Thursday, January 31, 2013

Modern European Philosophy: Rationalism - Descartes, Spinoza & Leibniz

Rationalism vs. Empiricism

Last time, we covered the rise of Europe and the Enlightenment as a golden age that followed similar golden ages in China and the Middle East.  We then spoke of the divide between the Analytic and Continental traditions, and how the former is dogmatic and the later skeptical relative to each other.  In the beginnings of Modern European philosophy, there was a similar split between two groups, one leaning dogmatically and the other skeptically.

By 1700 CE, Europe had become powerful and wealthy, and with this came a surge of new developments in science and technology that overturned many older preconceptions, assumptions and understandings.  Some Europeans interpreted this dogmatically, arguing that science had discovered unshakable truth, while others interpreted this skeptically, arguing that science had uncovered the impermanence and and ignorance of human understandings.  In the first camp were the Rationalists, such as Descartes, Spinoza and Leibniz, who argued that reason can eliminate problems to reveal the uncontradicted truth.  Rationalism will be our topic for today.  In the second camp were the Empiricists, such as Locke, Hume and Berkeley (though Berkeley is sometimes considered an Idealist), who argued that all understandings are based on experience, and experience is always limited.  Empiricism will be our topic for next time.

Both sides believed in the value of pursuing greater understandings through philosophy and science, and that this involves both reason and experience.  However, the Rationalists stressed reason’s independence of experience, arguing that universal truth can be determined independently of and prior to experience, while the Empiricists stressed reason’s dependence on experience, arguing that understandings are determined after and depending on experience.  Rationalists argued that, like mathematics, philosophy and science can determine absolute universal principles, and then from these proceed to additional truths that will be absolute and universal.

Consider one of Descartes’ central examples which he uses to support Rationalism, that two plus three equals five.  If I know this, and also that five plus six equals eleven, then I can put the two together to reason that two plus three (which is five) plus six equals eleven.  I can do this regardless of and prior to experiences with sets of two or three things.  Empiricists would agree that “two plus three equals five” is a useful understanding, but that it is true given that we continue to experience it as true, not because reason determines it to be true regardless of experience.  Empiricists argued that, unlike simple arithmetic, philosophy and science are complex and contingent, dependent on time and place, and so cannot prove understandings to be absolute or universal.

In the Ancient Greek Philosophy class, we cover skepticism and the works of Sextus Empiricus.  Sextus argues that there are two fundamental modes skeptics can use to question all human understandings.  Things must either be known in themselves independently, or known via something else dependently.  If things are known in themselves, it results in circular reasoning.  How can we know someone speaks the truth based solely on their own testimony?  If things are known in something other than themselves, it results in infinite regress.  How can we know someone speaks the truth based on the testimony of another, as that testimony would require another to verify it, and then another and another.  Things can be relatively known in themselves and through other things, but they cannot be known absolutely without escaping the dual problem of circular reasoning and infinite regress.

Descartes the Rationalist was well aware of Sextus’ skepticism, known as Pyrrhonism after Pyrrho, the ancient Greek skeptic who traveled with Alexander the Great to India.  Descartes considered Pyrrhonism to be a threat to rationality, and the Catholic Church did occasionally use Pyrrhonism to attack discoveries in science that countered orthodox dogmas.  Similar to attacks on the theory of global warming today, the Catholic theologians argued that all human understandings are mere theory, which is true but no reason to question specific theories and uphold others.  Descartes believed that he could refute Pyrrhonism by starting with consciousness, which he considered to unquestionably exist, writing, “I think, therefore I am”.  He could then proceed as a Rationalist from this single irrefutable truth to prove the understandings of both science and the Catholic Church.

Hume the Empiricist was also well aware of Pyrrhonism.  Hume argued that all human understandings are assumptions, habits, and prejudices formed from experience, and that we would all be Pyrrhonians, skeptical yet practical with each and every understanding, if our nature were not too strong for it.  For Hume, understandings, which are always assumptions based on experience, can become so entrenched that we fail to remember that they are not universal or dictated by pure reason.  Kant, who we will study after the Empiricists, was “awoken from dogmatic slumbers” by Hume, and attempted to, like Descartes, overcome the challenge of Pyrrhonism by appealing to reason apart from all experience.  Hegel, who we will study after Kant, attempted to fuse the dogmatism of Kant and the skepticism of Hume together to form what he believed was the full true philosophy.  Of course, we are getting ahead of ourselves, and must start first with Descartes and his fellow Rationalists.


