By Gerald Therrien
“A little learning is a dang’rous thing;
Drink deep, or taste not the Pierian spring:
There shallow draughts intoxicate the brain,
And drinking largely sobers us again.”
(from ‘An Essay on Criticism’, by Alexander Pope)
The year 2020 marks the 500th anniversary of the death of the great Florentine artist Raffaello Sanzio. One of his most famous works is the fresco painted at the Vatican in the Stanza della Segnatura, originally called ‘Causarum Cognitio’ or ‘Knowledge of the Causes’. The most important mural within this multifaceted stanza has famously been dubbed the ‘School of Athens’. Let us then, in Raphael’s memory, take a new look at his fresco, in order to try to learn from one of the leading artists of the Florentine renaissance, how they succeeded in pulling their culture out of a dark age.
When I first began to try to identify the different personalities in this fresco, almost 20 years ago, I found that the so-called ‘accepted interpretations’ were haphazard, disjointed and unconnected, and were in fact more confusing than helpful. So, following the lead of the late philosopher and economist Lyndon LaRouche (1923-2019), I threw these interpretations into the circular file, and started afresh. While my interpretation may not be 100% correct, I have at least tried to do so in a coherent order, with a respect to the actual history involved, in telling my tale.
I would like to preface my essay with a short exerpt from LaRouche’s 2001 book ‘The Economics of the Noösphere’ :
“Look at Raphael’s ‘School of Athens’. I propose that the reader work through the following exercise.
Make a list of each of the historical figures represented. Take a map of the relevant area of the Mediterranean and its littoral for the period from the time of Homer through the entirety of the Classical and Hellenistic phases of Greek and related culture. Locate the place and date of existence of each figure on that map. Then identify the relationship among these figures in terms of those leading ideas which bear upon the irreconcilable dispute between the cognitive Plato and his opponent, the reductionist Aristotle. Ask yourself, is the gloomy figure in the foreground, perhaps the Classical Platonist Raphael’s recognition of the Romantic tendencies in his contemporary, Michelangelo?
In this collection as a whole, there are sequences of time, and sequences of ideas, or beliefs, such as Aristotle’s, substituted for ideas. In the painting, these figures are represented as contemporaries, as if the entire period represented by these figures’ mortal lives, had been compacted into a kind of simultaneity of eternity. Yet, when one considers the medley of interacting ideas and other beliefs represented by the whole assembly, there is an order defined in terms of action among both kinds of notions treated as principles by the user, either ideas or substitutes for ideas, or a combination of both.
Ask: What is the meaning of Raphael’s resort to such a portrayal of a simultaneity of eternity? Is it not the case, that that painting corresponds to the way in which a well-educated student’s mind, even a graduate of a decent sort of secondary education, sees such figures from that period of history? His mind is a simultaneity of eternity, but there is also an ordering, in the sense of sequences, among the elements of that otherwise timeless eternity.
In other words, by introducing the notion of change as such, in the form of continuing, superseding generation of ideas, the time during which the changes unfold is collapsed into a relatively very short lapse of time within the bounds of what is otherwise a simultaneity of eternity.”
The Pre-Socratic Paradox
With that in mind, let us begin our journey. But, were do we start?
Let’s stand back for a minute and look at the painting as a whole. The painting itself is divided into three areas – those figures in the foreground at the bottom of the stairs, those figures in the background at the top of the stairs, and lastly, the top half of the painting (which is the sky and also the columns and arches of the building in which this whole scene takes place) – done in this way so that everyone fits into this one picture.
At first glance it would seem that there is no one in this top half of the painting; but, on second glance, it would appear that there are two persons – the two statues: on the right wall is a statue of someone holding in one hand a spear and with the other hand a shield; and on the left wall is a statue of someone who is leaning on one arm and in the other arm is holding a stringed musical instrument.
This should be Athena and Hephaestus: Athena, the Goddess of Athens – ‘that goddess who is allotted the guardianship both of your city and ours, and by whom they have been educated and founded: yours, indeed, by a priority to ours of a thousand years’; and Hephaestus, from whom the Athenians are descended – ‘receiving the seed of your race from Hephaestus and the Earth’ (as told to Solon by the priest of the city of Sais in Egypt, from Plato’s Timaeus dialogue).
