As a middle term for making the transition from the rational to the empirical, from the "possible" to the "actual," a mete physical idea is used by Descartes as well as by Kepler. The actual world must correspond to the supreme laws of reason, because it is the work of an infinite mind, because it is a creation of the divine intellect. The applicability of pure mathematics to physics, to the concrete phenomena of nature, seems explainable only on this presupposition. It is valid because nature itself is the product of a "divine mathematics": cum Deus calculat, fit mundus.
For Leibniz, too, there is a continuous harmony between "truths of reason" and "truths of fact," between the empirical and the rational world. The pure laws of thought as exhibited in logic, arithmetic, geometry and abstract dynamics, apply to all objects in nature, and to all changes taking place therein.
This metaphysical rationalism is further developed by Leibniz so that the eternal truths of reason constitute the essence of the divine mind, and God, therefore, cannot desert them in his activity, in his creation. Creation consists in transition from "essence" to "existence," from the "possible" to the "actual." Leibniz developed this view of rationalism in two directions. It determines, first of all, the entire structure of his metaphysics; it forms the logical and methodical basis of his monadology. The system of "monads," i.e., of perceiving minds, is graded, accord ing to Leibniz, in such a way that each monad resembles the others as regards the content of its perception ; for each of them represents and reflects the total universe from a definite angle. Accordingly, the difference between the various minds can consist in nothing other than the form of perception, the greater or lesser degree of clarity. Hence a gradation from the dim and confused mode of perception, such as we must assume, for instance, in plant or animal consciousness, up to the divine cognition which consists in completely distinct and adequate ideas. Human knowl edge lies in the middle between the two extremes; it knows "con fused" ideas, e.g., those of sense-qualities, as well as "distinct" ideas, e.g., those of logic and mathematics.
However, its specific task consists in referring progressively the former to the latter, in transforming all data into pure objects of thought, all merely factual presentations into notions continu ously connected by proof and thus conceived by reason. This task
can be accomplished in detail only by presupposing a general system of the possible forms of thought and of the universal laws of connection which those forms obey. Leibniz attempted to satisfy this demand in the grandiose outline of his "general char acteristique" in which the primary elements of all cognition were to be set forth in conjunction with the demonstration of a method by which all truths, however complex, could be exhibited as combinations of those primary elements. Through this outline of his "general characteristique," Leibniz became the founder of that "symbolic logic" which reached its complete development only in the nineteenth century through the works of Boole and Schroder, of Peirce and Peano, of Whitehead, Frege and Russell. (Cf. Couturat, La Logique de Leibniz, 1900 In the eighteenth century, on the other hand, philosophical rationalism became dominant only in that more limited form which it had received in the system of Christian Wolff (1679 Wolff's doctrine, too, rests entirely on the distinction between contingent "truths of fact" and necessary "truths of reason"; he, too, contends that the specific task of cognition, especially the task of philosophical knowledge, consists in trans forming all contingent elements into rational ones by understand ing them according to the principle of sufficient reason.
Consequently, we cannot claim a philosophic insight into a region of facts unless we succeed in bringing the factual details into a rational order so that each member can be completely under stood from the context and from the necessary laws which deter mine this context. Accordingly, Wolff supplements each form of empirical cognition by a corresponding "rational" form. The propositions, for instance, which in the field of physics result directly from observation and from experiments, must be raised to the rank of genuine cognitions of reason by being deduced from the principles of general ontology and general cosmology. Specifically, Wolff's system is subdivided into Logic as the doc trine of the operations of the understanding in general, into Ontology as the doctrine of Being and its most universal deter minations, Cosmology as the doctrine of the world, of the simple substances and their combination, Psychology, Theology, and, finally, universal Teleology, the doctrine of ends in general and of the end of human action in particular.