RENE DESCARTES (1596-1650) is known as the first great modern European philosopher.  He is known for the first canonical modern European philosophy texts, his Discourse on Method and his Meditations, and also in mathematics for the Cartesian coordinate system (X and Y as two dimensions), a device useful for algebra and critical for the later European development of calculus by Newton and Leibniz.

Descartes was born in Touraine, France, a town which has since been renamed ‘Descartes’ after its most famous citizen.  Descartes’ father was a member of parliament, though his mother died when he was very young.  He went to law school to follow his father and become a merchant, but decided to become a mercenary instead travel and fight in the 30 years war, ‘to seek truth’.  It seems that he did not find truth in law school.  As a soldier, he had much time waiting for battle, and studied mathematics and science in his spare time.  On the night of November 10th, 1619, Descartes had a series of visions that convinced him that the world is a rational and mechanical system profoundly in tune with the rationality of the human mind.

At first, he intended on writing books on physics, but in 1633 Galileo was condemned by the Church for his solar-centric theory, the idea that the earth moves around the sun, which India and Islam had for more than 700 years.  Interestingly, many put the sun at the center of the universe, replacing the earth as center.  Because of Galileo’s troubles, Descartes decided not to publish his views on physics, his Treatise on the World, but his ‘Discourse on Method’, his philosophy text, instead, and it is today considered the first work of modern European philosophy.  This caution did not spare Descartes however, as the work was condemned by the Pope in 1663, thirty years after Galileo’s work was condemned and after Descartes’ death, and put on the prohibited index of books alongside other authors who are foundational for European scholarship.  Like Aquinas, even though Descartes argued that reason teaches us that the Catholic Church is the one true religion and there is a monotheistic god, his heresy was teaching that it is reason that shows us this, not the institution of the Church.  Descartes remained a practicing Catholic until his death.

Descartes’ death is famous and unfortunately funny.  For the majority of his life, he worked in bed until noon each day, an aristocrat who had the time and leisure to do this.  After he became famous and his works were prohibited by the Catholic Church, the Protestant Queen Christina of Sweden invited him to Stockholm to be her private tutor.  Unfortunately for Descartes, she wanted morning lessons, each and every morning at five o'clock.  Between the snow and the early mornings, Descartes was soon sick with pneumonia, and died.  Maybe we should all work on our problems every day until noon, safe in bed.  This is similar to Francis Bacon’s famous death, catching pneumonia after repeatedly stuffing snow into chickens to try to preserve the meat and keep it from rotting.  Some have argued that Descartes was killed with a poisoned communion wafer given by a priest who feared Descartes’ Rationalism, but the sources on this are questionable, and it is likely this story was invented by Swedish protestants.

Descartes’ philosophical writings, particularly the Meditations, drew the reactions of several philosophers who themselves went on to become famous, particularly Spinoza, Hobbes, Hume, Leibniz, and Locke.  In the Meditations, Descartes asks: What we can know for certain if it is possible that everything is an illusion of the mind?  Like Avicenna, Descartes concludes that we can be certain that we are aware and conscious.  From this, he proceeds to conclude that we can be certain that our thoughts are our own, that the world is real, that there are regularities in the world that we can know for certain, and that there is a good and loving monotheistic god who would not deceive us about these things.

Some philosophers agreed with this very much, but did not find Descartes’ argument convincing and tried to come up with more satisfying proofs. Other philosophers who were more skeptical, such as Hume, did not buy it and argued that human truth and certainty is always, in some way, an assumption.  The two sides of the debate became known as Rationalism and Empiricism.

Descartes, in a world of increasing algebra and mechanics, turns from an understanding of causes up in the heavens to cause as the mechanics of this world.  Just like many Islamic and medieval European thinkers, Descartes identifies the mind and heavens with freedom and consciousness while putting the mathematical order of things down in the world.  The heavens remain the good and pure, but the order and mathematics becomes a thing of this world and not the heavens above, a conception ancient civilizations got from watching the stars and seasons.  This change, which is very modern, comes with a world increasingly full of algebra and mechanics.  While Descartes argued that a monotheistic god clearly created the world, as reason tells us all things have causes, he was condemned like Hobbes, Newton and others for arguing that nature works like a machine, and once caused proceeds largely on its own.

