Pythagoras. Mathematics and Mysticism

1. Pythagoras and his school

All right, let us turn to the last Presocratic school that we are going to look at this evening, which is the school of Pythagoras, the Pythagorean School.  Now Pythagoras flourished about 530 BC, so technically, he’s actually right after Thales in order, and prior to Parmenides and Heraclitus; he’s about sixty years after Thales in terms of flourishing.  But we have no idea what Pythagoras said as distinct from his followers because of the absence of documents, so it’s common simply to talk about the Pythagoreans as a school, and not attempt to differentiate which one was responsible for which particular idea.  And I may say, the Pythagoreans endured right on to the very end of pagan philosophy, and underwent various modifications in their views, so it’s common to talk about early, middle, and late Pythagoreans, but we’ll hover around middle Pythagoreans.


Now Pythagoras founded an enormously influential school; it had overwhelming effects on Plato, and of course, therefore, later on Christianity.  Neither Plato nor Christianity would have been possible without Pythagoras and his school, or some equivalent.

2. Pythagoreanism and the Orphic religion

Now basically, the early Pythagoreans at least were a mystic sect.  They lived communistically, without private property. They were, in effect, a religious order or brotherhood.  They were far and away the most other-worldly, the most mystic, of all of the Presocratics.  They are actually the first religious philosophers that we encounter in this course.  And therefore, I have to tell you at the outset something about the religion to which they subscribed.  They were not adherents of the religion of the gods of Olympus; they did not take the anthropomorphic view of the gods, the polytheistic view, and so on.  They represented a somewhat different—or rather, take out the “somewhat”—an enormously different trend in Greek religion.


They advocated what was called a mystery religion, which is much more religious than the Mt. Olympus divinities ever dreamed of.  This is really religious.  It was a rabid, mystic, supernaturalist cult in the early years, of a very primitive order.  And there were quite a number of them.  And the one that the Pythagoreans subscribed to was called the Orphic mystery religion.  So what did Orphicism teach?  Now Orphicism is not a philosophy; it’s an Oriental mystery cult imported into Greece, and advocated only by a minority (it was not the dominant viewpoint). 


Well, the Orphics preached tenets like this—Man has two parts, a high part and a low part.  The low part is the body, the high part is the soul.  These two are in eternal conflict with each other.  The soul is akin to God, to another dimension.  Once, it was a God-like creature, inhabiting another, superior, spiritual world.  But it sinned.  And the result was it fell from grace.  And, as a punishment, was included in the body on this earth.  The body is therefore the prison, or the tomb, of the soul.  And we are destined, each of us, to go through a series of reincarnations.  At the end of our earthly span, our soul goes back to the other world, and it gets its appropriate reward or punishment (depending upon its behavior), and then it comes around again, what they call the “wheel of birth.”  Sometimes it comes up in another human body, sometimes in an animal body.  It lives out its cycle, and goes back again, round and round the wheel of birth, until (and this was their ultimate hope) the soul can escape from the body and this earth permanently, reunite once and for all with God, and thereby achieve true happiness and salvation.  In effect, the idea was, go back home. 


How do you get to do it? Well, they said, you have to engage in a process they called purification.  That’s essentially a process of decontaminating the soul of any physical influences.  You have to live a good life, which means essentially an ascetic life, a pleasure-denying life.  Now, I remind you, we are in ancient Greece, and therefore the Pythagoreans at their most ascetic are frenzied hedonists in comparison to the Christians that are yet to come.  But nevertheless, they made a start.  And, of course, you must also engage in the rituals of the Orphic mystery religion.  Now in the early days, these rituals included something on the order of what goes on and off Broadway now—mass orgies, intoxication, frenzied dancing, secret initiation rites (that’s why they were called mystery religions)—it was highly primitive, to say the least. 


