot and Buffon (see Bacon, De Augmentis Scientarum, III, 6, in Bacon 1857, p. 578; Vartanian 1992, p. 130).
Buffon, “De la manière d’étudier l’Histoire Naturelle,” in Buffon (1749), I, “Premier discours,” p. 54.
On Diderot’s mathematical ability (his capacity to follow differential calculus but not the work of Euler or D’Alembert, and his work in probability theory), see Dhombres (1985).
Eric Schliesser has pointed out that this resembles Hume, Treatise I.iv.1; the question of Diderot’s debt to Hume is not easy to make out, although for a convincing textual confrontation between Hume’s Dialogues and Diderot’s Letter on the Blind that reveals surprising resonances and perhaps chains of influence, see Paganini (ms. 2015).
Buffon (1749), I, pp. 54–55.
Fréret (1745/1986), ch. VII, pp. 339–340, 370–371. Fréret continues with a less frontal critique of arguments for the divisibility of matter. In his 1751 report on the Abbé du Resnel’s mémoire on the utility of mathematics versus that of belles-lettres, Fréret enumerates many positive traits of mathematics both internally and for its concrete accomplishments, but notes (Fréret 1751, p. 24) that the “esprit de calcul” can indeed be extended beyond its legitimate realms of applicability, with results that then turn negative.
Diderot, Pensées sur l’interprétation de la nature, § III, in Diderot (1975), IX, p. 30.
In addition, neither of these claims are particularly skeptical in the senses I discussed earlier. In the first workshop in which we presented our ideas on anti-mathematicism (Warwick University 2013) Eric Schliesser set out a very suggestive distinction between global and containment strategies in eighteenth-century anti-mathematicism, where “global” refers to arguments that challenge and undermine the epistemic authority and solidity of mathematical applications as such, while “containment” refers to arguments restricting the application of mathematical tools to specific domains (astronomy, optics). This distinction resembles my distinction between ontological and skeptical forms of anti-mathematicism, but notice that Schliesser’s “global” strategies are presented in epistemic terms, neatly contrasting with my ontological emphasis. His “containment” strategies seem to fit rather well within the spectrum of more or less skeptical challenges to mathematics that I describe, perhaps closer to the weaker form of skepticism.
Indeed, more recent examination suggests it is an overstatement to call Rouelle an “anti-Newtonian” as well (Franckowiak 2003). And the opposition between a chemically ‘rich’ conception of matter and a more ‘crude’ mechanistic picture is ... specific to a given program: one could also cite chemists of the period for whom Newtonian attraction was a liberation from strict mechanism.
Diderot did understand Newtonianism as an ideological construct associated with natural theology earlier on, most dramatically, in the figure of the blind mathematician Saunderson in his 1749 Letter on the Blind).
Diderot’s (not especially aggressive) criticisms of the ontology of action at a distance occur in an “Observation” at the end of the Interprétation de la nature and later in the 1761 Réflexions sur une difficulté proposée contre la manière dont les newtoniens expliquent la cohésion des corps (in Diderot 1975, IX; a text printed anonymously in the Journal de Trévoux in April 1761, in which he also presents attraction as a “general property of matter”: Diderot 1975, IX, p. 341). The most significant author at the heart of this Diderot-Newton relation would be John Toland, since his matter theory is an influence on Diderot’s and he was perhaps the strongest materialist critic of Newtonianism, but the comparison indicates a stronger anti-Newtonianism in Toland. For more on Toland and Newton see Schliesser (ms.).
Rouelle, Cours de chimie, 1754–1758, ms., cit. in Franckowiak (2003), p. 244; see also Guédon (1979), p. 191. Interestingly, the language of sympathies and affinities was also used in this period to describe properties of organic interdependence which earlier mechanistic medicine had failed to account for (thus further illustrating the relation between this ‘vital chemistry’ and medical vitalism): see e.g. Ménuret de Chambaud (1765), p. 318b; Grimaud (1776), p. 43 (although de Sauvages 1772 is critical of the term ‘sympathies’, e.g., p. 65, he ends up using it positively later on in this work). The same language is found in Diderot’s Éléments de physiologie (in Diderot 1975, vol. XVII, p. 499). Hoquet notes the presence of the concept of sympathy in Buffon, now as a term explaining properties of the nervous system, in the chapter of the Histoire naturelle dealing with ... puberty (Hoquet 2005, p. 218).