Descartes argued that the natural world, including animals and human bodies, nothing but mechanics and causation, completely devoid of intention or feelings that require a mind.  Descartes argues for a radical dualism, an exclusive division, between the mechanics of the world below (body) and the consciousness and intention of the world above (mind).  Consciousness or mind or spirit is in the upper world, while all in the given world is mindless mechanics.  The worst consequence of this was that Descartes practiced vivisection, cutting animals apart while alive to learn about anatomy, and helped popularize the practice in Europe, arguing that animals do not have minds and thus do not feel a thing, their behavior being mere automatic reflexes of causal forces.  Descartes even argued that the belief that animals can have conscious sensations is one of the worst errors possible, a great hindrance to science and rationality.

In his Discourse on Method, he lays out the famous “I think therefore I am” thought experiment, remarkably similar to Avicenna’s Floating Man thought experiment.  In the beginning of the work, Descartes says he won’t tell us about his first meditations, “for they are so abstract and unusual that they will probably not be to the taste of everyone”.  He starts with the meditations he will tell us about.  Descartes argues that we all accept things that we believe to be certain, but sometimes these then turn out to be wrong.  Therefore, we cannot use certainty as the sole criterion for truth.  We have to separate out the categorically certain from the seemingly certain.

Descartes says that it seems certain that he is sitting by the fire writing, but we can doubt this and believe that Descartes is simply dreaming that he is Descartes, by the fire.  He uses the example of madmen who think that they are kings or that their bodies are made out of glass.  Obviously, Descartes had some familiarity with at least literature about types of madness and delusions, as did Avicenna, who understood imagination and mental conditions such as hysteria and hallucinations.  King Charles the Sixth (VI), also known as Charles the Mad, ruled France until 1422.  He would sometimes forget his own name and run through his castle believing himself to be a wolf.  Also, he was afraid of being touched by others, fearing that he was made of glass.  When Descartes says that his audience is familiar with instances of insanity such as people believing they are made of glass, he is referring to Charles VI without needing to mention his name.

Let us remember Avicenna’s floating man thought experiment, in which he suggests that the reader imagine floating in a void and having all sensation, including of the body or senses, slowly taken away.  What are you left with as the essential factor once the accidental sensual factors are removed?  Self consciousness, with the awareness of consciousness and mind itself.  For Avicenna, as for Descartes, this awareness and self-circling is the small piece of God, the big all awareness, that is one’s soul, humanity and life.  Descartes proposes a very similar thought experiment.  He asks the reader to imagine that there is a deceiving demon that is trapping us in an illusion of a world, casting doubt on everything except the essence of the human being and soul, the self-awareness which Descartes believes must exist.  Thus, his famous line:  “I think, therefore I am”.

Where does the deceiving demon of Descartes come from?  Why the radical psychological skepticism, and then the simple positive affirmation?  To see this, we must speak of the Cathars, a Gnostic Christian and Manichean heresy that was being persecuted in France in the 1400s.  Descartes is writing in France in the late 1600s, two hundred years later.  Gnosticism spoke of a deceiving demon false god, the devil, that controls the appearance of this false world below, similar to the Indian doctrine of the world below as not only evil but illusion and false.  Manichaeism was a religion started by a Syrian named Mani (200-276 CE), who claimed to be the final coming of Jesus, the third Persian Zoroastrian saoshyant, and the Buddha Amitaba, the messiahs of three great religious traditions.  Buddhism and Christianity flourished in Syria and Afghanistan as a middle ground of cultures, where they were both in contact with ancient Persian Zoroastrianism, then later Islam.  The religion spread up through Europe in 300 CE, and the Cathars were an offshoot that survived in France up until the persecutions of 1400s.

Thus, Descartes (the first modern philosopher) is arguing for Christianity and its simple positive faith in the world vs. the Cathar-Manichean-Gnostic deceiving demon.  Notice that Descartes’ thought experiment suggests that a Demon could not keep us in the dark the way the Cathars believe.  Instead, because of our consciousness/mind/soul that we get from God, and then using this as an anchor of certainty, Descartes argues that God does not completely deceive us in this world, and thus we can know certain truth in the name of both science and religion.