Here’s a description from one commentator.  Orphicism worshipped the god Dionysus, and he describes it as follows.  Now, in an act of heroic self-abnegation, I will steadfastly abstain from commenting or drawing parallels to any subsequent Western religion:


“The god Dionysus was elaborated in the Orphic mysteries.  Originally a Thracian deity of vegetation, and particularly of the vine and wine, and of the sense of liberation from human bondage that intoxication bestows, he was worshipped in the beginning by orgiastic rites of frenzied dancing and drunkenness.  Probably in the beginning, his priest (in whom he was supposed to be incarnate) was sacrificed and eaten by his worshippers, who thus partook of the manna, or strength, of their god.  But before the cult entered Greece, the sacrifice of the priest had given way to that of a sacred animal—the wild bull—which now became the vehicle for communicating the divine substance of the god to his devotees.”


“Brought down into Greece from the north, his cult became more civilized and developed a complicated theology.  First begotten by Zeus from a divine mother, Persephone, he [Dionysus] was slain in the form of a wild bull by the evil Titans, and was torn to pieces and devoured by them.  But his heart was saved.  This Zeus ate and begot him a second time from a human mother, Semele.  She, demanding to see her divine lover face to face, was consumed by a thunder bolt.  Her unborn child was preserved and placed in the thigh of Zeus, from which, in the fullness of time, it was brought forth and made lord of the world.  The Titans also Zeus slew with a thunderbolt and formed man from their ashes.” 


“Hence man is a dual creature, a mixture of the evil substance of the Titans, and of the divine substance of the god they devour.  His soul, or mind, is a fragment of Dionysus, his body a heritage from the Titans.  Salvation consists in freeing the divine within us from the bondage of the body.  This can only be accomplished by a long series of reincarnations, at the end of which, if she has sufficiently purified herself, the soul may escape from the wheel of birth and rebirth, and be reunited with her divine source.  This purification, however, can only be effected by joining the Orphic cult, assisting with its mysteries, and following its rule of life.”


Now this, historically, philosophically, is the primary source of the soul-body opposition in Western civilization.  No better argument for that opposition has ever been put forth.  Now I read recently that something like fifty percent of the women on the continent of Europe suffer from some type of sexual frigidity, partly caused by the feeling that sex is vulgar and materialistic.  You know how many businessmen feel guilty because they are after money, and they are money grubbers; and how many people attack capitalism because it’s simply physical?  Well, if you asked the ultimate root of that view, it goes back to these tales on Dionysus, back to the Orphic.  And prior to that, of course, it has a long, long history.

3. Mathematics and mysticism

Now, the Pythagoreans subscribed to Orphicism.  They believed in two different worlds, the world of god and this world, the soul-body conflict, they yearned for immortality and escape from the body; they believed in reincarnation. Pythagoras, is alleged (whether this is true, nobody knows) to have seen a dog being beaten one day, and asked the man to stop, because he recognized from the cries a friend of his from a preceding life.  Now the Orphic religion is obviously enormously primitive.  There’s a whole series of typical taboos.  Here a few typical ones—if you are a good Orphic, you have to obey these rules (these are, so to speak, some of the divine commandments if you’re an Orphic; I’m just reading you a few): to abstain from beans; not to pick up what has fallen; not to stir the fire with iron; not to walk on highways; not to let swallows share one’s roof; when the pot is taken off the fire, not to leave the mark of it in the ashes, but to stir them together; when you rise from the bed clothes, roll them together and smooth out the impress of the body; etc.  Now, this commentator says, “It would be easy to multiply the proofs of the close connection between Pythagoreanism and primitive modes of thought, but what has been said is sufficient for our purpose.”  And that is certainly sufficient.


Now, this sort of thing, I may say, was looked at askance by most of the Greeks.  It was certainly not in the mainstream of Greek religious views.  It was, in effect, regarded as a lunatic fringe.  The question is, how did any of this stuff get into the history of philosophy?  Because this is the caliber of stuff that there was thousands and thousands of years of prior to Thales.  And the answer is that Pythagoras had a scientific side to him also, he and his school.  He was concerned, they were concerned, with the same question as all the other Presocratics, namely, what is the nature of the universe, what is the world stuff?  And in this connection, they made some valid and enormously important points.  The result was that their scientific discoveries and their mystic Orphicism were propagated along together as a kind of package deal, and, in fact, the combination became very influential.


