In the tradition of Modern philosophy, the rationalist movement was spearheaded by Descartes and then Spinoza, both of whom devised profound and logical systems built solely on reason. Gottfried Wilhelm von Leibniz, another of the great rationalists, a polymath by nature, a scientist and physicist, mathematician, logician, theologist, diplomat, linguist, geologist, politician, and, among other things, philosopher, lived in the mid 17th century and was a contemporary of the natural philosopher Isaac Newton, with whom he would feud on several key points. Besides being a brilliant philosopher, he was an amazing and talented mathematician and scientist who developed his own method of calculus, leading to one of the greatest scientific controversies in history. While Newton thought of and expounded his calculus first, for which he deserves the most credit, Leibniz published his own independent calculus several years before Newton. Unfortunately, Newton was much more revered and had a higher reputation, so Leibniz was soon forgotten and faded into history, neither his physics nor his philosophy being put in the spotlight, such that his predecessors’ names are remembered more than his. But perhaps Leibniz is most known for being the victim of Voltaire’s lampoon: He is represented as Dr. Pangloss, the unconditional optimist who claims it is the “Best of all possible worlds,” in Voltaire’s novel Candide. The following essay shall provide a succinct and, hopefully, simple and comprehensible summary of and look at Leibniz’s philosophy.
Bertrand Russell, in The History of Western Philosophy, remarked that Leibniz was one of the only philosophers to construct his whole system—even his metaphysics—using the foundations of a logic; it is thus that I shall begin. Leibniz begins by dividing all truths into two types: Those of reasoning, and those of those of fact. A truth of reason is necessary, which is to say that it has to be the way it is, that it cannot be otherwise. He uses the law of noncontradiction in order to justify them. It states that the opposite of a truth of reason results in a self-contradiction. For example, to say that 2+2=5 is a contradiction because is it not true, but rather is contradictory, for it goes against the truth, namely that 2+2=4. As such, 2+2=4 is a truth of reason: To say its opposite is a self-contradiction. Truths of reason are impossible to refute. They are incontrovertible. Later, the German philosopher Kant, having read Leibniz, would borrow this idea and call it an analytic a priori judgement. Basically, a truth of reason is true by definition, it is given, it is innate. In this manner, Leibniz stands in contrast to Locke, who claimed innate knowledge is impossible; Leibniz, then, is an innatist, in that he believes that certain truths, truths of reason, are already in our minds. Truths of fact, on the other hand, are contingent. This means they can either be true or false; it is not necessary for them to be one way over another. Whereas truths of reasons when refuted become self-contradictions and are therefore impossible to confute, the opposite of a truth of fact is possible, for truths of facts are, in essence, possibilities. An example would be saying that an apple is red. Saying an apple is not red does not result in a contradiction because it does not necessarily have to be red, but can be green as well. Being red is a possibility, but it is a possibility that an apple may be green, too. Leibniz justifies truths of fact with the principle of sufficient reason, which states that everything exists for a reason. There is a reason why one particular apple is red, another green, and this is God’s doing, according to Leibniz. He states that while everything has a reason, we humans are incapable of conceiving the final cause for all things—only God can. Another support for the principle of sufficient reason is the argument for metaphysical perfection, whereby Leibniz argues that existence is better than non-existence. It is better for more things to exist than for fewer things to exist. Hence, Leibniz calls upon us to always appeal to logic and reason in order to find the reason for everything. A question may come to mind right now: If God creates everything with a sufficient reason, including contingent, or possible, truths, does that imply that contingent truths are actually necessary? If there is a reason one apple is red, does that mean that that particular apple is necessarily red and cannot be green, for that possibility has not been actualized? As said earlier, God knows the sufficient reason for everything, so we do not. Just with analytic a priori judgements, Kant adapted this type of truth and turned it into synthetic a posteriori judgements, which are propositions that are gained from experience and are contingent. Similarly, Hume, who preceded Kant, is famous for his logical fork, which divides truths respectively into matters of fact and relations of ideas. The theme of contingency is essential to Leibniz’s philosophy. Contingent truths are everywhere, and they exist because there are sufficient reasons for them. When two or more possibilities are compatible and can co-exist without logical problems, a condition is met called compossibility, which translates to “possible with.” Problems arise when one possibility is not compatible with another. An illustration: It is a fact that humans have two eyes, but this is one of an infinity of possibilities, another being that humans have one eye, like a cyclops. It is impossible for both possibilities to co-exist: We cannot have two eyes and only one eye at the same time. If you were to look around, you would see that we have two eyes, not one. Accordingly, when one possibility is actualized, it negates the other possibility. Contrast this to a truth of reason. One cannot say “All triangles have four sides,” as this is a contradiction; it is simply impossible. Leibniz proposes that a world such as ours is the sum total of all its compossibilities. In our world, humans have two eyes, two ears, and a nose. However, Leibniz says that there are infinite possible multiverses. It is important to note that they are possible multiverses, not plain multiverses, because the existence of our world negates the existence of the other universes. In another contingent universe, humans have an eye, an ear, and two noses, but because this world exists and not that one, it does not exist in actuality. One may ask the age-old question “Why is there something rather than nothing?” to which Leibniz would reply: The principle of sufficient reason. God created the world based on metaphysical perfection and the identity of indiscernibles. The identity of indiscernibles says that if A and B are completely identical and share every property, then they are indistinguishable and consequently the same thing. One can substitute A for B and B for A. Using this principle, Leibniz reasons that, in creating our world, God would be foolish in choosing here vs. there or now vs. then, insofar as they are all identical before the existence of the world. For this reason, everything is unique, and no two things are the same.