‘thus diverse gods received diverse districts as their portions and reigned over them. But Hephaestus and Athena, as they had one nature, being brother and sister by the same father, and at one, moreover, in their love of wisdom and artistry, so also obtained one lot in common, this our land, to be a home meet for prowess and understanding’ (from Plato’s Critias dialogue)
‘the figure and image of the goddess, whom they of old set up in armor, according to the custom of their time, when exercise of war were common to woman and man alike’ (from Plato’s Critias dialogue)
[Note: this reference to Athena dressed in armour should be especially read today, to address the important issue of equality for women in the world!]
‘the class of artificers whose crafts have equipped us for the daily needs of life will be under the patronage of Hephaestus and Athena’ (from Plato’s Laws dialogue)
‘Prometheus therefore, being at a loss to provide any means of salvation for man, stole from Hephaestus and Athena the gift of skill in the arts, together with fire and bestowed it on man’ (from Plato’s Protagoras dialogue)
What was this gift to man from Prometheus? Perhaps, we shall find out in the course of studying this painting.
Now, let us continue our journey. Since we read from left to right, let’s start at the left side of the painting. Or rather, let us simply start at the entrance.
In the foreground at the far left of the painting, where the painting seems to be missing a small corner because of an actual door that enters the room, is a young man writing in a book that is placed on top of a pillar where a statue might be placed. And, while all the other persons in the painting seem to be grouped as if in a discussion, this person is set off alone, by the entrance and facing outward towards the viewers who are entering the room, as if he is addressing them abut the painting.
While very little knowledge has been preserved concerning the philosophers of Athens, there is one book that has somehow managed to survive the passage of time – ‘The Lives of Eminent Philosophers’ by Diogenes Laertius. Although it contains more gossip and trivia on the philosophers than on their actual ideas, and although it divides the philosophers into strange categories or schools – such as the ‘Ionic School’, the ‘Italic School’, and the ‘Promiscuous Philosophers’ – nonetheless, it has become a primary source for our attempts to understand the Greek philosophers.
Perhaps, this is Diogenes, along with many others – some whose works are partly found and some that are lost, some old and ancient and some new and modern, and some who simply gave a helping hand along the way – as if they are all, opening up this book for us to read. As if Diogenes is the Maitre D’, welcoming us into the dialogue.
[Note: A translation of this book was made by Ambrogio Traversi in Florence in 1433 and was widely circulated.]
Next, looking at the figures in the left foreground, we see different people writing or copying or watching, except for one person who is standing, with one foot on a block of stone, pointing to an open book he is holding, and not looking at this book, but looking at the others; as if he is trying to explain something to them, like a teacher; as if he is the first one in this line of people. This then, should be Thales – the father of the ‘Ionic School’.
(The following is from “Lives and Opinions of the Eminent Philosophers” by Diogenes Laertius)
I. Thales, then, as Herodotus and Duris and Democritus say, was the son of Euxanius and Cleobule; of the family of the Thelidae, who are Phoenicians by descent; among the most noble of all the descendants of Cadmus and Agenor, as Plato testifies. And he was the first man to whom the name of Wise was given …
II. After having been immersed in state affairs, he applied himself to speculations in natural philosophy; though as some people state, he left no writings behind him …
According to others he wrote two books, and no more, about the solstice and the equinox; thinking that everything else was easily comprehended. According to other statements, he is said to have been the first who studied astronomy, and who foretold the eclipses and motions of the sun, as Eudemus relates in his history of the discoveries made in astronomy; on which account Xenophanes and Herodotus praise him greatly; and Heraclitus and Democritus confirm this statement.
