An Introduction to Gottfried Leibniz

Austin Tannenbaum
8 min readJan 7, 2021

Gottfried Leibniz was a German philosopher and polymath of the early modern period. Born in Leipzig on July 1, 1646, he was raised by his mother from the age of six after his father, an ethics professor, passed away in 1652. Leibniz inherited his father’s extensive library, which facilitated his early self-education in a variety of advanced subjects. Leibniz was a high achiever, earning his bachelor’s degree at age 15, his master’s degree at age 16, and his doctorate of law at age 18. His first job out of school was a secretarial position for an alchemical society.

Throughout his life, Leibniz was employed in a variety of vocations, including that of policymaker, diplomat, inventor, librarian, and political advisor. In his off time, he wrote voluminously: while Leibniz published only two books during his lifetime, he left behind a stack of manuscripts and 15,000 letters to more than a thousand correspondents, both of which are still being published today. Leibniz died in 1716 from complications related to gout. At the time of his death, he suffered a poor reputation owing to the public perception that he had plagiarized Newton’s unpublished work on calculus. Today, while Leibniz is acknowledged to have engaged in dubious behaviors including falsifying and backdating documents, the modern scholarly consensus is that he developed his ideas on calculus independently of Newton.

Arguably the most important logician in his time since Aristotle, Leibniz sought to treat philosophy like mathematics, suggesting that,

“The only way to rectify our reasonings is to make them as tangible as those of the Mathematicians, so that we can find our error at a glance, and when there are disputes among persons, we can simply say: Let us calculate, without further ado, to see who is right.”

Leibniz went so far as to hypothesize a universal language of logical symbols, or a characteristica universalis, that would act as an alphabet of human thought. He envisioned feeding queries written in this characteristica universalis into his theorized “calculus ratiocinator,” which would process the information and output an answer. In this way, Leibniz foreshadowed Wittgenstein’s maxim that “what can be said at all can be said clearly” and, more generally, analytic philosophy’s symbolic representation of language as a means of problem-solving. Leibniz’s idea of the calculus ratiocinator anticipated the modern computer, with its ability to calculate complex functions. Leibniz himself was the first to construct a calculator capable of performing all four arithmetic functions (addition, subtraction, multiplication, and division).

Being an advocate of logic, Leibniz attempted to ground his philosophy in axioms, or logical principles. Among the most important to his system of thought are:

  • The principle of non-contradiction, which states that a proposition cannot be true and false at the same time.
  • The principle of the identity of indiscernibles, which states that if two things share all properties, they are identical.
  • The principle of sufficient reason, which states that nothing is without a cause.
  • The principle of predicate in notion, which states that for all true affirmative propositions, the predicate is always contained within the subject.
  • The principle of simplicity, which states that within all composites exist simples that cannot be broken down further and which are the constituents of composites.
  • The principle of the complete individual concept, which states that all substances contain all predicates of themselves past, present, and future.
  • The principle of continuity, which states that change does not happen suddenly. In Leibniz’s words, “nature does not make leaps.”
  • The principle of substantial form, which states that composites possess a shaping force that makes them what they are as opposed to an indistinguishable lump of matter.

Leibniz argued that these principles are “innate,” as they cannot be derived from experience. Instead, they are “necessary truths” that are present in the mind from birth. However, just because these ideas reside in the mind does not mean that one is automatically aware of them. Presaging Freud’s theory of the unconscious, Leibniz posited the existence of “petite perceptions,” or latent ideas “unaccompanied by awareness or reflection.” These perceptions are said to reside in the background of one’s mind with the potential of being manifested in one’s direct consciousness in much the same way as veins in a block of marble imply shapes that a sculptor can exploit to manifest a sculpture, to use a favorite analogy of Leibniz’s.

In embracing this theory of innate ideas, Leibniz rejected Locke’s tabula rasa model of the mind as a “blank slate” that only becomes filled with knowledge once it encounters the world. Instead, Leibniz proposed a rationalist epistemology in which knowledge is chiefly derived from reason rather than the senses. According to Leibniz, our inborn reason allows us to derive truths that are necessary per se, or truths whose contraries imply a contradiction, such as in logic, arithmetic, and geometry. For instance, there is no possible world in which 1 + 1 =/= 2 given the realities of quantity and addition. On the other hand, the senses are limited to deriving truths that are necessary ex hypothesi, or truths whose contraries do not imply a contradiction, such as empirically derived truths. For instance, while it is true that in our world, leaves typically appear green, it is possible that in another world leaves typically appear gray or purple.

