Gottfried Wilhelm von Leibniz (1646-1716) was an outstand­ing German philosopher, mathematician, scientist, historian, and diplomat. He tried to develop an adequate metaphysical system to answer the fun­damental question, “Why is there something rather than nothing?” and examine the worldview resulting from his answer. After all, he observed, nothing is simpler and easier than something. But there is something, so why is that so? This entry discusses Leibniz’s core ideas on metaphysics, including his concepts of space and time.

Two of Leibniz’s guiding basic principles were the principle of contradiction (whatever implies a contradiction is false; thus, every true proposition is a tautology—always true) and the principle of sufficient reason (nothing exists without a suffi­cient reason why it is so and not otherwise). In an argument analogous to one of Saint Thomas Aquinas’s five ways to prove the existence of God, he argued that the reason for the existence of the world cannot lie in the contingent things (they might have all gone out of existence at the same time, and then what?); it must lie in a necessary being—God. God is the metaphysically perfect substance, containing all perfections, such as omni­science and omnipotence. Leibniz’s idea of God seems to be like a kind of supermathematician; God examined all the infinite number of possible worlds and chose the best, that one that is “sim­plest in hypotheses and richest in phenomena.” In an effort similar to work done by Johannes Kepler in determining the optimum dimensions of a wine cask to contain the most liquid with the least mate­rial required, Leibniz’s God might have applied a kind of minimax procedure to come up with the optimum combination of characteristics for the world. If there had been no best combination, there would not have been a sufficient reason for God to create a world, and there would be none; thus this must be the best possible world. When God thought the best possible world, his thoughts became the world. (Leibniz argued that thoughts require signs, and the world is the sign of God’s thoughts.)

Rene Descartes (1596-1650) had thought that the essence of (physical) substance was extension (as contrasted with mental substance, whose essence was thinking), and so a geometrical account could explain all properties of bodies. Leibniz saw that this was inadequate, that a geometrical account of motion failed to take inertia and momentum into account. Thus Leibniz concluded that the essence of substance is action, it has a force (conatus), a striving to change (for the better). The basic building block of the world, thought Leibniz, must be indivisible, a formal atom—a monad. Leibniz’s monads are like little minds; it is as if bodies are a byproduct of these minds (he sometimes refers to a body as a momen­tary mind). These monads are “windowless,” unaffected by anything other than their own pro­grams. It is as if each monad is driven by its own program (something like a computer program), its internal tendency to move from one state to the next. This “program” has existed as long as the monad and determines its current state and what state it will be in next. It is like a finite-state automaton, with its initial state and the function that describes how it changes; these totally define it. Its principle of change Leibniz calls “appetition”—it is a striving for perfection. The world itself cannot be perfect, for then it would be God, and there could not be two Gods (there is not a sufficient reason for any two identical things, according to Leibniz); but the world strives toward perfection, and it is this striving that underlies change. Each monad, since its program totally defines it, contains its future and the traces of its past: “The present is big with the future, the future might be read in the past, the distant is expressed in the near.”

Each monad has perceptions, which are its per­spective on the universe, and Leibniz says that each monad reflects the whole (universe), though imper­fectly. Thus it may contain the whole, but not be aware of all its aspects, or some of them may be less “in focus” than the nearer ones. A monad’s perceptions are its properties; thus the monads form a plenum, because otherwise a monad could perceive nothingness, but nothingness cannot be one of its properties. A monad is a “concentration and a living mirror of the whole universe, accord­ing to its point of view.” Thus monads make up the world and perceive the world at the same time; they are all part of the world harmony created by God’s thought. Thus there is hope for knowledge of the truth regarding objective reality (of that world). The dominant monad of the aggregation of monads that gives rise to a body is its soul monad, which is dominant over the others. It has memory and reason and is farther up the hierarchy of monads. A rational soul, in discovering truth through science (or mathematics or logic), imitates what God does in the world as a whole; it is a kind of image of God. It tries to know God, but since God is infinite, it can never achieve full knowledge, but it can continue striving in “perpetual progress” (and never get bored!).

Leibniz argues that there are two realms: the realm of Nature and the realm of Grace. Because perceptions (and feelings) cannot be explained by mechanical causes (like trying to find your perception/idea of red by surgically examining your brain), there must be another realm (of final causes) that governs the soul monads (in their striving toward the best, to maximize good over evil). In the realm of nature, bodies follow the laws of efficient causes; these two realms will, according to Leibniz, always be in harmony, as God thought them. There will be two possible explanations, one following final causes, the other following efficient causes in the realm of nature, for every event; Leibniz says they are “equally good” explanations. Thus the mental and the physical realms are in sync because of God’s preestablished harmony; they are like two clocks created and started off by the same watchmaker that continue to tell the same time even though there is never any interac­tion between them, or like members of a chorus who sing the same music even though they never touch each other or directly interact. They run in perfect parallel (which is his explanation to Descartes’ problem of how mind and body affect each other, without Descartes’ desperate solution that they interact in the pineal gland).

Leibniz views space and time as relative (see the entry on Newton and Leibniz). Space is created by the positioning of bodies, bodies are not placed in an absolute preexisting container space, and time is the succession of states (physical or mental) of bod­ies or minds. Without bodies, there is no space; without change, no time. Space and time are thus, for Leibniz, relations; they are ideal (based in ideas), phenomenal. Time is the more fundamental, because monads have their internal programs to move from one state (condition) to another, in their striving toward perfection. The difference between one state and another state creates their temporal relation (first one state, then the next, creates the temporal relation of earlier and later time, of past and present, or present and future). This would be time in the realm of grace, from one perceived state to another. Monads that congregate together as a body guided by a soul monad act and change in the realm of nature, so time in that realm would mea­sure the difference between different bodily states. Derivatively, physical space would be defined by the relative position of bodily monadic aggregates.

Stacey L. Edgar

See also Descartes, Rene; God and Time; Idealism; Metaphysics; Newton and Leibniz; Ontology; Space; Spinoza, Baruch de; Theodicy; Time, Relativity of

Further Readings

Leibniz, G. W. (1989). Monadology. Principles of nature and grace. Discourse on metaphysics. In R. Ariew & D. Garber (Eds.), G. W. Leibniz: Philosophical Essays. Indianapolis, IN: Hackett. (Original works published 1686 and 1714)

Leibniz, G. W. (1996). New essays on human understanding (P. Remnant & J. Bennett, Trans.). Cambridge, UK: Cambridge University Press. (Original work published 1764)