All is monads. So says Leibniz. A monad, from the Latin monas or mon, meaning “one,” is an independent, individual, and self-contained entity. The monad is defined as its own entity to the extent that it is completely separate from all other monads and contains within it its own individuality, by which it distinguishes itself from the others, as in the identity of indiscernibles. Leibniz claims monads are “windowless.” Unlike biological cells, which have a permeable membrane allowing for resources to come in and out, monads are enclosed and shut off from everything else, allowing nothing to either come in or out or affect them. Thus, when Leibniz speaks of monads as being self-contained, he means they cannot be affected from the outside, but contain inside themselves their own causality. Another thing about monads is that they are not like your average atoms, inasmuch as they are simple, indivisible “points” of consciousness. A “point” in geometry lacks any and all dimensions yet constitutes a location in space, and this is what an atom does. This proposition is countered by Leibniz, who says atoms are not the fundamental constituents of reality. Arguing against the Cartesian concept of matter, which states that matter is “extended,” which is to say that it has physical shape and size, that it is located in space, Leibniz says that anything that is extended is divisible. Like in Zeno’s paradoxes, take a line and divide it in half, then divide that half by half, and then that half, and so on: The line, which is extended, can always be broken down—it can be made simpler. Leibniz claims that atoms are the same way. Atoms are not simple, but complex. Because material atoms can be infinitely divided, Leibniz suggests that the building blocks of reality are immaterial. Such a building block would be simple because it has no parts; in fact, it is the part from which complexities, or aggregates—a grouping of simple parts into a more complex one—are made. In another argument against atomism, Leibniz tackles the physics laid down by Descartes and Newton. If an atom is a lifeless extension, then it requires an outside body or force to move it; but, Leibniz points out, mere extension offers no resistance, and so cannot be moved by outside force alone. Monads, then, are energy. Inherent in monads are inertia and force. Leibniz posits a vis viva, or living force, an entelechy, or internal drive, that is inherent to monads, a force which has a tendency to motion. This mirrors the concept of conatus, which is like the starting succession of motion; conatus is that initial force in the instant that makes a body move. Calculations by Leibniz showed that a certain amount of energy remains constant in a collision, a calculation he formulated into mv^2 (mass x velocity^2). Singlehandedly, Leibniz invented a formula for kinetic energy, a type of energy many knew existed, but for which there existed no mathematical proof. Leibniz states that kinetic energy, not momentum as Newton said, is the real cause of motion. And because kinetic motion is energy in action and requires potential energy first in order to be active, it must mean activity is intrinsic to monads. Amazingly, Leibniz was the precursor to modern physics. He almost anticipated Einstein’s famous E=mc^2, and he was off on kinetic energy by ½ (the real formula is ½mv^2)! Leibniz, nearly 300 years before Einstein, was nearly able to prove through reasoning that matter is actually energy. Monads are substances. Substances, as opposed to matter, are simple. Substance is like a noun: It is a concept and a proper thing that can be described. Descriptors, adjectives, are called “accidents,” because qualities are contingent, whereas substance is necessary; contingent properties are applied to the substance, but they do not change the substance’s form, for they are additions and merely add to it. Leibniz proceeds to construct his philosophy with the aid of grammar. As in English, a subject is an actor, and a predicate is an action done thereby. He defines substance, then, as “unextended subjects… individuated by predicates”; i.e., immaterial forms are made distinct by their actions, or what is said (predicated) of them. Here, Leibniz puts forth his famous idea of the “pre-established harmony.” Simply put, it is known that monads cannot interact with each other, so they are set in harmony before creation by God. In short, all predicates are contained in their subjects. This somewhat echoes predestination because it says that everything—past, present, and future—is hardwired into each monad so that they act not on each other, but with each other, such that “the state of the whole universe could be read off from any one Monad.” God creates monads as though they are clocks, each of which is designed to strike the same hour at the same time without cooperation between them. Because God designed them, He is the clock of which they are copies, so they mirror Him. Man is limited in his reason, so he cannot grasp this harmony