Pythagoras: Mathematics and Mysticism by Leonard Peikoff

I let us turn to the last pre-socratic 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 Haley's in order and prior to permitted he's in Heraclitus there's about 60 years after thais 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 in 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 I will hover around middle pythagoreans now Pythagoras founded an enormous the influential school and had overwhelming effects on Plato and of course therefore later on Christianity neither played on nor Christianity would have been possible without death agamous and his school or some equivalent now basically the early pythagoreans at least were a mist except they lived communistical ii without private-property they were ineffective religious order or Brotherhood they were far and away the most otherworldly the most mystic of all of the pre-socratics 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 enormous ly different trend in Greek religion they advocated what was called a mystery religion which is much more religious than a Mount Olympus divinity has ever dreamed of this is really religious it was a rabid mystic supernaturalists cult in the early years of a very primitive order and there were quite a number of them and the ones that the pythagoreans subscribed to what's called the orphan mystery religion ORP HIC with the capital so what it or facism teach now or facism is not a philosophy it's an oriental mystery cult imported into Greece and that advocated only by a minority was not the dominant viewpoint well the oyx preached tenants like this man has two parts I part in 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's sin and the result was it fell from grace and as a punishment wasn't 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 reincarnation at the end of our earthly span we go our soul goes back to the Otherworld 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 an animal body lives out its cycle and goes back again round and round the wheel of birth until and this was their ultimate hope one day a soul can escape from the body and this earth permanently reunite once and for all with God and thereby achieved true happiness and salvation in fact the idea was go back home how do you get to do it well they said you have to engage in the process they called purification purification that's essentially a process of D contaminating the soil 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 that their most ascetic our 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 in off-broadway now mass orgies intoxication the frenzied dancing secret initiation rites that's why they were called mystery religions it was a highly primitive to say the least here's a description from one commentator office isn't worshipped that god Dionysus and he describes it as Falls now enacted heroic self-abnegation I will steadfastly abstain from commenting or drawing parallels to any subsequent Western religion quote the god Dionysus was elaborated in the Orphic mysteries originally a three station 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 priests in whom he was supposed to be incarnate was sacrificed and eaten by his worshippers who thus partook of the mana or strength of their God but before the cult entered Greece the sacrifice of the priests had given 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 was he'd ionised 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 Cinelli she demanding to see her divine lover face-to-face was consumed by a thunderbolt 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 jewel creature a mixture of the evil substance of the Titans and of the divine substance of the God they devoured his soul or mind as 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 could only be effected by joining the Orphic cult assisting in its mysteries and following his rule of life unquote 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 50% of 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're after money and there are money grubbers and how many people attack capitalist capitalism because it's simply physical well if you ask the ultimate root of that few he goes back to these tales on Dionysus back to the Orphic and prior to that of course it has a long long history now the Pythagorean subscribed to orifices they believed in two different worlds the world of God in this world the soul body conflict they yearn for immortality and escape for the on the body they believed in reincarnation Pythagoras has alleged whether this is to know but he 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 preceding life now the Orphic religion is obviously enormous ly primitive it's a whole series of typical taboos here are a few typical ones if you're a good Orphic you have to obey these rules these are so to speak some of the divine Commandments if you're a Norfolk 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 ones 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 bedclothes roll them together and smooth out the impress of the body etc now this commentator says quote it would be easy to multiply the proofs of the close connection between pythagoras pythagorean ism and primitive modes of thought but what has been said is sufficient for her purpose unquote 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 a 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 theories and the answer is that Pythagoras had a scientific side to him also he in his school he was concerned they were concerned with the same question as all the other pre-socratics namely what is the nature of the universe what is the world stuff and in this connection they made some valid and enormous ly important points the result was that their scientific discoveries and their mystic or facism 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 interest chivas 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 and of course you know about the Pythagorean theorem still call 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 an interval of a fifth or a fourth or an octave which means an eighth and such they discovered 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 then if you have just the right amount of each you're healthy but if one and grows voraciously and destroys the right mathematical balance well today we would say you have cancer they would say you're sick you're out of harmony 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 you know word by numbers numbers popped up everywhere and who would have expected consequently they did in effect what families did when he thought water was the key or what Eric laddus did when he thought change was the key they seized on their particular thing with him energy 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 as their famous fragment all things are numbers numbers are the world stuff now commentators have worked for centuries to try and figure out what could this have meet because how can you talk about numbers there isn't something being numbered suppose I pointed this glass you asked me what is it and I say it's six you say six what how could