Leibniz employs his logical principles and rationalist epistemology to construct a strange and compelling model of the universe. As a metaphysician, Leibniz belongs to the idealist camp, proposing that the physical world is not real, but rather an illusory epiphenomenon of “monads” and their ideas. By monads, Leibniz means simple, intangible substances that together make up our ultimate reality. Monads are inferred to be both simple and intangible to satisfy the principles of simplicity and sufficient reason. The argument is roughly as follows:

  • Every composite consists of simples.
  • If composites were infinitely divisible, they would lack simples, and therefore lack a reason for being (i.e. lack an ultimate substance that explains them), rendering them unreal.
  • Inherent in the idea of physical objects is infinite divisibility, as physical objects can always be split into parts materially or conceptually divided spatially (e.g. into a “left” and a “right”).
  • Therefore, to satisfy the principle of sufficient reason, to be able to explain why things ultimately are, our reality must be made up of simple, intangible substances.

Now, according to Leibniz, God endowed all monads with two principal characteristics:

  1. Perception: the ability to represent the world.
  2. Appetition: the tendency to transition from one representation to another.

Monads make the world appear to us as it does because God programmed them to represent it in certain ways. Additionally, monads make the world appear to change because God programmed them to represent it differently in a set sequence. Crucially, Leibniz rejects the notions of space and time as separate, independent phenomena on the grounds that if space and time were real, there would be no sufficient reason to explain why certain representations appear in a particular space rather than one millimeter to the left or right, or why representations appear at a particular time rather than one millisecond before or after. Instead, space and time are said to be nothing more than monadic representations, with each monad projecting its particular space and time in accordance with its complete individual concept.

Recall that the principle of the complete individual concept states that all substances (i.e. monads) contain all predicates of themselves past, present, and future. According to Leibniz, this is made possible by God, who, at the moment of creation, pre-programmed all monads in such a way that all of their future perceptions and appetitions would perfectly synchronize with one another in a “pre-established harmony.” With this assertion, Leibniz denies the existence of causality, which he says cannot withstand the principle of sufficient reason. In a rebuke to Cartesian dualism, Leibniz holds that there is no way to explain how two dissimilar entities, e.g. body and mind, can influence each other — there is no mechanism, or sufficient reason. The reality must therefore be that they do not influence each other, and that they are merely programmed by God to give the appearance of influencing each other, in much the same way as two clocks are wound in advance to tick in sync with each other, to use another famous Leibniz analogy. Thus, while every monad is a “mirror of God” reflecting “the whole universe,” monads are in reality “worlds apart,” being “windowless” substances that do not admit of any influence in or out. Indeed, “monad” is derived from the greek monos, meaning alone or solitary.

To complete our account of Leibnizian metaphysics, we must answer a final question: how do we know that God is real and acts as Leibniz posits? In his proof of God’s existence, Leibniz infers that since everything happens for a reason, there must have been a first reasoner responsible for all subsequent reason, akin to Aristotle’s “first mover” argument and Aquinas’s “first cause” thesis. Without a first, we are faced with an allegedly illogical infinite regression (of reasoners, or movers, or causes) that cannot explain how anything came to be without resorting to a prior being whose being in turn depends on a prior being and so on, leaving being without a sufficient reason. Leibniz designates God as this first being and reasoner, who is by extension omnipotent (as creator of being) and omniscient (as creator of knowledge). What follows is that God qua reasoner does not create arbitrarily, but for a reason. And since rationality dictates that one should choose what is best, God, being all-powerful and all-knowing, must have created “the best possible world” for us. Against critics who cite evil as an invalidation of this thesis, Leibniz argues that some amount of evil is metaphysically necessary: since omnipotence and omniscience may only belong to one being (i.e. God), all humans possess imperfect strength and knowledge, predisposing them to weaknesses of the will and erroneous judgement.

Despite these limitations, Leibniz believes that humans are capable of self-improvement. In Leibniz’s hierarchy of monads, bare monads such as inanimate objects and plants merely represent the world, whereas souled monads such as animals and humans are capable of sensation and memory. Only human souls are capable of apperception, or self-awareness. This apperception is a prerequisite to morality: without a sense of self, one is incapable of feeling a sense of responsibility for one’s actions. Human beings, having such self-hood, are uniquely moral beings.

As a moral intellectualist, Leibniz equates moral goodness with reason, which he says teaches us what ought to be willed. According to Leibniz, reason dictates that humans naturally prefer harmony to discord and that it is therefore rational for us to concern ourselves with the well-being of others. This rational compassion is reflected in Leibniz’s conception of love, which he defines as “taking pleasure in the happiness, or perfection, of another.”

Whether this ethical project is possible given the implications of Leibniz’s metaphysics on free will is a matter of controversy. If everything is pre-programmed by God, is there any room left for moral choice? In a way that mirrors both Spinoza and the Stoics, Leibniz seems to suggest that free will lies paradoxically in reflecting on the nature of determinism. By recognizing that God, being capable of doing only the best, made all monads and their perceptions and appetitions in a choiceworthy manner, one may take solace in the natural unfolding of the universe, knowing that it accords with divine reason. In doing so, one is able to maintain equanimity in times of both joy and suffering and secure what Leibniz regarded as “the greatest cause of his philosophizing”: peace of mind.