of how the human mind could influence and direct actions of the physical body, even though mind and body were two different kinds of substance: the mind was generally thought to be an immaterial being without spatial dimensions; the body was material and extended. It was difficult to imagine how the former could be the cause of movement in the latter. Leibniz had concluded that mind and body did not interact with each other causally at all. Each of the two followed its own internal and necessary laws of development. They only appeared to influence each other because God had taken care that the
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changes in both were closely coordinated, like the movements of two synchronized clocks. This idea of a preestablished harmony, however, contradicted a conventional belief in the freedom of the human will. For if mind and body each followed its own necessary laws of change, humans appeared to have no power of acting differently from the way they did. Lange, for example, believed that the human will, in order to be free, had to be “indifferent” to several possible courses of action and capable of choosing between them. Wolff replied that the acts of human volition could never be free in the sense of being indifferent to various courses of action. Every act of the human will required a sufficient reason. Unless the will was determined by such a sufficient reason, the will would never arrive at a decision. The will, Wolff added, was nevertheless free, because its choices were not determined by external, physical causes, but by its own, internal reasons. It was therefore “free” in the sense of acting according to its own impulses.20
Wolff’s critics replied that such a state of affairs would represent no genuine freedom at all. Humans had to have a capacity for choice between different actions, and the decisions of the will had to influence the actions of the body directly. Lange argued that this influence occurred by means of a “physical influx” (influxus physicus), which was probably the most common theory used to describe the relationship between mind and body. Wolff’s theory, Lange claimed, was just a variation on the philosophical “fatalism” associated with the thought of the Dutch Jewish philosopher Baruch Spinoza, which made it impossible to hold humans morally accountable for their actions. It was on the
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grounds of Wolff’s “fatalistic” philosophical teachings that Lange finally persuaded King Frederick William I of Prussia to force Wolff into exile and forbid him on pain of death from returning. According to Wolff, the “soldier-king,” as he was often known, was finally convinced by Lange’s argument that it would no longer be possible to punish army deserters if Wolff’s theory were true.21 In November 1723, as soon as he had received the king’s order to leave, Wolff departed for the University of Marburg, which had already offered him a professorial chair some months before. Toward the end of his reign, Frederick William acknowledged that Wolff’s doctrines were probably not as harmful as he had been led to believe, and in 1739 gave Wolff permission to return and take up a chair at the University of Frankfurt an der Oder. Wolff declined the offer, but when Frederick William’s son and successor Frederick II, later known as “the Great,” invited him to return to Halle, he accepted. Wolff arrived in December 1740, eventually rose to the office of chancellor at the university, was made a baron of the Holy Roman Empire, and remained in Halle until his death in 1754.
The “Scientific Method” in Philosophy
Throughout his career Wolff followed what he called the “scientific method.” His commitment to it is reflected in the titles of many of his main works. In 1728, for example, Wolff’s Rational Philosophy or Logic, according to the Scientific Method appeared.22 In 1730 he published his Ontology, which was, again, “according to the scientific method.”23 There followed several more works that were all “according to the scientific method”: Empirical Psychology, 1732;24 Rational Psychology, 1734;25 Natural Theology, 1736;26 Universal Practical Philosophy, published between
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1738 and 1739;27 The Law of Nature, which appeared between 1740 and 1748;28 and Moral Philosophy or Ethics (1750–53), to name just a few.29 The model for this “scientific method” was mathematical reasoning, which, according to Wolff, was founded on clear and distinct notions, and in which each step of the argument followed necessarily from what went before. But the usefulness of the “scientific method” was not limited to mathematics; it extended to improving philosophical argument.
Many other thinkers similarly believed that philosophy might benefit from mathematical forms of reasoning. An important part in encouraging this belief was played by Descartes’s mathematical discoveries in the first half of the seventeenth century, in particular his successful application of algebraic notation to the solution of geometrical problems. One main advantage of the use of algebraic notation, as Descartes and others argued, was that progression from one step in the solution of a geometrical problem to the next was always clear and perspicuous. Descartes distinguished this “modern” method from the approach of the ancient mathematicians such as Euclid or Pappus, who had relied on geometrical constructions rather than algebraic formulae to solve problems in geometry. The approach of these ancients meant that each step in the solution of a problem was always capable of being represented visually. This made it immediately evident how the solution was applicable to the relevant geometrical problem. It was less clear, however, how the principles on which this answer was based were discovered in the first place. The approach of the ancients seemed to depend on intuition and a process of trial and error, not a method that could be learned and then applied to other cases. Descartes argued that the system of algebraic notation, which he used and which had first been applied by the French mathematician François Viète (1540–1603) to equations with more than one unknown variable, was superior to ancient geometry because each step in the argument leading to the answer to the problem
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was transparent, even if none of these steps could be expressed in pictorial terms as the geometric constructions of the ancient mathematicians could.30 The method proposed by Descartes was to substitute variables for unknown lengths of lines and angles and express the relationship between these in algebraic formulae, which were then manipulated until a general solution for the geometrical problem had been found. This method of “analysis” (or resolutio), as Descartes called it, made it possible to ascend from the particular facts that required explanation to the general principles on which they depended. The particular facts that had been the starting point of the “analysis” could then be derived from these general principles by a reverse process of deductive reasoning, termed “synthesis” (or compositio), which moved from definitions to axioms to propositions about these particular facts. A powerful demonstration of the value of this method was Descartes’s solution to Pappus’s four-line problem, which had defeated ancient geometers, but which Descartes solved by using his analytical method.31
Not every prominent mathematician of the seventeenth century was won over by this “modern” method. Isaac Newton believed that one had to be able to picture each step of the solution to a geometrical problem. It was not possible to work blindly through a series of permutations of algebraic formulae that did not relate in any evident way to the geometrical figure in question and yet trust the correct result to emerge at the end. Contrary to Descartes, Newton believed that the ancient mathematicians had in fact possessed a proper method for solving geometrical problems, which had been lost and needed to be recovered.32
Many other thinkers, however, were persuaded by the apparent success of Descartes’s method, which he had always intended to be applied
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to other areas of learning.33 From the mid-seventeenth century it became popular to present a philosophical argument more geometrico, in quasi-mathematical terms, as a sequence of definitions, axioms, and propositions. Like Descartes, other thinkers hoped that the method of “analysis,”