III. Some again (one of whom is Chaerilus the poet) say that he was the first person who affirmed that the souls of men are immortal; and he was the first person, too, who discovered the path of the sun from one end of the ecliptic to the other; and who, as one account tells us, defined the magnitude of the sun as being seven hundred and twenty times as great as that of the moon. He was also the first person who called the last day of the month the thirtieth. And likewise, the first to converse about natural philosophy, as some say…
VI. He asserted water to be the principle of all things, and that the world had life, and was full of daemons; they say, too, that he was the original definer of the seasons of the year, and that it was he who divided the year into three hundred and sixty-five days. And he never had any teacher except during the time that he went to Egypt and associated with the priests. Hieronymus also says that he measured the Pyramids: watching their shadow, and calculating when they were of the same size as that was…
IX. And the following are quoted as sayings of his: – ‘God is the most ancient of all things, for he had no birth: the world is the most beautiful of things, for it is the work of God: place is the greatest of things, for it contains all things: time is the swiftest of things, for it runs through everything: necessity is the strongest of things, for it rules everything: intellect is the wisest of things, for it finds out everything.’
Next, if we now look in the direction that Thales is looking, at that person to the left of Thales, we see someone sitting on a block, with one foot also on a small stone block, with others behind him observing his work, while he is writing in a book, with a person holding in front of him a slate, and on this slate is written ‘1 + 2 + 3 + 4 = 10’ (a tetraktys). This then, should be Pythagoras – the father of the ‘Italic School’.
(The following is from Diogenes Laertius)
III. And as he was a young man, and devoted to learning, he quitted his country, and got initiated into all the Grecian and barbarian sacred mysteries. Accordingly, he went to Egypt, on which occasion Polycrates gave him an introduction to Amasis; and he learnt the Egyptian language, as Antipho tells us, in his treatise on those men who have been conspicuous for virtue, and he associated with the Chaldaeans and with the Magi.
Afterwards he went to Crete, and in company with Epimenides, he descended into the Idaean cave, (and in Egypt too, he entered into the holiest parts of their temples,) and learned all the most secret mysteries that relate to their gods. Then he returned back to Samos, and finding his country reduced under the absolute dominion of Polycrates, he sent sail, and fled to Crotona in Italy. And there having given laws to the Italians, he gained a very high reputation, together with his scholars, who were about three hundred in number, and governed the republic in a most excellent manner; so that the constitution was very nearly an aristocracy.
V. Now, some people say that Pythagoras did not leave behind him a single book; but they talk foolishly; for Heraclitus, the natural philosopher, speaks plainly enough of him, saying, ‘Pythagoras, the son of Mnesarchus, was the most learned of all men in history; and having selected from these writings, he thus formed his own wisdom and extensive learning, and mischievous art’ …
And there are three volumes extant written by Pythagoras. One on Education; one on Politics; and one on Natural Philosophy …
XI. It was Pythagoras also who carried geometry to perfection … the part of the science to which Pythagoras applied himself above all others was arithmetic. He also discovered the numerical relation of sounds on a single string; he also studied medicine …
XIII. He was also the first person who introduced measures and weights among the Greeks …
XV. But until the time of Philolaus, there were no doctrines of Pythagoras ever divulged; and he was the first person who published the three celebrated books which Plato wrote to have purchased for him for a hundred minae.
XIX. … Alexander also says, in his Successions of Philosophers, that he found the following dogmas also set down in the Commentaries of Pythagoras: – That the monad was the beginning of everything From the monad proceeds an indefinite duad, which is subordinate to the monad as to its cause. That from the monad and the indefinite duad proceeds numbers. And from numbers signs. And from these last, lines of which plane figures consist. And from plane figures are derived solid bodies. And from solid bodies sensible bodies, of which last there are four elements: fire, water, earth and air. And that the world, which is endued with life, and intellect, and which is of a spherical figure, having the earth, which is also spherical. And inhabited all over in its centre, results from a combination of these elements, and derives its motion from them …
He also says that the soul of man is divided into three parts; into intuition, and reason, and mind, and that the first and last divisions are found also in other animals, but that the middle one, reason, is only found in man.
(The following is from Aetius, in the Doxographi Graeci by Hermann Diels)
And again from another starting-point, Pythagoras, son of Muesarchos, a Samarian, who was the first to call this matter by the name of philosophy, assumed as first principles the numbers and the symmetries existing in them, which he calls harmonies, and the elements compounded of both, that are called geometrical.
