Uppsala studies in history of science ; 7. 1990 VIII, 411 S. Hardcover Berkeley, Univ. of California Press,

The Quantifying Spirit in the Eighteenth Century

By Tore Frangsmyr, J. L. Heilbron, and Robin E. Rider, editors

University of California Press

Copyright © 1990 Tore Frangsmyr, J. L. Heilbron, and Robin E. Rider, editors
All right reserved.
ISBN: 0520070224
1
The Mathematical Philosophy
By Tore Frängsmyr

There are two distinct opinions regarding the status of science in the 18th century. One dismisses the period as an uninteresting interval between the breakthroughs of the 17th century and the expanding industrialism of the 19th. The opposing view holds that the 18th century was the time when all the important work of the previous century bore fruit.

The dismissers argue that nothing really new emerged in the 18th century. "By many historians the century has been deplored for allegedly producing science that was boring, unoriginal, lacking in rigour and overspeculative." It has been castigated as "comparatively undistinguished in its science"; if its science is included in its reputation, the siècle des lumières cannot be freed from "an element of dullness."1

In direct opposition to these nay-sayers, other historians have identified much of the intellectual life of the 18th century with the fostering of its heritage from the scientific revolution. The Enlightenment thus climaxes the development of early modern science.2 The most recent general assessment of the role of science in the Enlightenment gives particular weight to the century's efforts to consolidate and organize what it had received. "The creation of the new scientific disciplines was probably the most important contribution of the Enlightenment to the modernization of science, and one that we might easily overlook. It marks the Enlightenment as a period of

G.S. Rousseau and Roy Porter, eds. The ferment of knowledge: Studies in the historiography of eighteenth-century science (Cambridge: Cambridge University Press, 1980), introduction.

Preserved Smith, A history of modern culture , 2 vols. (New York: H. Holt and Co., 1930–4), 33–5.

transition between the old and the new."3 That careful and informed students of the 18th century have reached diametrically opposed evaluations of its science is largely a consequence of their differing ideas about what counts as science. In this volume we sidestep the difficulty by restricting our attention to the working out of a particular method, or, as it might better be called in many instances, of an appeal to a slogan. That slogan, as Galileo formulated it, holds that "the book of nature is written in the language of mathematics."4

In the 18th century, this proposition inspired the work of the most productive mathematicians and underlay the program of the most ambitious philosophers, who proposed to extend it beyond the book of nature to the books of man—that is, to all exercises of human reason.5 The languages of reason and nature were thereby to agree. We see two phases in the 18th-century elaboration of this proposition. Until about 1760, "mathematics" was applied to the general exercise of reason (as opposed to mathematics itself and the quantified parts of astronomy and physics) more as a symbol and slogan than as a useful tool. In this first phase the philosophy of Leibniz's epigone, Christian Wolff, is exemplary. In the last third of the century, however, the equation of reason with mathematics inspired instrumentalist and quantitative approaches to a wide range of problems in various sciences, arts, and technologies. We take the activities of this quantifying spirit to have been progressive, in the sense that under its inspiration the achievements of the scientific revolution were extended and reinterpreted in a way that made possible rapid advance in mathematics, physical sciences, and statistics (conceived as the sciences of the state) in the early 19th century.

In what follows, Wolff's method is seen as representative of the process by which reason was "naturalized" during the first half of the 18th century. The purpose is to provide both an introduction and a contrast to the applications of the quantifying spirit later in the century that form the subject matter of the other essays in this volume.

Thomas L. Hankins, Science and the Enlightenment (Cambridge: Cambridge University Press, 1985), 5.

Smith, A history of modern culture .

Ibid., 118.

Universal Mathematics

Leibniz wanted not only to see the world as a machine with a "static structure of matter in geometrical and mechanical relation"; he also wanted to give exact mathematical expression to all the processes and changes that took place in the world. Through the infinitesimal calculus he found a constant law that remained valid for an infinite number of processes and changes. The elements constituting the universe, nature, and human life were not particles of matter, but forces and motions. Each element or individual substance—Leibniz called them "monads"—was complete in itself, a microworld or a mirror of the universe, and yet intimately related to all other individuals in a system of pre-established harmony. The mathematical system came by its harmony naturally.

Given this structure of the world it was natural for Leibniz to take another step: to organize human knowledge in a mathematical pattern. Drawing both on the Lullian tradition that sought a universal language and on his own mathematical work, Leibniz wanted to create a mathesis universalis or ars characteristica , which would represent, combine, and produce all possible knowledge. This language would serve not only as a philosophical method but also as the key to a true encyclopedia. In the mathesis universalis , each human concept or idea corresponded to a different symbol or combination of symbols. By combining these symbols according to mathematically defined rules, Wolff's method could produce long lists of new truths and confirm old ones. The new language became for Leibniz both a means of communication and a new kind of logic, a way to formulate statements and an instrument of reason.6

The most influential philosopher in the Leibnizian tradition was Christian Wolff. Wolff was not an original thinker. Instead, he took the foundation of his system from his teacher Leibniz, systematized it, and put it within the grasp of any educated person. Because of his

Louis Couturat and L. Leau, Histoire de la langue universelle (Paris: Librairie Hachette, 1903); Louis Couturat, La logique de Leibniz d'après des documents inédits (Paris: F. Alcan, 1901), esp. chaps. 2–4; cf. C.I. Lewis and C.H. Langford, Symbolic logic (New York: The Century Company, 1932), 5ff.

firm insistence on the rationalism that was characteristic of his "mathematical method," Wolff came to be regarded as a philosopher of the Enlightenment. Mathematics held symbolic value as the driving force behind the progress of science, and also the progress of reason and free thought. As Newton had given the universe a mathematical structure, so Wolff aimed to subsume human and society within a vast mathematical system. He pushed his mathematical method into every possible area: philosophy and science, theology and ethics, politics and public finance.

Wolff's "Rational Thoughts"

Many historians of philosophy have described Wolff as one of the most influential philosophers of his time,...