This text first appeared in Latin in 1751 under the title Dissertatio inauguralis metaphysica de universali naturae systemate, signed with the pseudonym Dr Baumann; it was translated by Maupertuis in 1754 as Essai sur la formation des corps organisés and later was included in his 1756 Œuvres under the title Système de la nature.
Maupertuis, Système, § III, in Maupertuis (1756/1965), p. 141.
Système, § XIV, in Maupertuis (1756/1965), pp. 146–147.
In the Rêve de D’Alembert Diderot wonders whether sensitivity is a “general property of matter” or rather a property of organized matter alone (Diderot 1975, vol. XVII, p. 105). Fifteen years earlier, he already described life as a “physical property of matter” in the Encyclopédie article “Animal,” influenced by Buffon (Diderot et al. 1751, p. 474a); in the later, unfinished Éléments de physiologie (1770s), he names sensitivity, life and motion as properties of matter, but goes on to discuss cases of organic matter (“flesh”) in particular (Diderot 1975, vol. XVII, p. 333).
Diderot, entry “Leibnizianisme” Enc. IX, 1765, p. 374a; he also identifies monads with “entelechies” (p. 374b), an identification which is very close to Maupertuis’s letter on monads (letter VIII), in which monads are presented as the prime elements of matter (as they will be in Charles Bonnet and Jean-Claude de La Métherie as well). For more on Diderot as a Leibnizian, albeit somewhat loosely argued, see Belaval (1976).
Diderot’s Prospectus of the Encyclopédie, in Diderot (1975), vol. III, p. 410.
Bordeu, Recherches anatomiques sur la position des glandes et leur action (1751), in de Bordeu (1818), I, pp. 178–180.
Diderot, Pensées sur l’interprétation de la nature, § III, in Diderot (1975), IX, p. 30.
Diderot to Voltaire, 19 February 1758, in Diderot (1997), p. 73.
I thank an anonymous reviewer for making me clarify these two points (what mathematization might entail and to what extent it should be opposed to the new life science projects, and how). For the complexity of earlier forms of mathematization, see Roux (2010).
References
Anon. (1765). Méchanicien (Médecine). In D. Diderot, & J. le Rond D’Alembert (Eds.), Encyclopédie ou dictionnaire des arts et métiers (Vol. X, pp. 220a–222a). Paris: Briasson.
Bacon, F. (1857). The works of Francis Bacon. In J. Spedding et al. (Eds.), Vol. 1. London: Longmans.
Belaval, Y. (1976). Études leibniziennes. Paris: PUF.
Bognon-Kuss, C., & Wolfe, C. T. (Eds.). (in progress). Philosophy of biology before biology. London: Routledge (contracted2015)
Bordeu, T. de. (1818). Œuvres complètes, précédées d’une Notice sur sa vie et ses ouvrages par Monsieur le Chevalier de Richerand, 2 vols. Paris: Caille et Ravier.
Bylebyl, J. J. (1977). Nutrition, quantification and circulation. Bulletin of the History of Medicine, 51, 369–385.
Cockburn, W., & Southwell, E. (1704). Solutio problematis de purgantium & emeticorum medicamentorum dosibus determinandis. Philosophical Transactions of the Royal Society, 24, 2119–2122.
Cunningham, A., & Jardine, N. (Eds.). (1990). Romanticism and the sciences. Cambridge: Cambridge University Press.
Dacome, L. (2012). Balancing acts: Picturing perspiration in the long eighteenth century. Studies in History and Philosophy of Science Part C, 43(2), 379–391.
Dewhurst, K. (1963). John Locke (1632–1704), physician and philosopher: A medical biography with an edition of the medical notes in his journals. London: Wellcome Historical Medical Library.
de Buffon, G.-L. L. (1749-1788). Histoire naturelle, générale et particulière, 36 vols. Paris: Imprimerie Royale.
de Sauvages, F. B. (1772). Nosologie méthodique ou distribution des maladies en classes, en genres et en especes suivant l’esprit de Sydenham, & la méthode des botanistes,... traduite par M. Gouvion. Lyon: Jean-Marie Bruyset.