And again he includes the monad and the undefined dyad among the first principles; and for him one of the first principles tends towards the creative and form-giving cause, which is intelligence, that is god, and the other tends towards the passive and material cause, which is the visible universe.
And he says that the starting point of number is the decad; for all Greeks and all barbarians count as far as ten, and when they get as far as this they return to the monad. And again, he says, the power of the ten is in the four and the tetrad. And the reason is this: if any one returning from the monad adds the numbers in a series as far as the four, he will fill out the number ten (i.e. 1 + 2 + 3 + 4 = 10); but if he goes beyond the number of the tetrad, he will exceed the ten. Just as if one should add one and two and should add to these three and four, he will find out the number ten; so that according to the monad number is in the ten, but potentially in the four. Wherefore the Pythagoreans were wont to speak as though the greatest oath were the tetrad: “By him that transmitted to our soul the tetraktys, which has the spring and root of ever-flowing nature.” And our soul, he says, is composed of the tetrad; for it is intelligence, understanding, opinion, sense, from which things come every art and science, and we ourselves become reasoning beings.
The monad, however, is intelligence, for intelligence sees according to the monad. As for example, men are made up of many parts, and part by part they are devoid of sense and comprehension and experience, yet we perceive that man as one alone, whom no being resembles, possesses these qualities; and we perceive that a horse is one, but part by part it is without experience. For these are all forms and classes according to monads.
Wherefore, assigning this limit with reference to each one of these, they speak of a reasoning being and a neighing being. On this account the monad is intelligence by which we perceive these things. And the undefined dyad is science; fittingly, for all proof and all persuasion is part of science, and farther every syllogism brings together what is questioned out of some things that are agreed upon, and easily proves something else; and science is the comprehension of these things, wherefore it would be the dyad. And opinion as the result of comprehending them is the triad; fittingly, for opinion has to do with many things; and the triad is quantity, as “The thrice-blessed Danaoi”. On this account then he concluded the triad.
Next, if we look to the right of Thales, we see someone who is sitting on a block and writing upon a large block, and who seems to be looking at his foot, as if thinking about where he will put it – this then, should be Heraclitus. Heraclitus seems out of place, writing on a block that seems to be the remnant of some pedestal or something. While Pythagoras was born in Ionia but left for Sicily to establish his school, Heraclitus was born and lived in Ionia, staying there even under the wreckage of the Persian conquest and occupation of Ionia. Heraclitus could be considered as part of the ‘Ionic School’, but not of the ‘Italic School’, and so, he is placed beside Thales but opposite from Pythagoras; and is placed in Diogenes’ strange classification of ‘Promiscuous Philosophers’.
The fragments of Heraclitus can be found in ‘Ancilla To The Pre-Socratic Philosophers’, translated by Kathleen Freeman (Harvard University Press) from the Vorsokratiker Fragmente by Hermann Diels.
(The following is from Diogenes Laertius)
I. Heraclitus was the son of Blyson, or as some say, of Heraceon, and a citizen of Ephesus.
II. He was above all men of a lofty and arrogant spirit, as is plain from his writings, in which he says, “Abundant learning does not form the mind; for if it did, it would have instructed Hesiod, and Pythagoras, and likewise Xenophanes, and Hecataeus. For the only piece of real wisdom is to know that idea, which by itself will govern everything on every occasion”.
V. There is a book of his extant, which is about nature generally, and it is divided into three discourses; one on the Universe; one on Politics; and one on Theology. And he deposited this book in the temple of Diana, as some authors report, having written it intentionally in an obscure style, in order that only those who were able men might comprehend it, and that it might not be exposed to ridicule at the hands of the common people …
Theophrastus asserts, that it was out of melancholy that he left some of his works half finished, and wrote several, in completely different styles … And his book had so high a reputation, that a sect arose in consequence of it, who were called after his own name, Heracliteans.
(The following is from Diogenes Laertius, under Socrates)
VII. And they say that Euripides gave Socrates a small work of Heraclitus to read, and asked him afterwards what he thought of it, and he replied, “What I have understood is good; and so, I think, what I have not understood is; only the book requires a Delian diver to get at the meaning of it.”