Now , I want to look at their more philosophical side.  Well, they asked the question, what is the essence or nature of the universe?  What is the world stuff?  Is it water, is it air, is it fire, is it change?  No, they said.  Well now, to understand their answer, you have to know something about their special interests and achievements. 


The Pythagoreans were really the discoverers of mathematics, in any serious way.  Now other civilizations had discovered mathematical knowledge, but the Pythagoreans were the first to discover that mathematics is somehow everywhere.  They did a lot of work in mathematical theory.  Of course, you know about the Pythagorean Theorem, still called that to this day.  They discovered many interesting things about the connection of mathematics to musical phenomena, a thing which was absolutely unheard of prior to their discovery of it.  They discovered, for instance, that harmony in music (as distinct from noise) is based on mathematical ratios, the length of the string being plucked.  They discovered that musical relations can be expressed numerically, which was a staggering discovery.  And we, to this day, use mathematical terms to talk about musical relationships (like we talk about the interval of a fifth, or a fourth, or an octave, which is an eighth, etc.). 


They discovered that mathematics is somehow relevant to medicine that mathematics is relevant to astronomy.  They uncovered the first hints that mathematical law governs the heavens.  They discovered that mathematics is somehow relevant to medicine—they had the idea that physical health consists of the mathematical ratio of the various elements of the body, and that if you have just the right amount of each, you’re healthy, but if one grows voraciously and destroys the right mathematical balance, well, today, we would say, you have cancer, while they would say you’re sick, you’re out of harmony. 

4. Numbers as the world stuff

In a word, wherever they looked—and these are the subjects that are known at this time—astronomy (I mean, some hints of it are known), mathematics, music, medicine, they found a fact that had not been known—that somehow or other, the distinctive character and action of things is governed by numerical relationships, by mathematical laws—in a word, by numbers.  Numbers popped up everywhere, and who would have expected it?  Consequently, they did in effect what Thales did when he thought water was the key, or what Heraclitus did when he thought change was the key—they seized on their particular think with avidity and proceeded to make it metaphysical.  By a gigantic leap, they generalized, and they said, you want to know what the world stuff is?  You want to know what all things really are?  “All things are numbers.”  That’s their famous fragment—“All things are numbers.”  Numbers are the world stuff.


Now, commentators have worked for centuries to try to figure out what could this have meant.  Because, how can you talk about numbers if there isn’t something being numbered?  Suppose you point to this glass and you ask me “What is it?”, and I say “It’s six.”  You say, “Six what?”  How can you have a universe made of quantity, without any things being quantified?  Now of course, Heraclitus has a universe of activity without any things performing it; why shouldn’t Pythagoras have his, too?  But in any event, commentators have struggled to try and figure out what they could have meant.  Now, a lot of this is speculative, because there are no surviving data, fragments, or documents that would establish it definitely. But, some people point out that because we’re at such an early stage of knowledge and the Pythagoreans are so primitive, they took the following view—they represented numbers by physical things; for instance, little pebbles arranged; three little pebbles would be three, and six little pebbles would be six, and so on; or sometimes by dots, the way we have on dice.  And so six for them meant six dots or six pebbles arranged in a certain way.  In other words, they confused numbers with the physical entities which represent them, or symbolize them.  And so sometimes, when they said “All things are numbers,” they meant, “All things are composed of tiny physical particles.”  So this was like a primitive version of what later became the atomic theory, but the Pythagoreans never developed it.