‘D.G.’ [Grimaud, J.C.M.G. de]. (1776). Essai sur l’irritabilité. Avignon: Bonnet frères.
Dhombres, J. (1985). Quelques rencontres de Diderot avec les mathématiques. In A. -M. Chouillet (Ed.), Denis Diderot, actes du colloque international de 1984, 269–280. Paris: Aux amateurs de livres.
Diderot, D. (1751). Animal (Ordre encyclopédique. Entendement. Raison. Philosophie ou science. Science de la nature. Zoologie). In D. Diderot & J. le Rond D’Alembert (Eds.), Encyclopédie ou dictionnaire des arts et métiers (Vol. I, pp. 468a–474b). Paris: Briasson.
Diderot, D. (1765). Théosophes. In D. Diderot & J. le Rond D’Alembert (Eds.), Encyclopédie ou dictionnaire des arts et métiers (Vol. XVI, pp. 253–261). Paris: Briasson.
Diderot, D. (1975). Œuvres complètes. In H. Dieckmann, J. Proust, & J. Varloot (Eds.). Paris: Hermann.
Diderot, D. (1997). Correspondance. In L. Versini (Ed.). Œuvres, Vol. 5. Paris: Laffont, coll. “ Bouquins ”.
Diderot, D., & Le Rond D’Alembert, J. (Eds.). (1751–1780). Encyclopédie ou Dictionnaire raisonné des arts et des métiers, 35 vols. Paris: Briasson, David, Le Breton & Durand. Reprint, Stuttgart/Bad Cannstatt, 1966.
Distelzweig, P. (2016). “Mechanics” and mechanism in William Harvey’s anatomy: Varieties and limits. In P. Distelzweig, B. Goldberg & E. Ragland (Eds.), Early modern medicine and natural philosophy (pp. 117–140). Dordrecht: Springer.
Duchesneau, F. (2000). Stahl, Leibniz and the territories of soul and body. In J. P. Wright & P. Potter (Eds.), Psyche and soma. Physicians and metaphysicians on the mind-body problem from antiquity to the enlightenment (pp. 217–235). Oxford: Clarendon Press.
Fabre, J. (1961). Diderot et les théosophes. Cahiers de l’AIEF, 13(1), 203–222.
Formey, J. H. S. (1747). Recherches sur les éléments de la matière. n.p.
Foucault, M. (1975). Surveiller et punir. Paris: Gallimard.
Franckowiak, R. (2003). Rouelle, un vrai-faux anti-newtonien. Archives internationales d’histoire des sciences, 150–151(53), 240–255.
Fréret, N. (1751). Discussion of “Réflexions générales sur l’utilité des belles-lettres, et sur les inconvénients du goût exclusif qui paraıt s’établir en faveur des mathématiques et de la physique,” by the abbé Jean-François du Resnel. Histoire de l’Académie Royale des Inscriptions et Belles-Lettres, Vol. XVII, pp. 11–37.
Fréret, N. (1986). Lettre de Thrasybule à Leucippe (1745), a cura di S. Landucci. Florence: Olschki.
Grmek, M. D. (1972). A survey of the mechanical interpretations of life. In A. D. Breck & W. Yourgrau (Eds.), Biology, history and natural philosophy (pp. 181–195). New York: Plenum Press.
Grmek, M. D. (1980). La théorie et la pratique de l’expérimentation biologique au temps de Spallanzani. In G. Montalenti & P. Rossi (Eds.), L. Spallanzani e la biologia del Settecento. Teorie, esperimenti, istituzioni scientifiche (pp. 321–352). Florence: Olschki.
Guédon, J.-C. (1979). Chimie et matérialisme. La stratégie anti-newtonienne de Diderot. Dix-huitième siècle, 11, 185–200.
Harvey, W. (1976). Exercitationes Anatomica De Motu Cordis et Circulatione Sanguinis (1628) (G. Whitteridge Trans. & Ed.). Oxford: Blackwell Scientific Publications.
Harvey, W. (1981). Exercitationes De Generatione Animalibus (1651) (G. Whitteridge Trans. & Ed.). Oxford: Blackwell Scientific Publications.
Hoquet, T. (2005). Buffon: Histoire naturelle et philosophie. Paris: Champion.
Hoquet, T. (2010). History without time: Buffon’s natural history as a nonmathematical physique. Isis, 101, 30–61.
