Gottfried Wilhelm (1646–1716), German rationalist philosopher who made seminal contributions in geology, linguistics, historiography, mathematics, and physics, as well as philosophy. He was born in Leipzig and died in Hanover. Trained in the law, he earned a living as a councilor, diplomat, librarian, and historian, primarily in the court of Hanover. His contributions in mathematics, physics, and philosophy were known and appreciated among his educated contemporaries in virtue of his publication in Europe’s leading scholarly journals and his vast correspondence with intellectuals in a variety of fields. He was best known in his lifetime for his contributions to mathematics, especially to the development of the calculus, where a debate raged over whether Newton or Leibniz should be credited with priority for its discovery. Current scholarly opinion seems to have settled on this: each discovered the basic foundations of the calculus independently; Newton’s discovery preceded that of Leibniz; Leibniz’s publication of the basic theory of the calculus preceded that of Newton.
Leibniz’s contributions to philosophy were known to his contemporaries through articles published in learned journals, correspondence, and one book published in his lifetime, the Theodicy (1710). He wrote a book-length study of Locke’s philosophy, New Essays on Human Understanding, but decided not to publish it when he learned of Locke’s death. Examination of Leibniz’s papers after his own death revealed that what he published during his lifetime was but the tip of the iceberg.
Perhaps the most complete formulation of Leibniz’s mature metaphysics occurs in his correspondence (1698–1706) with Burcher De Volder, a professor of philosophy at the University of Leyden. Leibniz therein formulated his basic ontological thesis: Considering matters accurately, it must be said that there is nothing in things except simple substances, and, in them, nothing but perception and appetite. Moreover, matter and motion are not so much substances or things as they are the phenomena of percipient beings, the reality of which is located in the harmony of each percipient with itself (with respect to different times) and with other percipients. In this passage Leibniz asserts that the basic individuals of an acceptable ontology are all monads, i.e., immaterial entities lacking spatial parts, whose basic properties are a function of their perceptions and appetites. He held that each monad perceives all the other monads with varying degrees of clarity, except for God, who perceives all monads with utter clarity. Leibniz’s main theses concerning causality among the created monads are these: God creates, conserves, and concurs in the actions of each created monad. Each state of a created monad is a causal consequence of its preceding state, except for its state at creation and any of its states due to miraculous divine causality. Intrasubstantial causality is the rule with respect to created monads, which are precluded from intersubstantial causality, a mode of operation of which God alone is capable. Leibniz was aware that elements of this monadology may seem counterintuitive, that, e.g., there appear to be extended entities composed of parts, existing in space and time, causally interacting with each other. In the second sentence of the quoted passage Leibniz set out some of the ingredients of his theory of the preestablished harmony, one point of which is to save those appearances that are sufficiently well-founded to deserve saving. In the case of material objects, Leibniz formulated a version of phenomenalism, based on harmony among the perceptions of the monads. In the case of apparent intersubstantial causal relations among created monads, Leibniz proposed an analysis according to which the underlying reality is an increase in the clarity of relevant perceptions of the apparent causal agent, combined with a corresponding decrease in the clarity of the relevant perceptions of the apparent patient. Leibniz treated material objects and intersubstantial causal relations among created entities as well-founded phenomena. By contrast, he treated space and time as ideal entities. Leibniz’s mature metaphysics includes a threefold classification of entities that must be accorded some degree of reality: ideal entities, well-founded phenomena, and actual existents, i.e., the monads with their perceptions and appetites. In the passage quoted above Leibniz set out to distinguish the actual entities, the monads, from material entities, which he regarded as well-founded phenomena. In the following passage from another letter to De Volder he formulated the distinction between actual and ideal entities:
In actual entities there is nothing but discrete quantity, namely, the multitude of monads, i.e., simple substances. . . . But continuous quantity is something ideal, which pertains to possibles, and to actuals, insofar as they are possible. Indeed, a continuum involves indeterminate parts, whereas, by contrast, there is nothing indefinite in actual entities, in which every division that can be made, is made.
