Weighing in the Balance

Which side of Wolff attracted his contemporaries—the mathematical-rationalist or the teleological-apologetic? The answer must be that many accepted both sides, viewing them as two parts of the same entity. The mathematical method tied them together, and became the guiding principle for Wolff's pupils, even for those most inclined to apologetics.^[18]

One of the first of these pupils was Ludwig Philipp Thümmig, appointed professor in Kassel on the master's recommendation. His extensive Institutiones philosophiae Wolfianae (2 vols., 1725–6) differed little from Wolff's own account, and functioned as an authoritative source for later Wolffians. Another pupil, regarded as even more significant, was Georg Bernhard Bilfinger, professor of philosophy first at Tübingen, then at St. Petersburg, and again at Tübingen. His

Dilucidationes philosophiae de Deo, anima humana, mundo et generalibus rerum affectionibus (1725) followed up, in title and contents, Wolff's Vernünfftige Gedancken von Gott, der Welt und der Seele des Menschen . Bilfinger emphasized the twin foundation stones of reason and experience, and stood ready to point out correspondences between natural science and Christian faith. Alexander Gottlieb Baumgarten, first in Halle, then at Frankfurt, wished above all to apply Wolff's philosophy to aesthetics. His well-balanced Metaphysics (1739), extremely faithful to Wolffian systematics, amounted to a reference book or compendium of Wolffian doctrine. In Leipzig, Johann Christian Gottsched and Carl Günther Ludovici wrote historical works on Wolff but were not themselves leading philosophers. Israel Theophil Canz at Tübingen did much to inject the doctrine into theology, as did Jacob Carpov at Jena, who sought to prove divine revelation using Wolff's teleological method. Important expositions of the mathematical method were also offered by Friedrich Christian Baumeister at Gölitz and Georg Heinrich Ribov at Göttingen.

Outside Germany Wolffianism found adherents in England, France, the Netherlands, Switzerland, and Scandinavia. In Denmark, Wolff's doctrines exerted influence through a number of mathematicians and philosophers: Christian Hee, who stayed for a time with Wolff at Marburg; Friedrich Christian Eilschow; and, above all, Jens Kraft, eminent as both a mathematician and a philosopher, who published a series of textbooks in imitation of Wolff. In Sweden, too, mathematicians introduced Wolff's ideas, which spread to the Swedish university at Åbo (Turku) in Finland.^[19]

In Sweden

The tendency of Wolff's disciples to tread confidently in their master's footsteps, to accept both his philosophical and his theological views, and to tie them together via the mathematical method, was muted in Sweden by resistance to the casual combination of philosophy and theology. Sweden's true introduction to Wolff came through

the efforts of the mathematicians Anders Celsius and Samuel Klingenstierna, whose reputation at Uppsala University recommended their opinions to many students. In a manual of arithmetic (1727), Celsius spoke warmly of the existence of the mathematical method and also of its importance to other disciplines.^[20] By the following year, in a pro gradu dissertation on the existence of the soul or the intelligence, Celsius completely embraced the philosophy of Wolff. He praised not only Wolff's method but also followed the master in setting out his dissertation in traditional Euclidean form, with short propositions under such headings as axioma, theorema, definitio, observatio, demonstratio , and scholion . The dissertation argues that the soul can be proved to exist by means of Wolff's philosophical laws, and Wolff himself is called "the greatest philosopher of our time," philosophus nostra aetate summus .^[21]

Several theses reminiscent of Celsius' approach appeared over the next few years, all of them loud in praise of the mathematical method and bearing the imprint of the mathematical form favored by Wolff. Early in June 1729, the brothers Erik, Nils, and Johan Gottschalk Wallerius and their close friend Olof Hammaræus performed as respondents to four Wolffian dissertations. Presented first pro exercitio , two years later all four dissertations were defended pro gradu , under Celsius and Klingenstierna as tutors. Several of the dissertations describe the mathematical method without employing it; one stresses that certain philosophical knowledge is impossible without it. Jacob Friedrich Müller, professor of philosophy at Giessen, was quoted in support of this statement, although, unknown to the author, Müller had just defected to the camp of Wolff's denigrators.^[22]