you have a universe made of quantity without any things being quantified well of course Heraclitus has a universe of activity without anything's 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 that would be 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 6 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 confuse numbers with the physical entities which represent them or symbolized 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 pythagorean's never developed in part I may say the explanation of this is simply their autism their errant mysticism they were the real numerological mystics and they carried that to fantastic lengths that you wouldn't believe about justice for instance I believe if I remember correctly there was a quarrel among the Pythagorean as to whether justice was four or nine see the ideas they have to be a square number because it had to return equal for equal but whether it was 2 times 2 or 3 times 3 I hadn't decided marriage was 5 and I once heard the explanation I can't remember it love is 8 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 deep explanation and this is the Western source of those skyscrapers I mentioned earlier that have the 13th floor blanked out except that isn't fair because the moderns are worse than the pythagoreans if the pythagoreans thought that 13 was bad luck they would stop the building on the 12th floor they wouldn't add subjectivism they didn't call the 13 14 now in part besides these other features there 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 the vital importance of mathematics and 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 who discovered that mathematics was the keystone and for instance Kepler in the modern world in the beginning of modern science man who discovered the first mathematical laws of planetary motion couldn't find them for years but he was a devout pythagorean and he went on looking the grounds that all things are numbers in there must be mathematical laws governing the planets is sure enough you found in this sends modern science is in part a development of this discovery of the pythagoreans however it did not bear fruit until the Renaissance and when it was confined combined with other theories 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 now by the time we get to the 4th century BC the later pythagoreans understood that there is something funny about saying that things are made out of numbers the numbers are literally the ingredients of things they realize that's too primitive and so they took the line that numbers or numerical relations somehow govern 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 considered people today saying for instance that the law of gravity governs the behavior of bodies now you understand today that values 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 two things so to speak you better fall or else like a king governs his subjects but the pythagoreans apparently did when they said that numbers govern the things of this world they apparently believed that there were two dimensions this is the later Pythagoras 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 to itself you have to grasp by reason and on the other hand this world is graspable by the census another point of difference the world of numbers is unchanging numbers don't change - and to cut makes four goes on forever without any alteration now any individual two things can come into existence grow decay die and vanish but - as such goes on forever - is two and two and two is four and so on you know word the world 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 changed the Pythagorean said okay there is a changing world for you in this world or light everything is flowing para manatee said but true reality has to be unchanging they said you're right - true reality is the world of numbers now this particular attempt to solve the apartment of the inherit legend dilemma by apportioning two worlds for 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 have now given an effective philosophic grounding to their Orphic religion they now had their heaven and earth tied in with their two philosophic world the world of numbers in this world they had a philosophic basis for their soul body opposition they had so to speak synthesize their religion with their science and they were happy now a few last points to mop up the pythagoreans I didn't mean that pejoratively but one legacy in epistemology of Pythagorean ISM is the view that to be to knowledge something must be mathematical but 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 or not to say older and that or as 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 quote a 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 the immorality or something then that makes it mathematical now that's a legacy of the Pythagorean number fixation in regard to ethics of course the major legacy left by the pythagoreans was the mind body a 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 hadn't answered that God giveth and God taketh away it effect you belong to God and have you commit suicide I'm parroting 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 now what did you 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 distinguish 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 a 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 and sell 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 to qua a fleet not by the disappoint of the pythagoreans not by the desire for money but for something somewhat more spiritual namely honor fame triumph glory now there 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 attached 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 silane 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 sure they are and therefore the pythagoreans preached the supreme importance of knowledge but it had to be disinterested in 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 right as a rite of purification of the soul so long as it was disinterested non-commercial and non materialist 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 it ends up with the view that there should be complete communistic dictatorship that however is all we're going to say that about the pythagoreans they are the first to reality school that we've met in a major way and in this sense they are the oldest religious super naturalistic 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 alright let's draw a line here and next week we will continue with the founders of the atomic theory dear founders of skepticism and then Socrates and Plato

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Keywords: history of philosophy, history, philosophy, history of western philosophy, western philosophy, leonard peikoff, ayn rand, ayn rand institute, objectivism, objectivist, political theory, modern philosophy, ancient philosophy, school of life, crash course, lecture, educational video, secular humanism, Pythagoras, greek philosophy, greek philosophers, Mysticism, mathematics, Orphic religion, influence on plato

Id: DlomMDhKYLg

Length: 29min 58sec (1798 seconds)

Published: Fri May 01 2020