Gottfried Wilhelm Leibniz


The German philosopher Leibniz (also spelled as Leibnitz) was one of the greatest minds of all time. He is also known as the ‘Aristotle of the Seventeenth Century’ because he touched nearly every subject under the sun. His works cover a broad range of topics such as mathematics, philosophy, theology, law, diplomacy, politics, history, philology, and physics. He invented calculus independently of Newton, and is considered the forefather of modern mathematical logic.

There are, however, two philosophical systems associated with Leibniz; one, which he proclaimed and publicized, the other that he kept to himself and was discovered from his manuscripts very later after his death. The former is shallow, and doesn’t reveal the real intellect of Leibniz. The latter philosophy is profound, consistent and logical.

Let us begin with Leibniz’s philosophy of substance. As we know, Descartes believed in two substances matter and mind, apart from God; Spinoza believed in only one substance, namely God, and considered extension and thought as two attributes of God. Leibniz, however, disagreed with both. He believed in an infinite number of substances, which he called ‘monads’. He didn’t consider extension to be an attribute of a substance, because extension involves plurality and could develop only as a result of aggregation of substances. Leibniz maintained that extension was divisible, but substance was not, therefore extension could not be ascribed to a substance. Each monad is unextended, and possesses only thought as its attribute. Hence, each monad is a soul. Each monad is an entelechy, and has in it a certain perfection and self-sufficiency.

Humans are composed wholly of monads, each of which is an immortal soul, but there is one dominant monad, which is the soul. Each monad is different from any other monad, and is continuously changing. These changes have an internal cause because nothing external can influence them. Leibniz retained the Cartesian notion that two substances cannot interact. This he expressed in his words that monads are ‘windowless’. So, all the apparent causal interactions between monads are deceptive and unreal. They only seem to affect each other because there is a ‘pre-established harmony’ between changes in one monad and another, which gives rise to the apparent interaction. As the reader will remember, this is an extension of the philosophy of ‘two clocks’ of Geulincx. Since it is odd that these infinite monads should be so precisely synchronized, Leibniz used it as a proof of the existence of God; there must have been a single outside cause, which regulated all the monads.

Leibniz doesn’t give only the pre-established harmony of monads as a proof of God’s existence. Having a sharper mind, he refined many of the old arguments of the existence of God. For example, he added to the Ontological argument the definition of perfection. He defined perfection as a ‘simple quality which is positive and absolute, and expresses without any limits whatever it does express.’ Using this definition, it was possible to show that no two perfections can be logically incompatible. However, even after the addition, the argument is still refutable by the fact that existence is not a predicate.

Another argument was the Cosmological argument. Leibniz proclaimed a belief in the law of sufficient reason [only in his popular philosophy; this law in his unpublished philosophy has a different statement], which states that there is no fact or truth that lacks a sufficient reason, why it should be so. Leibniz says that everything in the world is contingent i.e. it was logically possible for it not to exist, and therefore it doesn’t contain within itself any reason for its existence. Since, the whole of universe is contingent, there must be a sufficient reason outside the universe, which is the necessary being called God.

Kant maintained that this argument was based on the Ontological argument. If a necessary being exists, it must be a being whose essence involves existence, and this is how the Ontological argument defines God. It would be meaningless to call God the sufficient reason for the existence of the universe unless it is assumed that God is a being whose essence involves existence. Therefore, this argument, like the Ontological argument, is also not valid. Another common objection raised against this argument is that only propositions can be called logically necessary, and that it is a misuse of language to speak of a logically necessary being. Another powerful criticism is that the cosmological argument presents two possibilities: either there is a necessary being or the world is ultimately unintelligible[1]. The arguments proves the existence of God only if the second possibility has been ruled out, which it is not logically possible to rule out.