Other dissertations under Celsius follow the same pattern. One deals with the subject of "incomprehensible books," which provided

the opportunity to laud Wolff as an example of lucidity and intelligibility.^[23] Evidence suggests that Celsius was behind the most detailed presentation of Wolff's philosophy, a dissertation in two parts (1731–2) on the subject of "how to attain worldly happiness through philosophy." The subject may appear novel, but the theme is familiar. The philosophy that can promote profit and happiness is contained in logic and mathematics. Hence the mathematical method is superior to earlier instruments and Wolff is the greatest of philosophers, outshining lesser lights like Plato, Aristotle, and Descartes. With Wolff's method, the author "brushes aside the weapons of atheism and defends the truths of the Christian religion." Ad pleniorem scientiam , the dissertation demonstrates that mathematics and physics are of fundamental importance to all other sciences, technology and mechanics, medicine, law, economics, and military subjects such as fortification and pyrotechnics.^[24]

Samuel Klingenstierna had already earned a name for himself as a mathematical genius when he set off to study abroad in 1727. He went first to Marburg to hear the much admired Wolff. It is recorded that the pupil much impressed the teacher. When the chair of mathematics at Uppsala became vacant, Klingenstierna applied for it. Because Marburg was within the native state of King Fredrik I of Sweden, Wolff had access to the king and recommended Klingenstierna in the strongest terms. Appointed to the post in 1728, Klingenstierna did not take up his professorship until 1731, when he returned to Sweden with newly purchased books and fresh reports on the fashionable new philosophy. His were popular lectures, and students sought him as tutor for their doctoral theses. These theses are filled with quite simple Wolffian propositions about the excellence of the mathematical method or the role of contingency in the creation of the world, and frequently make reference to Wolff and Bilfinger. Mathematics thus linked up with philosophy, notably in Klingenstierna's seminars in philosophiam naturalem .^[25]

But enthusiasm for Wolff and the use of mathematics in philosophy went too far. Alert theologians, worried by the excessive spread of rationalism, castigated Wolff as "heathen and atheistic." In 1732 the chancellor of Uppsala, Gustaf Cronhielm, warned professors against dealing too casually with the new philosophy inspired by Wolff. The professors responded with promises to be careful and to protect their young students. Two years later the tone of admonition grew sharper. The chancellor decreed that professors should not preside at theses outside their own disciplines, a rebuke directed particularly at the professors of mathematics, who had been so ready to interpret the Wolffian philosophy. A year later, students were required to give a declaration of faith when enrolling at the university, to guard the purity of the doctrine. Such censorship and official criticism encouraged attacks on Wolff. His opponents asserted that mathematics and philosophy did not belong among the fundamental sciences; they saw all questions as ultimately teleological in nature. Philosophy, they insisted, should stick to its time-honored role as the handmaiden of faith.^[26]

The situation soon changed radically. Cronhielm was succeeded as chancellor by Gustaf Bonde, known for his deep interest in mysticism, alchemy, and Platonic mathematics. An admirer of physicotheology and of Wolff, he later published three volumes of "reflections on the wonders of God in nature." On a visit to Uppsala University in 1738, Bonde stressed the desirability of teaching the younger generation theologia naturalis as a timely defense against "atheists and indifferentists." The new chancellor thus recommended what the old one had forbidden. Bonde went even further when he engineered an offer to Wolff of the most highly regarded professorship in the university (which Wolff declined). Bonde's permissiveness sanctioned latent interests among the faculty. Petrus Ullén, professor of philosophy, became the first important figure in this new phase. By the time of his death in 1747, he had presided over a hundred theses, a third of which were Wolffian through and through. Ullén was no original

thinker. He praised mathematics for its ability to clarify and present problems in easily grasped diagrams and figures, and he insisted on the importance of the Wolffian philosophy to theology. He vehemently attacked all tendencies toward deism or "indifferentism"; true to the later Wolff, he used rationalism as a defense of orthodoxy and against the ideas of the Enlightenment.^[27]