There do seem to be universal truths that cannot be untrue in any situation, like 2 + 3 is equal to 5, or a square always has 4 sides, both examples Descartes uses.  Notice that both of these are mathematical examples.  However, we can even imagine that this itself is all delusion.  Hence, we assume for skepticism’s sake that there could be a deceiving demon (much like in the movie The Matrix).  He also says it could be someone extremely powerful who could use ‘industry’ to deceive me.  This is the “brain in a vat” mad scientist thought experiment used today rather than a demon in philosophy classrooms.  The demon or mad scientist can convince me of many false things, but they cannot convince me that I do not exist, and so I am certainly an existent thing that thinks.  The one point of certainty is self-awareness or consciousness, the one thing that we cannot be fooled about because it is self-evident.

Because we are sure of this, and because we get our truth from something that we are within, Descartes argues that we are not in the power of something that completely lies to us.  Descartes then quickly, and without much of a convincing argument, declares that we can trust that God is good, the world is not an illusion and 2 + 3 is equal to 5.  When we aspire to God and truth, using reason correctly, we discover certain truths, such as the truths of mathematics, the sciences, the existence of the soul, and of God, the certainty that the body is not our true self, and that animals do not have souls or awareness.  Note that everyone after Descartes found this reasoning a bit too quick and slim, both those who agreed with him and those who did not.  Note also that Descartes starts off saying he will be entirely skeptical of all truth to beat Pyrrhonians at their own game, but then concludes that we should believe what religion and science tell us.

I did not give you Descartes’ Meditations for this class, as I found a work that scholars have rediscovered, Descartes’ Principles of Philosophy.  In this work, Descartes carefully sets out the same argument he put forward in the Meditations, clearly aware that his earlier work was not rigorous enough and invited criticism.  As in the Meditations, Descartes argued that to seek truth one must start by doubting everything that can be doubted, and considering the case that everything that can be doubted is in fact false.  Even mathematics can be doubted, as mistakes in math are made all the time.  We have the freedom of will to doubt anything, no matter how certain it may seem.  What can be known in this extreme case?  While the body can be doubted (note the similarity to Avicenna), the mind’s awareness cannot, and hence things which seem self-evident can be counted as simply known in themselves, and must come from a source that is most certain, which is God.  While some are prejudiced and thus prevented from believing in the certainty of God and mathematics, reason necessarily leads us to affirm these as certain.


Baruch Spinoza (1632 - 1677 CE) was born in the Portuguese Sephardic Jewish community of Amsterdam, and was thus Jewish, Portuguese, and Dutch.  Jews had fled from Spain and Portugal to nearby lands during the Spanish Inquisition of 1492 and the Portuguese Inquisition of 1536.  If 1492 is a familiar date, that is because it is the year that Christians retook Spain from Muslims, and also the year Columbus chose to leave Spain and sail as far around the world as he could.  While Jews thrived in Spain and Portugal under Islamic rule, often occupying high places in the government, education, science and medicine, the Christians had not yet learned to be tolerant or multicultural.  The Portuguese Inquisition that caused Spinoza’s own Jewish community to flee to Amsterdam happened only a hundred years before his birth.  Some scholars argue that the Portuguese Spinoza family was originally of the Spanish Espinosa family, some of whom fled to Portugal to avoid the Spanish Inquisition while others remained in Spain and converted to Catholicism.  If this is true, Spinoza’s family successfully fled both inquisitions.

Spinoza was not only a great philosopher, but also a scientist, mathematician, and early scholar of serious biblical criticism, studying the bible critically to understand and interpret it’s authorship, meaning, and historical context.  Spinoza’s views of the bible and its authorship, radical for the time, got him not only kicked out of his Jewish community at the age of 23, but ostracized by the surrounding Christian community of Amsterdam.  Like Descartes’ work, his work was put on the Catholic Index of Forbidden Books.  He was also attacked as he was leaving synagog by a man with a knife who yelled out, “Heretic!”, and Spinoza wore his cloak with a tear made by the knife for years afterwards as a badge of honor.  Because Spinoza believed in undertaking philosophy and science rather than performing ritual, and because he never converted to Christianity, he is considered by some to have been one of the first secular Jews of Europe.

Amongst other radical views that I will discuss as we examine his philosophy, Spinoza was one of the first European biblical scholars to question the traditional understanding that the first five books of the Old Testament, for Jews the Torah, the only testament, were not written by Moses.  At the time, they were still known as the five ‘Mosaic Books’, until Spinoza and others pointed out that not only did the book of Exodus speak about Moses in the third person, but Moses dies near the end of the book of Exodus, making his authorship of the book quite questionable.  Islamic scholars had noted this centuries earlier.