Leibniz denies the space as it appears to the senses, or the space assumed by Newtonian physics (i.e. absolute space). Location of an object is not a property of an independent space, but a property of the located object itself - and also of every other object relative to it. Consider Leibniz’s own example of leaves; there are two leaves which are absolutely identical. But if the two leaves are identical in all respects, there is no sufficient reason why one leaf is in one place, while the other leaf is in another place and not the other way. Leibniz points out that the location is a property of a monad, and since they are at two different positions, they are not the same leaves. Space (and time) are internal features of the complete concepts of things, and not extrinsic. Space and time are just ways of perceiving certain virtual relations between substances.

An important feature of Leibniz’s popular philosophy is the idea of ‘the best of all possible worlds’. A world is ‘possible’ if it doesn’t contradict the laws of logic. God thought about all these worlds before creating this actual world. Since God is good, He wished to create the best world, but the best world is not a world in which there is no evil, but in which there is the greatest excess of good over evil. There could have been a world in which there was no evil, but that would also not have contained much good, because many goods are associated with certain evils. So, although this world contains evil, it has the greatest excess of good over evil than any other possible world. Therefore, this is ‘the best of all possible worlds’[2]. This also explains the connection of sin and free will. Free will is good, but it is logically impossible that free will exists, and sin doesn’t.

This philosophy of best possible world was extremely ridiculed by Voltaire, who wrote the short novel Candide as a satire. Leibniz was caricaturized as Doctor Pangloss:

'Pangloss was professor of metaphysicotheologicocosmonigology …. “It is demonstrable,” said he, “that all is necessarily for the best end. Observe that the nose has been formed to bear spectacles…legs were visibly designed for stockings…stones were designed to construct castles…pigs were made so that we might have pork all the year round. Consequently…all is for the best.'[3]

This doctrine of best of all possible worlds, although logically possible, is not necessary. A person can create a parallel argument claiming that this was the worst of all possible worlds, and good is present because certain evils are bound up with good. Good men exist so that the wicked can punish them, and this sin of punishing would not have existed had good men not existed. This idea, although highly incredible, is also logically possible! Leibniz realizes that this world contains both good and evil, but his assumption that the good preponderates evil has no justification, and is open to debate.

Let us now see certain elements of Leibniz’s unpublished philosophy. It gives a perfect example of the importance of logic in philosophy, and Leibniz uses logic as a basis of his metaphysics. An ‘analytic’ proposition is one in which the predicate is a part of the subject e.g. ‘All mortal men are men.’ Leibniz uses two logical principles. The first is the law of contradiction, which states that all analytic propositions are true. The second is the law of sufficient reason according to which all true propositions are analytic. But consider the proposition ‘John went to London in 1981’. Does the subject contain the predicate in itself? Apparently no, but Leibniz says yes. All the sentences, which have ‘John’ as the subject, would have predicates describing whatever happens to John. The sum of all these predicates makes up the notion of ‘John’. Hence, John’s going to London in 1981 is a part of his notion, and therefore a part of the subject ‘John’. (John’s notion will include all the facts such as that John had an accident last year, that John is now working at his job, and that he will go to France next year.) Seen in this manner, the proposition ‘John went to London in 1981’ is analytic. Since all that happens to one in past, present or future is already contained in the subject, it means that all things have already been decided, and whatever is going to happen is eternally determined. Hence, there is no free will. As this idea was contrary to the Christian doctrine of sin, Leibniz carefully abstained from making it public to avoid unpopularity.

Leibniz’s esoteric philosophy also gives a different account of the creation of the world. His popular philosophy of the best of all possible worlds maintained that only that thing can exist which is compatible with the absolute goodness of the Creator, but here he takes a different position, without involving the concept of God. Leibniz states that two or more things can exist only in so far as they are “compossible” i.e. their existing together is not logically contradictory. Therefore, this world contains the largest group of compossible things. [Suppose that A is compossible with C, D and E; and B is compossible with F and G; and A and B are not compossible, then A will exist because it is compatible with larger number of objects.]


[1] Or, in other words, the world is ‘absurd’, as the Existentialists would later call it.
[2] English philosopher F.H. Bradley (1846–1924) sarcastically wrote: ‘The world is the best of all possible worlds, and everything in it is a necessary evil.’ [Appearance and Reality, Preface]
[3] Voltaire, Candide