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
[6] 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, without, however, paying much attention to his ideas. He has been called "the master of the Enlightenment in Germany," and even outside Germany; Diderot sang Wolff's praises in his Encyclopédie . Paul Hazard made Wolff "the intellectual leader of Germany" and a general-purpose sage admired by all nations. Lewis White Beck portrays Wolff as a rationalist in the Enlightenment spirit: "Wolff is the best German representative of a general movement of thought towards deism, utilitarianism and free thought that was sweeping over Europe as a whole."[7]
These characterizations of Wolff and his influence claim both too much and too little. Too much, because terms like "rationalism" and "mathematics" did not necessarily imply Enlightenment, nor did Wolff's philosophy. It was the form of mathematics that interested him, its way of pursuing an argument to its proof. The characterizations claim too little because the association of Wolff's brand of rationalization with the Enlightenment neglects the vast effort at systematization of all knowledge inherited from Leibniz and the 17th century.
[7] Paul Hazard, European thought in the eighteenth century (London: Hollis, 1954), 40; Lewis White Beck, Early German philosophy: Kant and his predecessors (Cambridge, Mass.: Belknap Press, 1969), 256–76. Cf. Tore Frängsmyr, "Christian Wolff's mathematical method and its impact on the eighteenth century," Journal of the history of ideas , 36 (1975), 863–8.
Wolff turned to the connection between mathematics and philosophy early in his career. He obtained his doctorate in 1703 with a dissertation on ethics based on mathematical foundations. He soon came into contact with Leibniz, who nominated him for election to the Academy of Sciences in Berlin. In 1707 Wolff became professor of mathematics at Halle and later assumed the chair of philosophy. In Wolff's work the one subject cannot be distinguished from the other. As a mathematician he hardly made an original contribution, but his diligence yielded bulky volumes summarizing the contemporary state of knowledge—for instance, his Anfangsgründe aller mathematischen Wissenschaften (6 vols., 1710) and Elementa matheseos universae (5 vols., 1713–5).
Wolff announced his own particular specialty—the application of mathematics to philosophy—in his Ratio praelectionum Wolfianarum in mathesin et philosophiam universam (1718). This line of work culminated in a book in German with the monumental title Vernünfftige Gedancken von Gott, der Welt und der Seele des Menschen, auch allen Dingen überhaupt (1720). The book, usually known as his "German metaphysics," sets out Wolff's philosophy virtually in its entirety; it brought him wider renown and prefigured a whole literary genre during the 18th century. Wolff himself published a series of Vernünfftige Gedancken on various topics; elsewhere philosophers followed his lead and published "rational thoughts" on one subject after another.[8]
Wolff's stature as a liberal theologian has also contributed to his reputation as a rationalist philosopher of the Enlightenment. In Halle, the dominant theology was the conservative strain of Pietism developed by August Hermann Francke, which sought renewal within the Church. Competition came from influential orthodox
[8] Hans Werner Arndt, "Rationalismus und Empirismus in der Erkenntnislehre," in Werner Schneider, ed., Christian Wolff, 1679–1754: Interpretationen zur seiner Philosophie und deren Wirkung (Hamburg: F. Meiner, 1983), 31–47. The same collection contains six articles about Wolff's influence, among them Notker Hammerstein, "Christian Wolff und die Universitäten: Zur Wirkungsgeschichte des Wolffinanismus im 18. Jahrhundert," 266–77. See also Beck's chapter "A generation of epigoni," in Early German philosophy , 276–305, and Tore Frängsmyr, Wolffianismens genombrott i Uppsala (Universitet; Stockholm: Almqvist & Wiksell, 1972), with an English summary: "The emergence of Wolffianism at Uppsala University, 1720–1760."
pastors and from a group of "transitional theologians," who attempted the feat of mixing orthodoxy, Pietism, and rationalism.