In part, I may say, the explanation of this is simply their Orphism, their errant mysticism.  Now they were the real numerological mystics, and they carried that to a fantastic length that you wouldn’t believe about.  Justice, for instance, I believe (if I remember correctly), there was a quarrel among the Pythagoreans as to whether justice was four or nine.  (See, the idea is it would have to be a square number, because it had to return equal to equal; but whether it was two times two or three times three, they hadn’t decided.)  Marriage was five, and I once heard the explanation, but I can’t remember it.  Love is eight, because love is harmony between people, and the octave is a harmony.  Man, if I remember, was 250, plants 360.  Now this, of course, is just simply nonsense, and does not require a deep explanation.  This is the Western source of those skyscrapers I mentioned earlier that have the thirteenth floor blanked out.  Except that isn’t fair, because the moderns are worse than the Pythagoreans—if the Pythagoreans thought that thirteen was bad luck, they would stop the building on the twelfth floor; they wouldn’t add subjectivism in and call the thirteenth “fourteen.”

5. Mathematics as the key to nature

Now in part, besides these other features, this is a crucial point disguised in this primitive, mystic statement.  And the crucial point is the vital importance of mathematics in discovering the laws of the world, in making sense of the universe.  Now today, people take this for granted.  You understand that modern physics would have been impossible without the discovery that physical laws have to be formulated in mathematical terms.  Well, this discovery actually develops from the Pythagoreans; they’re the ones, although they didn’t discover any laws, they’re the ones that discovered that mathematics was the keystone.  And, for instance, Kepler, in the modern world and the beginning of modern science, the man who discovered the first mathematical laws of planetary motion, he couldn’t find them for years, but he was a devout Pythagorean, and he went on looking on the grounds that all things are numbers and there must be mathematical laws governing the planets, and sure enough, he found them. In this sense, modern science is in part a development of this discovery of the Pythagoreans.  However, it did not bear fruit until the Renaissance, when it was combined with other theories.

6. A metaphysics of two worlds

But for our purposes, what is important is what the later Pythagoreans did to make sense out of the theory that all things are numbers—that numbers are literally the ingredients of things—they realized that’s too primitive.  And so they took the line that numbers, or numerical relations, somehow governed the behavior of things.  Things, they said, are formed, or behave, according to numbers, and they took this in a very literal and still quite primitive sense. 

Now if you consider people today saying, for instance, that the law of gravity governs the behavior of bodies—now you understand today that that use of the word “govern” is metaphorical; you don’t think, when you say that, that there’s a disembodied law of gravity in another dimension, which says to things, so to speak, “You better follow, or else,” like a king governs his subjects.  But the Pythagoreans apparently did. 


When they said that numbers governed the things of this world, they apparently believed that there were two dimensions (this is the later Pythagoreans)—a world of numbers, of numerical relations, and then this world in which we live, which was somehow formed in accordance with the world of numbers.  What are the characteristics of the two worlds?  Well, of course, the world of numbers can’t be grasped by the senses. You can’t perceive the world of numbers—you can perceive two people, but not just “two.”  Two itself you have to grasp by reason.  And, on the other hand, this world is a world graspable by the senses.  Another point of difference—the world of numbers is unchanging; numbers don’t change.  “Two and two makes four” goes on forever, without any alteration.  Now any individual two things can come into existence, grow, decay, die, and vanish; but two, as such, goes on forever.  Two is two, and two and two is four, and so on.  In a word, the world of numbers is immutable, whereas the world in which we live is constantly changing.  So we have a metaphysical dualism, two realities, and of course, the true one is the world of numbers.


Now they thought, you see, that they had thereby solved the problem posed by Heraclitus and Parmenides, because they provided one world for each.  Heraclitus said true reality must be changing, constantly changing.  And the Pythagoreans said, “Okay, there is a changing world for you.  In this world, you are right—everything is flowing.”  Parmenides said, but true reality has to be unchanging.  They said, “You’re right, too.  True reality is the world of numbers.”  Now this particular attempt to solve the Parmenidean/Heraclitean dilemma, by apportioning two worlds, one for each, was picked up from the Pythagoreans by Plato (in a somewhat different form, as we’ll see next week).  In any event, the Pythagoreans had now given, in effect, a philosophic grounding to their Orphic religion.  They now had their heaven and earth tied in with their two philosophic worlds (the world of numbers and this world); they had a philosophic basis for their soul-body opposition; they had, so to speak, synthesized their religion with their science, and they were happy.