Israel, J. (2006). Enlightenment contested: Philosophy, modernity, and the emancipation of Man 1670–1750. Oxford: Oxford University Press.
Kang, M. (2011). Sublime dreams of living machines. Cambridge, MA: Harvard University Press.
Lundgren, A. (1990). The changing role of numbers in 18th-century chemistry. In T. Frängsmyr, J. L. Heilbron, & R. E. Rider (Eds.), The quantifying spirit in the eighteenth century (pp. 245–267). Berkeley: University of California Press.
Mandeville, B. (1730). A treatise of the hypochondriack and hysterick diseases, in three dialogues, 2nd ed. London: Tonson.
McLaughlin, P. (2002). Naming biology. Journal of the History of Biology, 35, 1–4.
Massey, G. (1995). Rhetoric and rationality in William Harvey’s De Motu Cordis. In H. Krips, J. E. McGuire & T. Melia (Eds.), Science, reason, and rhetoric (pp. 13–46). Pittsburgh & Konstanz: University of Pittsburgh Press & University of Konstanz Press.
Mayr, O. (1986). Authority, liberty, and automatic machinery in early modern Europe. Baltimore: Johns Hopkins University Press.
Ménuret de Chambaud, J.-J. (1765). Observation (Gram. Physiq. Méd.). In D. Diderot & J. le Rond D’Alembert (Eds.), Encyclopédie ou Dictionnaire des arts et des métiers (Vol. XI, pp. 313–321). Paris: Briasson.
Moreau de Maupertuis, P. L. (1965). Système de la nature. Essai sur la formation des corps organisés. In Œuvres, revised edition (1756), vol. 2. Lyon: Bruyset; reprint, Hildesheim: Olms.
Paganini, G. (ms. 2015). Diderot et Hume.
Pagel, W. (1976). New light on William Harvey. Basel: S. Karger.
Pépin, F. (2011). Vitalisme, chimie et philosophie autour de l’ Encyclopédie et de Diderot. In P. Nouvel (Ed.), Repenser le vitalisme (pp. 131–143). Paris: PUF.
Pépin, F. (2012). La Philosophie expérimentale de Diderot et la chimie. Paris: Garnier, coll. ‘Histoire et philosophie des sciences’.
Pitcairne, A. (1715). The works of Dr. Archibald Pitcairn; wherein are discovered, the true foundation and principles of the art of physic; with cases and observations upon most distempers and medicines. In G. Sewell & J. T. Desaguliers (Eds.). London: Curll, Pemberton and Taylor.
Pitcairne, A. (1718). The philosophical and mathematical elements of physick: In two books, the first containing the theory, the second the practice: Compos’d for the use of all who study the art of medicine. London: Andrew Bell and John Osborn.
Poggi, S., & Bossi, M. (Eds.). (1994). Romanticism in science: Science in Europe, 1790–1840. Dordrecht: Springer.
Porter, T. M. (2000). Quantification. In A. Hessenbruch (Ed.), Reader’s guide to the history of science (pp. 616–617). London and Chicago: Fitzroy Dearborn.
Reill, P. H. (2005). Vitalizing nature in the enlightenment. Berkeley: University of California Press.
Restrepo, G. (2013). To mathematize, or not to mathematize chemistry. Foundations of Chemistry, 15(2), 185–197.
Rey, R. (1997). L’âme, le corps et le vivant. In M. Grmek (Ed.), Histoire de la pensée médicale en Occident. De la Renaissance aux Lumières (Vol. 2, pp. 117–156). Paris: Seuil.
Roberts, L. (1995). The death of the sensuous chemist: The ‘new’ chemistry and the transformation of sensuous technology. Studies in History and Philosophy of Science, 26, 503–529.
Roger, J. (1963/1993). Les sciences de la vie dans la pensée française du XVIII \(^{e}\) siècle (revised ed.). Paris: Albin Michel.
Roux, S. (2010). Forms of mathematization (14\(^{{\rm th}}\)–17\(^{{\rm th}}\) centuries). Early Science and Medicine, 15, 319–337.
Salomon-Bayet, C. (1978). L’institution de la science et l’expérience du vivant: méthode et expérience à l’Académie Royale des Sciences, 1666–1793. Paris: Flammarion.