Wolff found himself at odds with this eclectic combination. In 1721 he delivered a formal address on the teaching of Confucius, Oratio de sinarum philosophia practica , which emphasized its strict morality.[9] By studying human nature, but without invoking divine revelation, Confucius had attained a lofty moral position. From this Wolff argued that morality could be comprehended by reason alone. Here he linked up with the deism that had been spreading steadily since the mid-17th century and that often saw in Confucianism the confirmation of its ideas. Wolff's address contained nothing new or sensational, but under the circumstances it was taken as a challenge. The Pietists retaliated by accusing Wolff of atheism; condemnatory sermons echoed in the churches and protests ascended to higher levels; the highly regarded theologian Johann Franz Buddeus, orthodox but favorably disposed to the Pietists, wrote an indictment of Wolff's views. The campaign finally succeeded in 1723, when Frederik Wilhelm I banished Wolff from Halle. Wolff retreated to Marburg, a little university town in the landgraviate of Hessen, an environment more conducive to his reputation. Within a few years he was being hailed as the greatest mathematician and philosopher of his age; students on their grand tours included a stop in Marburg to attend his lectures; scientific academies and universities throughout Europe wooed him. He began to write in Latin, which permitted access to a wider international audience. The 1730s saw the appearance of the great classical works, Philosophia prima sive ontologia (1730), Cosmologia generalis (1731), Psychologia empirica (1732), Psychologia rationalis (1734), Theologia naturalis (2 vols., 1736–7), and Philosophia practica universalis (2 vols., 1738–9). Again, they contained little new, but developed and refined Wolff's ideas in different philosophical disciplines and generated popularity, renown, and followers for their author.[10]
[9] Wolff's Oratio de sinarum philosophia is now published in a Latin-German parallel edition, Rede über die praktische Philosophie der Chinesen , ed. Michael Albrecht (Hamburg: Meiner, 1985), with a 100-page introduction. See also Beck, Early German philosophy , 258ff.
[10] Anton Bissinger, Die Struktur der Gotteserkenntnis (Bonn: H. Bouvier, 1970).
Wolff's reputation as a rationalist and freethinker derived more from his banishment than from his writings. His position was enhanced when Frederick the Great ascended the throne of Prussia and decreed that salvation was everyone's responsibility. One of Frederick's first acts was to recall Wolff to Halle and to shower him with honors. Wolff assumed positions as professor of law, vice-chancellor of the university, privy councillor, and, in three years, chancellor. In 1745 he was ennobled as baron von Wolff. The summons from Frederick the Great, prince of Enlightenment, confirmed Wolff's status as an Enlightenment philosopher.
The Mathematical Method
The characteristic aspect of Wolff's philosophical teaching was its strictly logical construction. He had a manic capacity for arranging and systematizing everything, step by step, clearly and paradigmatically, accurately and in detail. He worked from the principles of contradiction (principium contradictionis ) and of sufficient reason (principium rationis sufficientis ). He regarded the principle of contradiction as the first law of philosophy from which all other propositions could be derived. With the principle one could decide whether something was possible; that is, everything that might be held to have sufficient reason. Philosophy was the science of the possible, with the task of showing how and why things are possible.[11]
In working out his science, the philosopher had to observe certain rules. No principles could be employed unless adequately proved, and no new ones allowed unless derived from proven principles. No departure could be made from the meaning that words had generally acquired, and if new words or concepts were required, they had to be accurately defined. Intrinsically different objects and phenomena had to be given different names. Starting with axioms, clear definitions, and distinctions, deductive methods would link truths with one another and thus reach irrefutable conclusions. In this way results
[11] Vernünfftige Gedancken von den Kräfften des menschlichen Verstandes (Halle: Renger, 1723; 7th ed., 1733), 1. Cf. Cogitationes rationales (Frankfurt and Leipzig: Renger, 1730), 1.
obtained in philosophy would be as reliable as those in mathematics. In none of this did Wolff go beyond Leibniz, or, for that matter, Aristotle, Thomas Aquinas (whose influence he acknowledged), Descartes, Spinoza, or Tschirnhausen, whose Medicina mentis he had studied in detail. The mathematical method nevertheless became known as Wolffian, because Wolff systematized it as never before. In his hands it became an all-purpose means for establishing truth in any sphere.[12]
Wolff's epistemology is quite simple. Human knowledge outside Christian revelation can be acquired in three ways: by experience (historical knowledge), by reason (mathematical knowledge), or by a combination of the two (philosophical knowledge). The last of these three methods is preferable; the other two have value only to the extent that they can be of use to philosophy. Our senses awaken our most general concepts, which are innate in our consciousness, and provide many fresh ideas; reason clarifies them and puts them into context. Thus every philosophical discipline has both empirical and rational components. For Wolff, philosophy came to mean the same thing as science, as the German term for philosophy, "Welt-Weis-sheit," suggests.
Mathematics is not a part of Wolff's philosophy. Instead, it serves as an instrument of knowledge in its own right—a method, a means rather than an end. Mathematics, in both form and inherent logic, provides a model for all areas of human knowledge. From this point of view, the mathematical method was identified with the philosophical one, and assumed a central role in the scheme of all Wolffian philosophers, even if they did not all see mathematics in the same subtle light as Wolff did. For the imitators, in fact, mathematics at times meant little more than computation.[13]
Wolff held dear the idea of a system of knowledge. Knowledge was not merely a sudden insight or an idea, but arose from step-by-step deduction leading to reliable conclusions. The complex, reliable system therefore became an emblem of Wolff's entire philosophy—
[12] Philosophia rationalis sive Logica , 2d ed. (Frankfurt and Leipzig: Renger, 1732), 53–71; the "Discursus preliminaris" is the best explanation of Wolff's goal.