Next, if we look to the left of Pythagoras, we see two people behind him looking at his writing – one person on the left who is sitting behind and looking over his shoulder, and who seems to be copying, or writing in his own book (actually it looks a single piece of paper); and we see another person on the right who is standing beside him, who is also looking over the shoulder of Pythagoras at what he is writing, but not writing, only observing.
These two people, perhaps, also belong to that third school in Diogenes’ book – the ‘Promiscuous Philosophers’ – and so, they could be two of the better known philosophers of this school.
[Note: The fragments of Parmenides can be found in ‘Ancilla To The Pre-Socratic Philosophers’, translated by Kathleen Freeman (Harvard University Press) from the Vorsokratiker Fragmente by Hermann Diels]
And so, the person on the left – writing on a piece of paper, could be Parmenides, since he wrote one book – ‘a poem in hexameter verse, addressed to his pupil Zeno’.
(The following is from Diogenes Laertius)
I. Parmenides, the son of Pyres, and a citizen of Velia (Elea), was a pupil of Xenophanes.
[Xenophanes ‘was a citizen of Colophon (in Ionia) … (and) having been banished from his own country, lived at Zande, in Sicily … It is said that he argued against the opinions of Thales and Pythagoras … (he) wrote a poem on the founding of Colophon; and also, on the Colonization of Elea, in Italy’.]
And Theophrastus, in his Abridgement, says that he was also a pupil of Anaximander. However, though he was a pupil of Xenophanes, he was not afterwards his follower; but he attached himself to Aminias, and Diochartes the Pythagorean, as Sotion relates, which last was a poor but honorable and virtuous man. And he it was whose follower he became …
II. He was the first person who asserted that the earth was of a spherical form; and that it was situated in the centre of the universe. He also taught that there were two elements, fire and earth; and that one of them occupies the place of the maker, the other that of the matter. He also used to teach that man was originally made out of clay; and that they were composed of two parts, the hot and the cold; of which, in fact, everything consists. Another of his doctrines was, that the mind and the soul were the same thing …
III. … And he used to say that argument was the test of truth; and that the sensations were not trustworthy witnesses.’
And, the person on the right – observing but not writing, could be Democritus. However, with the form of his dress that is different from all the others, this figure somehow appears to be bringing in an influence from the East.
(The following is from Diogenes Laertius)
I. He was a native of Abdera …
II. He was a pupil of some of the Magi and Chaldaeans, who Xerxes had left with his father as teachers, when he had been hospitably received by him, as Metrodorus informs us, and from these men he, while still a boy, learned the principles of astronomy and theology. Afterwards, his father entrusted him to Leucippus …
[‘Leucippus was a native of Velia (Elea) … He was a pupil of Zeno’. ‘Zeno was a native of Velia (Elea) … And Zeno had been a pupil of Parmenides, and on other accounts greatly attached to him’.]
And Demetrius in his treatise on People of the same Name, and Antisthenes in his Successions, both affirm that he travelled to Egypt to see the priests there, and to learn mathematics of them; and that he proceeded to the Chaldeans, and penetrated into Persia, and went as far as the Persian Gulf.
IX. He also speaks of the theories of Parmenides and Zeno, on the subject of the One, as they were the men of the highest reputation in histories, and he also speaks of Protagoras of Abdera …
[Protagoras ‘was a native of Abdera’ and ‘was a pupil of Democritus’, and ‘who instituted contests of argument, and who armed the disputants with the weapon of sophism’.]
XII. Now his principal doctrines were these. That atoms and the vacuum were the beginning of the universe; and that everything else existed only in opinion. That the worlds were infinite, created, and perishable. But that nothing was created out of nothing, and that nothing was destroyed so as to become nothing. That the atoms were infinite both in magnitude and number, and were borne about through the universe in endless revolutions. And that thus they produced all the combinations that exist: fire, water, air and earth; for that all these things are only combinations of certain atoms; which combinations are incapable of being affected by external circumstances, and are unchangeable by reason of their solidity … and that everything that happens, happens of necessity. Motion, being the cause of the production of everything, which he calls necessity.