in its entirety. When the monads are created, they are created with internal, self-regulatory laws that tell them what to do and when, like a clock mechanism. These monads are therefore spontaneous: They change on their own because they contain within themselves their future. Take the statement, “Leibniz was born in 1646.” Leibniz is a monad, a substance, and subsequently a subject, a self-contained entity, and the predicate “was born in 1646” is contained in the subject, Leibniz, whereby I mean that part of what makes Leibniz Leibniz is the fact that he was born in 1646, and not in 1647, for example. Yet another characteristic of monads is that they are microcosms—miniature universes that mimic the cosmos inside themselves. Each monad reflects the universe from its unique perspective. This concept is hard to grasp, but think of a room with furniture in it. A painting on the wall will have a wide view of the room, and the carpet will see everything above it; yet the fan mounted on the ceiling has a bird’s eye view, but it cannot see from the perspective of either the painting or the carpet. Thus, each monad is essential to the universe, and their perspectives are unique. But what do monads actually do? Monads are capable of three things: perception, appetition, and apperception. Perception is active and non-reflexive, or outward. It is the external representation of the unfolding of other monads. A dog perceives a squirrel running up a tree, but this perception is just a phenomena; the dog is witnessing the squirrel enacting one of its predicates, namely running up a tree; it is unfolding. Appetition is the ability to progress from one perception to the next. Apperception is reflexive and passive—it is self-consciousness, and it is reserved for man alone. Humans are examples of monads, albeit in different forms. A human is a “corporeal substance,” which is made up of a dominant monad (the soul) and an aggregate (multiple monads). Regarding the mind-body problem, Leibniz rejects Cartesian dualism and the resulting interactionism and Malebranche’s occasionalism. I think it interesting that Newton likened God to a clockmaker who, every now and then, had to rewind the cosmic clock on the account that if he were to make the universe fully automatic, it would render him impotent; yet Leibniz claims the contrary for the exact opposite reason. Leibniz considered it silly to think that God had to continually rewind His own mechanism, which turned God into a functionary whose job was lowly, whereas He could exhibit His power by creating a self-regulatory universe. Leibniz’s solution to the mind-body problem is parallelism: The body and the mind, separate monads, work at the same time without causally interacting because of the pre-established harmony. Now, as monads are unique, it would be strange to assert that rocks are of the same order as humans, and humans God. To account for this, Leibniz creates a hierarchy of monads, the criterion of ranking being clarity of perception. There are aggregate, integral, and essential monads, which each correspond, respectively, to bare, animal, and rational/spiritual monads. Bare aggregates are composites, meaning they are composed of many monads. They are inanimate and unconscious, often with blurry or confused perceptions. An example would be a rock. Animal integral monads are, as the name says, animals that are made of an aggregate and a soul, endowed with the power of memory. Humans are integral but rational monads, which means they, like animals, are made of two parts: an aggregate, and, unlike animals, a spirit, not a soul. Man is also dispensed with consciousness. What distinguishes man from animals most saliently, however, is his knowledge of truths of reason. Because he is self-conscious, because he has the ability to introspect, and because a priori knowledge is innate to him, man can grasp necessary truths. Lastly are essential monads, which are equivalent to truths of reason. A triangle, or God, is an essential monad because it is simple and cannot be refuted. The last thing Leibniz has to say about metaphysics is his thought regarding space and time. Newton believed space and time were absolutes. Space is an entity that extends everywhere, and time is another entity in which events happen. Leibniz disagrees, stating that space and time are relative. Recall the identity of indiscernibles. If space and time are absolutes, then no instance of either can be differentiated from the next, meaning that they are only a single point, and not independent dimensions. Space is defined as the coexistence of bodies, time the succession of monads’ eternal unfolding. As a result, space is only space when it is used in reference to two or more bodies. Time, in a like manner, cannot be objectively measured, but must be made in reference to something. Spacetime, it can be implied, is relative, in that it depends on what you are measuring; in this manner, Leibniz can be seen as predicting the modern theory of relativity, too.