Salter, A., & Wolfe, C. T. (2009). Empiricism contra experiment: Harvey, Locke and the revisionist view of experimental philosophy. Bulletin de la SHESVIE, 16(2), 113–140.
Schaffer, S. (1989). The glorious revolution and medicine in Britain and the Netherlands. Notes and Records of the Royal Society of London, 43(2), 167–190.
Schaffer, S. (1999). Enlightened automata. In W. Clark, J. Golinski, & S. Schaffer (Eds.), The sciences in enlightened Europe (pp. 126–165). Chicago: University of Chicago Press.
Schliesser, E. (ms.) Spinoza and Anti-Mathematics.
Schofield, R. E. (1978). An evolutionary taxonomy of eighteenth-century newtonianisms. Studies in Eighteenth-Century Culture, 7, 175–192.
Shaftesbury, A. Cooper, Earl of (1978). The Moralists, in Characteristicks (1711). Reprint, Hildesheim: G. Olms.
Smith, J. E. H. (2011). Divine machines: Leibniz and the sciences of life. Princeton: Princeton University Press.
Stigler, S. M. (1992). Apollo mathematicus: A story of resistance to quantification in the seventeenth century. Proceedings of the American Philosophical Society, 136(1), 93–126.
Terada, M. (2006). La sphygmologie chinoise et la mise au point d’une nouvelle conception vitaliste de l’économie animale par des vitalistes montpelliérains. Archives Internationales d’Histoire des Sciences, 56(156–157), 149–163.
Vartanian, A. (1992). Buffon et Diderot. In J. Gayon (Ed.), Buffon 88 (Actes du colloque international) (pp. 119–133). Paris: Vrin.
Venel, G.-F. (1753). Chymie. In D. Diderot & J. le Rond D’Alembert (Eds.), Encyclopédie ou dictionnaire des arts et métiers (Vol. III, pp. 408–421). Paris: Briasson.
von Haller, A. (1757). Elementa physiologiæ corporis humani (Vol. I). Lausanne: Marc-Michel Bousquet.
von Haller, A. (1777). Oeconomie Animale. In Supplément à l’Encyclopédie ou Dictionnaire raisonné des arts et des métiers, par une Société de Gens de Lettres, IV (pp. 104-105). Amsterdam: Marc-Michel Rey.
Whytt, R. (1755). An essay on the virtues of lime-water in the cure of the stone, 2nd expanded edition. With an appendix, containing the cases of the right hon. Horace Walpole,&c. Edinburgh: Hamilton, Balfour, and Neill.
Williams, E. (2003). A cultural history of medical vitalism in Enlightenment Montpellier. Burlington: Ashgate.
Wolfe, C. T. (2009). ‘Cabinet d’Histoire Naturelle’, or: The Interplay of Nature and Artifice in Diderot’s Naturalism. Perspectives on Science, 17(1), 58–77.
Wolfe, C. T. (2011). Why was there no controversy over life in the scientific revolution? In V. Boantza & M. Dascal (Eds.), Controversies in the Scientific Revolution (pp. 187–219). Amsterdam: John Benjamins.
Wolfe, C. T. (2014). Epigenesis as Spinozism in Diderot’s biological project. In O. Nachtomy & J. E. H. Smith (Eds.), The life sciences in early modern philosophy (pp. 181–201). Oxford: Oxford University Press.
Wolfe, C. T. (2017). Varieties of vital materialism. In S. Ellenzweig & J. Zammito (Eds.),The new politics of materialism. History, philosophy, science (pp. 44–65). London: Routledge.
Acknowledgements
Earlier versions of this paper were presented at Scientiae, Warwick University (2013), the workshop on ‘The Uses and Abuses of Mathematics in Early Modern Philosophy’ at the Institute of Philosophy, Hungarian Academy of Sciences, Budapest (2015) and the working group on early modern history and philosophy of science (fMod Centre) at the University of Turin (2016). I have benefited from the input of Tamás Demeter, Sebastiano Gino, Sebastián Molina, and Eric Schliesser.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wolfe, C.T. Vital anti-mathematicism and the ontology of the emerging life sciences: from Mandeville to Diderot. Synthese 196, 3633–3654 (2019). https://doi.org/10.1007/s11229-017-1350-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11229-017-1350-y