After having been banished from Amsterdam for a brief period and then returning, Spinoza lived as a lens grinder, making lenses for telescopes and microscopes, turning down several teaching positions for a quiet and private life.  Because Spinoza died at the relatively young age of forty four from an unknown lung condition, it is suspected that his death was in part caused by glass dust inhaled while grinding.  He was known as an outstanding producer of lenses, and these were used by scientists in the fields of optics, astronomy and medicine during the European enlightenment as they had been used in earlier forms by Islamic scientists.

After writing several short works on science, theology, and philosophy, particularly criticism of the work of Descartes, Spinoza wrote his masterpiece, the Ethics, which was only published after his death and written in Latin, as was most European scholarship for centuries.  Leibniz, who we will examine next, visited Spinoza and discussed the Ethics as yet unpublished, and according to some after Leibniz returned to Germany he plagiarized parts of the work and published them interspersed with his own without giving Spinoza credit.  Whether or not there was plagiarism, Leibniz was clearly influenced by Spinoza.  There are many instances in philosophy, both ancient and modern, of duplicated work that dances on the boundary between illegitimate plagiarism and legitimate influence.  Philosophers often fail to mention names when using ideas in the sequence of an argument.

Although Spinoza was interested in investigation and observation of the sciences, he was drawn to Rationalism and mathematics.  His Ethics is an attempt to do philosophy as a formal Euclidean geometric proof.  Euclid, the ancient Greek mathematician, is known for his geometric proofs, by which he proceeded from assumptions and principles to deduce conclusions that necessarily follow.  While Euclid did not have equations, which were invented with Algebra by Islamic mathematicians who drew on Indian symbolic mathematics as well as the work of Euclid, he worked systematically much in the way that mathematical and logical proofs work, and Spinoza attempted to follow Euclid’s method to make his thinking rigorous and sound.  This is why he is known as a Rationalist, falling under the same heading as Descartes.

Central to the work, Spinoza attacked Cartesian dualism (the dualism of Descartes), arguing that mind (also spirit) and body are not two but one, an anti-dualist position known as monism.  When teaching about ancient thought, I often use the term ‘philosophical monism’ to label the belief that all things are part of a great One without any entirely exclusive divisions.  This was not only central to the thinking of much Indian thought, of Chinese Daoism and Greek skepticism, but also to some medieval Islamic and European Neoplatonists, such as the Irish philosopher Eriugena who lived almost a thousand years before Spinoza in nearby Ireland and France.  While dogmatic and conservative thought tends to justify traditional divisions as exclusive, skeptical and progressive thought tends to attack traditional divisions and attempt to be inclusive in nontraditional ways.

For Spinoza, there is only one unified reality, which he identified with God, and any difference or separation is ignorance and misunderstanding.  What are perceived to be distinctions are really various modes and perspectives within the unified whole, an understanding quite similar to Eriugena and other European Neoplatonists who were influenced by Eriugena such as Nicholas of Cusa.  Each individual thing, including minds, are like a wave on the sea.  Nature, indeed all of Being, is God, a pantheism that infuriated the traditionally religious and got Spinoza barred as a heretic by both his Jewish community and the larger Christian community of Amsterdam.

In fact, right wing evangelical Christians in America today have taken to attacking the environmental movement as satanically inspired pantheism, a heretical worship of nature rather than of a god that created nature but is separate and distinct from it.  As a counterpoint to that, on the Eric Andre show (a surreal comedy skit show hosted by a guy who likes to crash through walls and furniture), he interviews famed 80s action-movie actor Dolph Lundgren, and, suddenly cutting off Lundgren as he is talking about his Nordic “rapist blood”, asks him if he believes in God.  Lundgren replies, “Well, there’s rocks and trees”, and trails off as Andre sits watching him, nodding thoughtfully, before suddenly and violently karate-chopping a birthday cake in two with his bare hand.

Like American and European deists, some of whom were American Founding Fathers, Spinoza believed that doing philosophy and science was the method of achieving greater visions of the whole through reason and thus regaining one’s identity with the whole.  Spinoza argued that God is not personal but abstract and transcendent, and he argued against the immortality of the soul, all of which helped to label him as a heretic.  Like Jains and Buddhists of ancient India (and modern everywhere), Spinoza believed that the self as an exclusive separate thing dissipates back into the whole, but the individual lives on in that with which they have come to identify.  This would mean that Isaac Newton would not live on as Isaac, but as a greater soul who had come to understand gravity he would live on not as an individual but as gravity and the eternal ways of the cosmos.  Unlike Jains and Buddhists, Spinoza did not believe in stages of reincarnation.