A theologian, Leibniz argued for the existence of God in two main ways: That of the Ontological Argument, and that of the pre-established harmony. Borrowed from Saint Anselm, the Ontological Argument runs as so: If a perfect being is imagined, it is predicated of it that is must have all perfect qualities, one of which is existence; but this would contradict a perfect being in imagination, so it stands that this perfect being must exist in order to be such a perfect being, and this perfect being is God; therefore, God exists. The argument of pre-established harmony is similar to the Teleological Argument in that it argues that there is a clearly observable harmony in nature, and this perfect harmony must have been orchestrated by some perfect being who oversaw it—God. His most famous work, the Theodicy, seeks to explicate the Problem of Evil, which asks how a benevolent, omnipotent God could allow evil. Assuming God is benevolent and omnipotent, Leibniz writes, He must have chosen, out of all the possible worlds, the best one, this one. The best world is the one with the least causes and most effects; in a word, an optimal world. For this reason, he proclaims we live in the “Best of all possible worlds.” He reminds us that happiness is not the only measure of good, and evil is the absence of good, a remark made earlier by Augustine. This world, he admits, is not perfect. But it does not need to be. Rather, because God Himself is perfect, it would be impossible for Him to create a perfect world in His image, so evidently, this world cannot be as perfect as He, but must be at least a little bit flawed, so as to distinguish it from Himself. Again, according to the principle of sufficient reason, everything happens and exists for a reason. Humans—imperfect, rational beings—cannot comprehend every reason God decrees, so even if we experience evil and cannot justify it reasonably, then it stands that it happened for a reason, albeit one of which we are ignorant; but, coming from God, it must be so. As God is the highest, clearest monad, all monads mirror Him imperfectly. Leibniz assures us that God did not create this world out of logical or metaphysical necessity, but out of ethical necessity. God created, in the words of Leibniz, “a moral world within the natural world.” Ruth L. Saw wrote bluntly, “Leibniz cannot be described as a man of great moral insight.” I would agree with generalization, only to the extent that he did not produce any substantial works on ethics. Leibniz equated knowledge with power. Happiness is correlative to clarity, so clearer monads will be happier because they are closer to perceiving God. Using this reasoning, Leibniz is able to take a jab at the ignorant, who are not actually bliss, but are rather in a stupor. Those with more understanding can follow and adhere to necessary truths, which, Leibniz says, are obligations of the moral man. Charity, in this manner, is an obligation, a necessary action. Utilitarianism was antedated by Leibniz, who devised a calculus similar to Bentham’s whose purpose it was to determine the benefits of more “perfect” (well-off) beings. A problem arises which has not yet been addressed and which remains an elephant in the room: The problem of free will. The pre-established harmony certainly seems to leave no room for free will, prompting the question, In a determined world, is freedom possible? Leibniz answers yes. He argues clarifies that some predicates are contingent, leaving room for free will. For example, taking “Napoleon became emperor 1804,” it may seem that it was necessary for Napoleon to become emperor in that year, seeing as it happened that way, not otherwise; however, while the subject Napoleon contains the predicate “became emperor in 1804,” thus defining Napoleon, it is possible that God may have made him emperor a year earlier, meaning the predicate is contingent, a compossibility. But while God leaves room for free will, do we have self-determination? Are we able to actually cause things through our own causal power? Technically, yes, says Leibniz, controversially. It all depends on how what exactly self-determination entails. “The free man is one who knows why he does what he does.” Our actions, mind you, are internally determined by our predicates, which are already contained within ourselves. In this sense, we have no free will. But, if we can understand our motives, if we can understand the pre-established harmony, we can realize our thoughts and total possibilities. Because we unfold according to a pre-drawn map, if we are able to find this map, study it, then predict it, we are, in a sense, in control of our actions. We know what we will do—we are just destined to do it.
One of the lesser-appreciated and lesser-studied philosophers, Gottfried Leibniz remains an insightful and prescient Rationalist, a truly modern philosopher whose genius was far ahead of his times, and whose cleverness was realized too late. A physicist just as much as a philosopher, he remains an important figure in the history of science. In his life, he designed several inventions that were revolutionary, although none of them worked. Leibniz has gone down in history as one of the first rationalist advocates for optimism, yet despite his Panglossian philosophy, he ironically did not find much success in life. Conclusively, Leibniz is one of the great systematizers of philosophy and one of the most intelligent men in history.
A very simple visual showing some of Leibniz’s main ideas and their connections:
 Ferm, A History of Philosophical Systems, p. 248
 O’Connor, A Critical History of Western Philosophy, p. 224
 Leibniz never really answers how immaterial points can constitute a physical body.
 According to Leibniz, a spirit is higher than a soul
 Leibniz, Monadology, §86
 O’Connor, op. cit., p. 234
 By “perfect” beings, he refers to wealthy, fortunate people. His determinism precludes simpler people, making him, arguably, an elitist.
 Stumpf, Socrates to Sartre, p. 250
For further reading:
The Columbia History of Western Philosophy by Richard R. Popkin (1999)
A Critical History of Western Philosophy by D.J. O’Connor (1964)
The History of Western Philosophy by Bertrand Russell (1972)
The Encyclopedia of Philosophy Vol. 4 by Paul Edwards (1967)
A History of Philosophical Systems by Vergilius Ferm (1950)
Socrates to Sartre by Samuel Enoch Stumpf (1982)
History of Philosophy by Julián Marías (1967)
The Philosophers by Ted Honderich (2001)