Gottfried Wilhelm Leibniz (1646 – 1716 CE) was a German philosopher and mathematician who invented calculus at the same time as Newton and we still use his system of notation.  His first job was as an alchemist’s assistant, then he became a lawyer’s assistant.  As also mentioned, he met Spinoza, and though the two disagreed on much, Leibniz is known to have borrowed, possibly plagiarized, parts of Spinoza’s Ethics.  Leibniz published little during his lifetime, and to this day no definitive collection exists of his various and disparate writings.  His most famous writings are his Monadology and his Discourse on Metaphysics.

Leibniz calculator

Leibniz invented the binary system still used by computers today, which may or may not give way to something else like quantum computers in the near future.  Leibniz was a sinophile (one who loves Chinese culture), studied Chinese thought, at least that which was available to him, and invented his binary system inspired in part by the Yi Jing divination system, the ancient Chinese binary divination system that represents all possible situations with solid and broken lines just as Leibniz’s binary system represents all numbers with ones and zeros.  Leibniz was communicating with Christian missionaries in China, and he, like some of the missionaries, believed that Europeans could learn much from Confucianism that was in line with Christianity.  Also an admirer of the Chinese abacus, Leibniz was one of the most important innovators of the mechanical calculator, an early computer which employed his binary system.

william blake great architect demiurge gnostic

Like Descartes and Spinoza, Leibniz believed that God created the world as a rational, mechanical apparatus.  Because of this, Leibniz famously argued that this is the best of all possible worlds.  As God is omniscient, God was aware of all possible worlds before creation, and chose this to be the created world, so it must therefore be the best.  Of course, many who ponder the problem of evil, the theological problem debated for centuries about how suffering in a rational world is possible, would question this assertion.  Like Spinoza, Leibniz tried to come up with pure deductive understanding of the world.  Unfortunately this meant the world was very unlike how we experience it.

kanada atomist

The infinite, the eternal, is for the mathematician Leibniz an infinite series of distinct points, not a unity beyond all division as it is for Spinoza.  These are the elementary particles of the universe, eternal and indivisible, like the atoms (“without cut”) of the ancient Indian and Greek atomists.  Unlike the ancient Indian and Greek atoms, however, Leibniz’s points are individual minds he calls monads.  This infinite plurality is entirely made of mind, yet they are many exclusively as opposed to Spinoza’s anti-dualist monistic God-mind.  It seems as if the minds perceive each other imperfectly, but in actuality they do not interact.  Each is its entire universe.  In what Leibniz calls a pre-established harmony, each monad was set apart from the central monad, God, and when the monads split and became individuals, they were set in motion such that they could all run independently but seem to share a universe and interact.  Space, matter and motion are subjective phenomena, not objectively real.  Notice how this follows Descartes insofar as all can be doubted other than mind, and that mathematics is given as true by virtue of the essentially quantitative nature of being.

George Berkeley

While there are similarities to Descartes, it is also similar to Berkeley the idealist, who thinks reality is God’s dream, and we are dreams within the dream, except in this case, we are each having God’s dream, but separate from God and each other, each privately having the same dream but not contained within a single dream.  Rather, each dreamer is derived from the original dream, each an individual dubbed copy.  Notice that for Spinoza and Berkeley, there is an underlying identity with God which allows the individual be eternal, while in Leibniz, it is the underlying complete separation that allows the individual to be eternal, unlike any substance, which is an illusion, but like the original mama Monad, and like the infinite nature of the endless series of numerals (1, 2, 3…).  It is also similar to Indra’s net of the Indian tradition, a net of mirrors that all reflect each other, a metaphor that Leibniz uses without referring to India or Indra.

Bertrand Russell pipe

There are several principles Leibniz draws upon again and again.  One is the Principle of Identity, also known as the Principle of Non-Contradiction (PNC)If a statement is true, then its negation is false, and if a statement is false, then its negation is true.  For example, if the statement, “Leibniz is a logician” is true, then the statement, “Leibniz is not a logician” is false, and vice versa.  Kant and Russell, advocates of logic and the principle of noncontradiction, studied the work of Leibniz intensely, advocating this principle.  In contrast, Hegel argued in his Logic that all things work by way of contradiction, of tension between opposites.  Another central principle of Leibniz’s is the Identity of IndiscerniblesIf two things are without any discernable difference, then they must be not two things, but identical, the same single thing.  Of course, if two things are in different locations or exist at different times, this is a discernable difference.  A third principle of Leibniz’s is the Principle of Sufficient ReasonIf something exists, there must be a reason why it exists the way it does.  Leibniz, a Rationalist, believes that the world was rationally created by God, who controls all in this best and most rational of all possible worlds, and so he assumes that each thing can be rationally explained because each thing was rationally created.

carlsbad caverns

This is a teleological view, what many call today intelligent design.  In the ancient world, as well as the early modern world of the Rationalist philosophers, the world and things in it were created with specific purposes, and so to understand the design of a thing is to understand it.  A Roman stoic author once wrote that he was terrified of a beautiful cavern because there was no one around to appreciate its beauty.  This was incomprehensible to him because beauty exists to be seen and appreciated, and so if a thing is hidden underground and goes unseen, there is no reason for it to be beautiful.  Today, many who do not believe in intelligent design still adhere to the Principle of Sufficient Reason, in spite of the fact that the universe does not need human reasons to exist.

diogenes with pot and dogs

In the Principles of Nature and of Grace Based on Reason, Leibniz argues, against the Cartesians by name, that they were mistaken to believe that animals do not possess minds or have sensations.  However, only human beings with reason can become not merely souls, but genuine, “sublime” spirits.  The Empiricists (who we will study in the next few weeks) are like beasts according to Leibniz, because they learn only from experience, like dogs afraid of a stick with which they have been beaten, rather than become sublime through the use of pure reason, like the Rationalists such as Leibniz himself.