Spinoza believed that reality, which is nature and God, is one substance.  Like waves on an ocean, all particular beings are modes or situations of this substance which are linked together by chains of causation.  Spinoza was a determinist, and believed that there was no real freedom or chance in the universe.  The will and mind of God was not the personal care of an emotional being with a personality, but the causal workings and design of nature.  Much like pre-chaos theory science, reason reveals the necessary causal connections between things.  Spinoza argued that human beings, like Descartes, believe in free will because they are aware of desires but do not understand the reasons behind these desires, and so they perceive the gap as freedom when in fact there is none, as the great rational mind is the necessary process of all things.

Just because there is no free will does not mean that human beings have no degree of control over their actions.  Indeed, if one understands the causes of one’s behavior and situation with reason, this gives one greater ability to act in various ways.  If one has a greater exercise of reason, one will naturally be determined to take a better path that one may not have been aware of before.  Spinoza noted that people who are driven by passions, such as the baby seeking the breast, the cruel boy who lashes out at others, and the drunk who seeks more to drink, all feel that they are free because they do not understand the forces that determine their actions.  

In this sense, one gains freedom by reason, but much as immortality is not immortality for the individual but the individual conforming to nature, so too is freedom not freedom for the individual but the individual conforming to nature, becoming more capable.  Scholars have noted that this is similar to Daoism of ancient China and Stoicism of ancient Greece and Rome.  As we become more active, we become the universe, the sum of all activity.  Like the Mutazilites of Islam, who believed that God is reason and the necessary logic of all being, Spinoza was committed to the position that God is not free to be illogical or be contradictory, but as the sum of all activity this absolutely determined being is the sum of all freedom.

Hegel was a big fan of Spinoza, writing in his History of Philosophy that one could not be a legitimate philosopher without being a Spinozist.  Considering Hegel geared his system to overcome and synthesize all dualisms, such as those he saw left incomplete by Kant, Hegel was of the opinion that Spinoza’s monism had overcome Descartes’ dualism just as his own monism had overcome Kant’s dualism.  Deleuze, a French postmodernist we will study at the very end of the course, called Spinoza the prince of philosophers.  Indeed, for many thinkers skeptical of exclusive dualist distinctions, Spinoza’s opposition to the dualism of Descartes became one of the first glorious moments of European thought.  I was myself quite inspired by Spinoza as an undergraduate philosophy major.

Einstein, who said that Spinoza had more influence on his views than any other philosopher, when asked if he believed in God, said, “I believe in Spinoza’s God”.  A determinist like Spinoza, Einstein argued against the chaos theorists who would surpass his work on relativity saying, “God doesn’t play dice with the universe”.  According to chaos theory, Einstein was right that time and space are relative, but he did not see that necessity and chance are also relative, and thus the absolute determinism of Spinoza and Einstein is impossible.


Gottfried Wilhelm Leibniz (1646 - 1716 CE) was a German philosopher and mathematician who, as mentioned, 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 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, 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 quite in line with Christianity.  Also an admirer of the Chinese abacus, Leibniz was one of the most important innovators of the mechanical calculator, the reason for which he invented his binary system.

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, unlike the Empiricists, this meant the world was very unlike how we experience it.

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 a mass of distinct plurality, 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.  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.  It seems similar to Frege and set theory, which we will study later with Logical Positivism.

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 but rather 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.  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.

There are several principles Leibniz draws upon again and again.  One is the principle of identity or noncontradiction: if a statement is true, then its negation is false, and if a statement is false, then its negation is true.  Kant and Russell, both like Leibniz fans of logic and the principle of noncontradiction, studied the work of Leibniz intensely, advocating his principles, which are often staples of dogmatic thought.  Another central principle of Leibniz’s is the Identity of indiscernibles: if 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 reason: if something exists, there must be a good enough reason that it exists and is the way it is.  Of course, Leibniz, as 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, quite teleologically, that each thing can be rationally explained because each thing was rationally created.

In the text I gave you by Leibniz, The Principles of Nature and of Grace Based on Reason, he argues against the Cartesians by name (the followers of Descartes), writing 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 next time) 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.  Hume, the Empiricist and skeptic, would agree, but argue that we are all dogs even when we are at our most rational, only capable of using reason in terms of experience.