Actual things are composed in the manner that a number is composed of unities, ideal things are composed in the manner that a number is composed of fractions. The parts are actual in the real whole, but not in the ideal. By confusing ideal things with real substances when we seek actual parts in the order of possibles and indeterminate parts in the aggregate of actual things, we entangle ourselves in the labyrinth of the continuum and in inexplicable contradictions.
The labyrinth of the continuum was one of two labyrinths that, according to Leibniz, vex the philosophical mind. His views about the proper course to take in unraveling the labyrinth of the continuum are one source of his monadology. Ultimately, he concluded that whatever may be infinitely divided without reaching indivisible entities is not something that belongs in the basic ontological category. His investigations of the nature of individuation and identity over time provided premises from which he concluded that only indivisible entities are ultimately real, and that an individual persists over time only if its subsequent states are causal consequences of its preceding states. In refining the metaphysical insights that yielded the monadology, Leibniz formulated and defended various important metaphysical theses, e.g.: the identity of indiscernibles – that individual substances differ with respect to their intrinsic, non-relational properties; and the doctrine of minute perceptions – that each created substance has some perceptions of which it lacks awareness.
In the process of providing what he took to be an acceptable account of well-founded phenomena, Leibniz formulated various theses counter to the then prevailing Cartesian orthodoxy, concerning the nature of material objects. In particular, Leibniz argued that a correct application of Galileo’s discoveries concerning acceleration of freely falling bodies of the phenomena of impact indicates that force is not to be identified with quantity of motion, i.e., mass times velocity, as Descartes held, but is to be measured by mass times the square of the velocity. Moreover, Leibniz argued that it is force, measured as mass times the square of the velocity, that is conserved in nature, not quantity of motion. From these results Leibniz drew some important metaphysical conclusions. He argued that force, unlike quantity of motion, cannot be reduced to a conjunction of modifications of extension. But force is a central property of material objects. Hence, he concluded that Descartes was mistaken in attempting to reduce matter to extension and its modifications. Leibniz concluded that each material substance must have a substantial form that accounts for its active force. These conclusions have to do with entities that Leibniz viewed as phenomenal. He drew analogous conclusions concerning the entities he regarded as ultimately real, i.e., the monads. Thus, although Leibniz held that each monad is absolutely simple, i.e., without parts, he also held that the matter–form distinction has an application to each created monad. In a letter to De Volder he wrote: Therefore, I distinguish (1) the primitive entelechy or soul, (2) primary matter, i.e., primitive passive power, (3) monads completed from these two, (4) mass, i.e., second matter . . . in which innumerable subordinate monads come together, (5) the animal, i.e., corporeal substance, which a dominating monad makes into one machine. The second labyrinth vexing the philosophical mind, according to Leibniz, is the labyrinth of freedom. It is fair to say that for Leibniz the labyrinth of freedom is fundamentally a matter of how it is possible that some states of affairs obtain contingently, i.e., how it is possible that some propositions are true that might have been false. There are two distinct sources of the problem of contingency in Leibniz’s philosophy, one theological, and the other metaphysical. Each source may be grasped by considering an argument that appears to have premises to which Leibniz was predisposed and the conclusion that every state of affairs that obtains, obtains necessarily, and hence that there are no contingent propositions.
The metaphysical argument is centered on some of Leibniz’s theses about the nature of truth. He held that the truth-value of all propositions is settled once truth-values have been assigned to the elementary propositions, i.e., those expressed by sentences in subject-predicate form. And he held that a sentence in subject-predicate form expresses a true proposition if and only if the concept of its predicate is included in the concept of its subject. But this makes it sound as if Leibniz were committed to the view that an elementary proposition is true if and only if it is conceptually true, from which it seems to follow that an elementary proposition is true if and only if it is necessarily true. Leibniz’s views concerning the relation of the truthvalue of non-elementary propositions to the truth-value of elementary propositions, then, seem to entail that there are no contingent propositions. He rejected this conclusion in virtue of rejecting the thesis that if an elementary proposition is conceptually true then it is necessarily true. The materials for his rejection of