Other Expressions of the Spirit

The opinions of Fontenelle are frequently trotted out in characterizations of the Englightenment. Fontenelle commended the esprit géométrique for its promise of certainty and rationality, which might improve polity, morality, literature, and oratory as it had enriched astronomy and mechanics.^[11] By the end of the 18th century, a wealth of treatises and textbooks had praised the merits of mathematics and the solidity of reasoning in Euclidean geometry, often in terms borrowed from the previous century. Recent scholarship has pointed to John Arbuthnot's arguments in favor of the utility of mathematics,^[12] the appeal of the axiomatic approach and the persistence of Cartesian methods as mixed with mathematics,^[13] and the wide-ranging

[11] Thomas Hankins, Science and the Enlightenment (Cambridge: Cambridge University Press, 1985), 2. Cf. Charles B. Paul, Science and immortality: The éloges of the Paris Academy of Sciences (1699–1791) (Berkeley: University of California Press, 1980); Alain Niderst, "Fontenelle et la science de son temps," Studies on Voltaire and the eighteenth century, 216 (1983), 323–4; Birgit Fenner, "Vernünftige Skepsis—skeptische Vernunft: Fontenelle und die Anfänge der Aufklärung," Germanisch-Romanische Monatsschrift, 32 (1982), 156–73.

[12] Eddie Shoesmith, "The continental controversy over Arbuthnot's argument for divine providence," Historia mathematica, 14 (1987), 133–46; Richard Olson, "Tory–High Church opposition to science and scientism in the 18th century: The works of John Arbuthnot, Jonathan Swift, and Samuel Johnson," in John G. Burke, ed., The uses of science in the age of Newton (Berkeley: University of California Press, 1983), 171–204.

[13] Michael Heyd, Between orthodoxy and the Enlightenment: Jean-Robert Chouet and the introduction of Cartesian science in the Academy of Geneva, International archives of the history of ideas, 96 (The Hague: Nijhoff; Jerusalem: Magnes Press, 1982); Gereon Wolters, Basis und Deduktion: Studien zur Entstehung und Bedeutung der Theorie der axiomatischen Methode bei J.H. Lambert (1728–1777), Quellen und Studien zur Philosophie, 15 (Berlin: de Gruyter, 1980); C. Hakfoort, "Christian Wolff tussen Cartesianen en Newtonianen," Tijdschrift voor de geschiedenis der geneeskunde, natuurwetenschappen, wiskunde en techniek, 5 (1982), 27–38; Jean Dhombres, "Un style axiomatique dans l'écriture de la physique mathématique au 18ème siècle: Daniel Bernoulli et la composition des forces," Sciences et techniques en perspective, 11 (1986–7), 1–-68; Daniel Klein, "Deductive economic methodology in the French Enlightenment: Condillac and Destutt de Tracy," History of political economy, 17 (1985), 51–71; Wolfgang Röd, "Descartes dans la philosophie universitaire allemande du XVIIIe siècle," Etudes philosophiques , 1985, 161–73; Pierre Costabel, "Euler lecteur de Descartes," Dix–huitième siècle, 18 (1986), 281–8; Mariafranca Spallanzani, "Descartes dans l'Encyclopédie: La méthode," Recherches sur le XVIIème siècle, 8 (1986), 1037–25; cf. Spallanzani, "Notes sur le cartésianisme dans l'Encyclopédie," Studies on Voltaire and the eighteenth century, 216 (1983), 326–7.

influence of what one author calls the mathematical method-model.^[14]

What was reasonable or certain in the 17th and 18th centuries was intimately bound up with questions of probability and risk, in contexts ranging from law to morality, economics to public health. The richness of the analysis and examples in recent studies on probability will warrant careful attention in subsequent exploration of the esprit géométrique and the quantifying spirit.^[15] As the 18th-century controversy over inoculation against smallpox makes clear, the stakes could be high in disputes over the validity of quantitative arguments.^[16]

[14] Hans-Jürgen Engfer, Philosophie als Analysis: Studien zur Entwicklung philosophischer Analysiskonzeptionen unter dem Einfluss mathematischer Methodenmodelle im 17. um frühen 18. Jahrhundert (Stuttgart-Bad Cannstatt: Frommann-Holzboog, 1982). For Wolff's influence and the ways in which he built on 17th-century systèmes , see Sonia Carboncini, "L'Encyclopédie et Christian Wolff: A propos de quelques articles anonymes," Etudes philosophiques , 1987, 489–504; Hakfoort, "Christian Wolff tussen Cartesianen en Newtonianen" (note 13); Werner Schneiders, ed., Christian Wolff, 1679–1754: Interpretation zu seiner Philosophie und deren Wirkung. Mit einer Bibliographie der Wolff-Literatur, (Hamburg: Meiner, 1983); Röd, "Descartes dans la philosophie universitaire allemande"; and Fabio Todesco, "Dal 'calcolo logico' alla 'riforma della metafisica': Johann Heinrich Lambert tra Wolff e Locke," Rivista di storia della filosofia, 77 (1986), 337–58.