An even louder champion of Wolffianism was Nils Wallerius, who started out as a mathematician and physicist, continued as a philosopher, and ended up as a theologian. He succeeded Ullén as professor of philosophy in 1746. Within the compass of philosophy he included logic, metaphysics, psychology, and natural theology, all slavishly arranged in accordance with Wolff's system. The mathematical method was fundamental in all philosophy, but mathematics must yield to theology, lest it lead to materialism and atheism. Wallerius shared the concern of both philosophers and theologians over theologia polemica —the struggle against Enlightenment philosophy. In 1755 Wallerius received a new chair in theology devoted to uncovering and combatting heretics. The new professor was to repudiate all freethinkers, "such as atheists, naturalists, deists, anti-scripturalists, indifferentists and other unbelievers."^[28] Wallerius warmed to the task: Moravian Brethren, Socinians, pantheists, and mystics, too—here he named Jakob Böhme, Paracelsus, Robert Fludd, and Johann Conrad Dippel—fell under his flail. In an essay on the repulsiveness and wickedness of materialism, Wallerius ranted at the ancient atomists Democritus, Epicurus, and Lucretius and their modern successors Thomas Hobbes and Pierre Bayle. "O stupida ingenia, sive mente ac ratione ," you are so blind that you cannot imagine anything beyond the bounds of the material.^[29] In 1756, Julien Offray de La Mettrie, the leading contemporary materialist, came in for particularly severe criticism.^[30] Wallerius decried the deists from Locke to Hume as

"naturalists"—Wallerius' favorite epithet for his opponents—and Voltaire as "the greatest fraud of the day."^[31]

Wallerius' guiding ambition was to reconcile mathematics, philosophy, and theology. At hand were all the necessary tools: a professional graps of mathematics, philosophy, and theology; a passion for system; and Wolff's method. His eminent elogist in the Royal Swedish Academy of Sciences, Torbern Bergman, showed restrained appreciation of Wallerius' contribution, and a like opinion was expressed in another contemporary biography: "Had he lived fifty years earlier and in a more scholastic era, his memory would have been even more illustrious."^[32]

By Kant

Wolff's use of mathematics usually made the best impression on those who knew the least mathematics. During the late 1740s, in a celebrated dispute between the supporters of Newton and those of Wolff, Pierre Louis Moreau de Maupertuis was the main adversary of the Wolffians. The most telling attack on Wolff came from Kant, however, who as usual went right to the core and challenged the mathematical method itself.

The Berlin Academy had posed the question of whether metaphysical truth could be equated with mathematical truth and, if it could not, what sort of truth it then was. Kant replied with the treatise, Untersuchung über die Deutlichkeit der Gründsätze der natürlichen Theologie und der Moral (1762, published in 1764), which struck a decisive blow to Wolff's philosophical teachings.^[33]

Kant had been influenced by Wolff's philosophy, but had never

followed it slavishly. The treatise of 1762 marked his rejection of the mathematical ideal in philosophy. In it Kant draws his well-known distinction between analytic and synthetic propositions, and concludes that metaphysics is not synthetic like mathematics but rather analytic. The synthetic structures of mathematics cannot be transferred to philosophy and its "mathematical method," for philosophy, unlike mathematics, does not have at its disposal definitions and axioms from which to proceed methodically. Application of the mathematical method to the field of philosophy had thus given rise to errors and mistakes: no dogma in philosophy could be likened to the definitions and axioms of mathematics.

Kant's criticism swept away the very foundations of Wolff's influence. Wolff's mathematical method depended on the possibility of applying procedures of mathematical proof to all philosophical and theological questions. Now Kant argued that the basic structures of mathematics and philosophy were different. Wolff's system crumbled.^[34]

Several conclusions emerge. Wolffian thinking became a fashionable philosophy in the first half of the 18th century, and its exponents and detractors both saw the mathematical method as the essential element of his doctrine. It is important to distinguish between form and content in our analysis of the Wolffian mathematical method, and to recognize that Wolff's philosophy fulfilled different functions in different situations. While "rationalism" and "mathematical method" were popular rhetorical flourishes in the 18th century, they also stood for a well-defined means of attaining certain intellectual objectives. Both friends and enemies of the Enlightenment appropriated that method, since mathematics as a method of proof promised results in all areas of human knowledge. That it collapsed so readily under Kant's attack reflected that Wolff's mathematical method had already proved inadequate: it failed to provide tools for revamping critical philosophy, or for creating instrumentalist science, or for solving practical problems facing the bureaucratic states of the late 18th century. The form and content of mathematics itself, however, would continue to speak to these needs.