Now a few last points to mop up the Pythagoreans. (Now, I didn’t mean that pejoratively, but…)  One legacy in epistemology of Pythagoreanism is the view that, to be true knowledge, something must be mathematical, that only mathematics qualifies as true knowledge.  Now that is a common view among a certain type today.  There’s a type who gives off what I guess you could describe as a Pythagorean aura, not to say odor.  And that aura is expressed in the fact that if you do not give him statements with numbers in them, he will not accept them as scientific.  If you tell him, for instance, that human beings need self-esteem, that is “vague, qualitative, unscientific, inexact.”  But if you say they need 3.9 units of self-esteem, and they need an extra point for every time they commit one-eighth of an act of immorality or something, then that makes it mathematical.  Now that’s a legacy of the Pythagorean number fixation.

7. Purifying the soul and escaping the body

In regard to ethics, of course, the major legacy left by the Pythagoreans was the mind-body, soul-body dichotomy, which they are the founders of in Western philosophy; and the idea that the ultimate goal is to escape from the body and have the soul be pure.  Now the development of that we will see in Plato, who got it from the Pythagoreans.  You may ask, “Well why didn’t they commit suicide if they were so anxious to escape the body?”  And they had an answer to that—God giveth, and God taketh away. In effect, you belong to God, and if you commit suicide (I’m parodying, but the idea is) you’re violating God’s property rights; it’s up to Him to decide whether or not to let you come home. 


Well what you should do while on earth? Well, as we say, you should purify yourself by withdrawing from the physical.  Well how are you going to do that?  Now here, the Pythagoreans made a very famous observation—they distinguished three types of men who come to the Olympic Games.  And I want to tell you those three because it was picked up later by Plato and became the basis of a whole theory of human psychology.  Three types of men, ranging in hierarchy from the lowest to the highest. 


Now the lowest is the one most directly involved with the physical—the guy who comes to make money, for instance, to buy himself popcorn.  The lover of gain, the man obsessed with the almighty drachma—that’s the lowest.  But above the lover of gain,  there are the athletes, and they are motivated qua athletes (according to the Pythagoreans) not by the desire for money, but for something somewhat more spiritual, namely honor, fame, triumph, glory.  Now they are still materialistic to an extent, because they still want their fame and glory in this physical world, but at least they’re not, so to speak, wallowing in the crude physical, and so they’re one rung higher.  And then there is the third type, the type most detached from the physical world, the type that doesn’t want money or fame, etc.—the people in the stands, the spectators, who simply want to look out and see what’s happening, the ones who have philein for sophia, who simply want to acquire knowledge in a completely disinterested way.  Now those are the ones, if they’re properly disinterested, who are cut off from the physical world (and they surely are). 


And therefore, the Pythagoreans preach the supreme importance of knowledge, but it had to be disinterested knowledge; the supreme importance of philosophy and science, but divorced entirely from any physical, practical consequences, or action regarding life on earth.  They preached philosophy, science, knowledge, as a religious rite, as a rite of purification of the soul, so long as it was disinterested, non-commercial, and non-materialistic.  And this, of course, is the earliest severing in Western philosophy of knowledge from life.  It’s the idea of knowledge as an end in itself. 


Now you’ll see what happens to this, and to the whole Pythagorean view of three types of human beings, in Plato, where it develops into a full-blown psychology and ends up with the view that there should be complete communistic dictatorship.  That, however, is all we’re going to say about the Pythagoreans. They are the first two-reality school that we’ve met in a major way.  And in this sense, they are the oldest religious-supernaturalistic school in Western philosophy.  As we continue, we’re going to trace the line from the Pythagoreans to Plato to the whole Christian axis.  But all of it, including the mind-body opposition, the yearning for an otherworldly immortality, the scorn for this life on earth, goes back originally to the Orphic Pythagoreans.


All right, let’s draw a line here, and next week we will continue with the founders of the atomic theory, the founders of skepticism, and then Socrates and Plato.  Thank you.


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