[15] Lorraine J. Daston, "Probabilistic expectation and rationality in classical probability theory," Historia mathematica, 7 (1980), 234–60, "Mathematical probability and the reasonable man of the 18th century," in History and philosophy of science: Selected papers , ed. Joseph W. Dauben and Virginia Staudt Sexton (New York: New York Academy of Sciences, 1983), 57–62, and Classical probability in the Enlightenment (Princeton: Princeton University Press, 1988); Lorenz Krüger, Lorraine J. Daston, and Michael Heidelberger, eds., The probabilistic revolution , 2 vols. (Cambridge: MIT Press, 1987), esp. 1: Ideas in history ; Luigi Cataldi Madonna, "Wahrscheinlichkeit und wahrscheinliches Wissen in der Philosophie Christian Wolffs," Studia Leibnitiana, 19 (1987), 2–40; Douglas Lane Patey, Probability and literary form: Philosophic theory and literary practice in the Augustan age (Cambridge: Cambridge University Press, 1984).

[16] The many studies of smallpox and its prevention in the 18th century include Andrea Rusnock, "When counting counts: The reception of quantitative arguments in eighteenth-century England and France" (unpublished paper, History of Science Society meeting, 1989); Jean-Claude David, "À la querelle de l'inoculation en 1763: Trois lettres inédites de Suard et du Chevalier d'Eon," Dix–huitième siècle, 17 (1985), 271–84; Maxine Van de Wetering, "A reconsideration of the inoculation controversy," New England quarterly, 58 (1985), 46–67; Jean-François de Raymond, Querelle de l'inoculation, ou, Préhistoire de la vaccination (Paris: Vrin, 1982); Antoinette S. Emch-Dériaz, "L'inoculation justifiée—or was it?" Eighteenth century life, 7:2 (1982), 65–72. Patricia Cline Cohen, A calculating people: The spread of numeracy in early America (Chicago: University of Chicago Press, 1982) also addresses the issue of smallpox statistics and risks.

Such arguments could still carry weight even when the numbers were soft or when measurement was out of the question, as in discussions of moral arithmetic, meandering rivers, or thermometers for female emotional response, as calibrated from modesty through impudence. Here it is necessary to attend to what quantification promised: useful comparisons whatever the scale, informative models without measurement, precision (clarity, distinctness, intelligibility) rather than a close fit with the real world.^[17]

Although moral barometers scarcely belong to the realm of exact science, comparisons of soft and hard quantification may prove instructive. In particular, it is worthwhile measuring the play of the quantifying spirit in the 18th century against conspicuous accomplishments in the mathematization of science in the 17th century and the successes of mathematical physics in the late 18th and early 19th centuries. The articles in Nature mathematized explore examples of 17th-century exact science that enlightened thinkers subsequently found so persuasive. A recent issue of Revue d'histoire des sciences investigates the "conquest of new territories" by mathematical science between 1780 and 1830. And Jean Dhombres links the achievements of mathématisation with the nature of the French scientific community in the half-century between 1775 and 1825 in another recent article.^[18]

[17] Daston, "The quantification of probability" (unpublished paper, History of Science Society meeting, 1989) and Classical probability in the Enlightenment (note 15); Garland P. Brooks and Sergei K. Aalto, "The rise and fall of moral algebra: Francis Hutcheson and the mathematization of psychology," Journal of the history of the behavioral sciences, 17 (1981), 343–56; Robin E. Rider, Mathematics in the Enlightenment: A study of algebra, 1685–1800 (Ph.D. dissertation, University of California, Berkeley, 1980; DAI 42/01A, 351), esp. chap. 9; Marguerite Carozzi, "From the concept of salient and reentrant angles by Louis Bourguet to Nicolas Desmarest's description of meandering rivers," Archives des sciences (Geneva), 39 (1986), 25–51; Terry Castle, "The female thermometer," Representations, 17 (1987), 1–27. Cf. Mark H. Waymack, Moral philosophy and Newtonianism in the Scottish Enlightenment: A study of the moral philosophies of Gershom Carmichael, Francis Hutcheson, David Hume, and Adam Smith (Ph.D. dissertation, Johns Hopkins, 1986; DAI 48/02A, 413), and a late 17th-century example in Paul McReynolds and Klaus Ludwig, "Christian Thomasius and the origin of psychological rating scales," Isis, 75 (1984), 546–53.

[18] William R. Shea, ed., Nature mathematized: Historical and philosophical case studies in classical modern natural philosophy (Dordrecht: D. Reidel, 1983); Revue d'histoire des sciences, 42:1 (1989), special issue "La mathématisation 1780–1830," quotation on 3; Jean Dhombres, "Mathématisation et communauté scientifique française (1775–1825)," Archives internationales d'histoire des sciences, 36 (1986), 249–93. The papers delivered at the international workshop, "The quantification of scientific concepts in their social context" (Tel Aviv, 1986) also speak to issues of quantification from the 17th century through the late 20th century.