[13] Ibid., 28–52, "De partibus philosophiae."
both theoretical (logic, metaphysics, psychology, natural theology, physics, and technology) and practical (law, ethics, economics, and politics).[14]
For Wolff, mathematics was the method and philosophy the content . This distinction is essential to an appreciation of his philosophy and its place in 18th-century thought.
For and Against Enlightenment
Wolff's working life falls into two periods. In the first he was active at Halle, wrote in his native German, formulated a more popular philosophy, and spoke so freely on religious matters that he was accused of atheism and banished. In the second period he lived in Marburg, wrote books in Latin, put forward a more theoretical philosophy explicitly addressed to the world of learning, and appeared in religious matters as an orthodox and unrelenting apologist. The watershed came somewhere around 1730. In the earlier phase he followed the precepts of the Enlightenment; in the latter he opposed them.
Wolff's German books aimed at a larger public are characteristic of his enlightened period. They have a pronounced practical and utilitarian tone and allot philosophy a "liberating" role, fully comparable to later manifestos of the French Enlightenment. Good examples are plentiful in his Vernünfftige Gedancken von der Menschen Thun und Lassen, zu Beförderung ihrer Glückseligkeit (1720). A critical indication of his popular, liberal position was his vacillation between physicotheology and teleology, two doctrines not easily distinguished and therefore often confused. Physicotheology rested on the ingenious organization of the natural world in general, but it often singled out particular features in nature as evidence of a creator behind the order. This search for an all-ordering God behind the exquisite subtlety of nature could justify, and even motivate, all scientific research. Where order served as a fundamental principle in physi-
[14] Carl Günther Ludovici, Kurtzer Entwurff einer vollständiger Historie der Wolffischen Philosophie (Leipzig: J.G. Löwe, 1736), 113ff. Cf. Bissinger, Die Struktur , 49f.
cotheology, so intention emerged as essential in teleology. If everything fulfills a definite purpose, there must be at least an implicit ordering principle—a God who intended the order. Many physicotheologists came to confuse proofs based on general order and those based on intent, and to subsume teleology under physicotheology. In either case, a "popular" proof of the existence of a divine creator was secured.
To see Wolff as a great representative of physicotheology, however, is to overplay his hand. Wolff attacked both the physicotheological and teleological approaches.[15] He recognized the legitimacy of demonstrating divine intent in nature, but demanded a prior proof of God's existence and of the creation of the world as a free divine act. Wolff's method required that the theoretical foundation be established first. Yet a few years later, Wolff appeared as a full-fledged physicotheologist in his great work Vernünfftige Gedancken von der Absichten der natürlichen Dinge (1723). Had his views suddenly changed? No, he had distinguished between two sets of readers—academic and popular. Wolff's major works in Latin do not feature physicotheology. In a foreword to a translation of Nieuwentyt's well-known book on physicotheology (1731), he referred to his own work in German and underlined that it was intended for readers who did not speak the languages of the erudite. Whatever he said, in practice he inferred God's perfection from the usual inventory of the natural scientist. He described the cosmos and all its bodies, the sun and the fixed stars, the earth and the planets; he dealt with air and winds, different kinds of precipitation, rainbows, lightning, and thunder. The quantitative philosopher will want to know that his evidence includes "the number of heavenly bodies."[16]
In sum, although Wolff demanded strict standards of logical proof in his mathematical method, he allowed himself to break the rules when addressing an unlearned audience. The end justified the means,
[15] Ratio praelectionum Wolfianarum in mathesin et philosophiam universam (Halle: Renger, 1718), 153-8.
[16] Wolff's preface reprinted in Gesammelte kleine philosophische Schrifften (Halle: Renger, 1736), 515f. Cf. Bissinger, Die Struktur , 232f.
for the religious objective was all-important. He made an even more significant adjustment in his major work Theologia naturalis , an extended exercise in apologetics, rapidly becoming his specialty. He devoted more than 350 pages to demonstrating the false steps and absurd notions of atheism.[17] He did not confine his attack to unbelievers but also took up cudgels against every conceivable kind of philosophical freethinker: atheists, fatalists, deists, naturalists, anthropomorphists, materialists, paganists, Manichæans, Spinozists, and Epicureans. Just as he had previously used the mathematical method to lend positive support to philosophy or theology, he now used it to expose and exclude those who were not orthodox. Fourteen years earlier he had been banished and accused of atheism; now Wolff attacked those who adopted the viewpoint he had then espoused. Yet he held fast throughout these sea-changes to his mathematical method and philosophical rationalism.