But, concerning Democritus, although (Diogenes says) ‘a large body of written work was produced at Abdera … Aristoxenus, in his Historic Commentaries, says that Plato wished to burn all the writings of Democritus that he was able to collect’. There is not a single mention of Democritus in any of Plato’s dialogues.
So perhaps, this figure represents an un-named person that we could simply call the ‘sophist’.
And so, we see here, not Diogenes’ ‘Promiscuous Philosophers School’, but the school that was started in Elea and can be called the ‘Eleatic School’ – Xenophanes, Parmenides, Zeno, Leucippus, Democritus and Protagoras – and, with Protagoras, the entering of the sophists into Athens.
This scene, in the left foreground of the painting, seems to be about the Greek philosophers who lived before the time of Plato and Socrates, and who are called the ‘Pre-Socratic Philosophers’. Here we see the teacher Thales, and on his left is his follower Heraclitus, and on his right is his student Pythagoras – the ‘Ionic School’ and the ‘Italic School’, and behind them, is the ‘Eleatic School’ of Parmenides.
Let us, however, very quickly, first look at the historic setting for this scene.
Following the end of the Trojan war (dated by Eratosthenes at 1184 BC), came the invasion by the Peoples of the Sea, and the following collapse of the Hittite Empire, the attempted invasion of Egypt, and a dark age for Greece. Soon, Babylon was restored, and with the help of their financial-and-priestly caste, the soon-to-be Assyrian Empire was begun.
By the end of the 7th century BC, and their short-lived conquest of Egypt, the Assyrians were destroyed by the Medians – with the help of Babylon. The Medians in their planned conquest of Lydia are stopped, when awed by Thales’ prediction of a solar eclipse.
By 559 BC the Medians were replaced by the Persians, who, by 546 BC had conquered Lydia, which had previously subjugated all the Greek cities of Ionia, except Miletus. (Thales had died and Pythagoras had left to eventually settle in Sicily).
The Persians were allowed to conquer Babylon, and then, to conquer Egypt, the Indus River region, Thrace and Macedon; to suppress the revolt of the Greek cities of Ionia, and by 494 BC to destroy Miletus. The Persians were now advancing on the Greek city states. In 490 BC the Athenians defeated the Persians at the famous battle of Marathon, and in 479 BC, the Greeks finally defeated the Persians and ended the Persian war. The oligarchs now decide that the Greeks cannot be defeated militarily, but first, must be defeated from within, by other means.
With this historic setting in mind, we can now look at this scene, and the coming attack on the philosophy of Thales, Pythagoras and Heraclitus. While the Eleatic School was trying to dispute the philosophy of Pythagoras and the monad (the One), with the philosophy of Heraclites that all is change, the sophists were allowed to enter the city of Athens.
Since we have very little of their own writings left to us – only fragments – and a few commentaries written by others who came later, our best hope of understanding them should come from reading Plato’s dialogues, and then we should be able to see how Plato looks back at this fight, and at solving the ‘Eleatic paradox’.
Plato says little about Heraclitus except that ‘Heraclitus is supposed to say that all things are in motion and nothing at rest; he compares them to the stream of a river and says that you cannot go into the same water twice.’ (from the Cratylus dialogue).
But, concerning Parmenides, (in the Thaeatetus dialogue) Socrates says that ‘A feeling of respect keeps me from treating in an unworthy spirit Melissus and the others who say the universe is one and at rest, but there is one being whom I respect above all. Parmenides himself is in my eyes, as Homer says, a “reverend and awful” figure. I met him when I was quite young and he quite elderly, and I thought there was a sort of depth in him that was altogether noble’.
[According to Diogenes, ‘Melissus was a pupil of Parmenides … his doctrine was that the Universe was infinite, unsusceptible of change, immoveable and one, being always like to itself, and complete; and that there was no such thing as real motion, but that there only appeared to be such.’]
In the Parmenides dialogue, that Antiphon describes as ‘an operose undertaking’ (i.e. pain-staking and tedious) a young Socrates asks ‘how is it you assert, O Zeno, that if beings are many, it is requisite that the same things should be both similar and dissimilar? But that this is impossible. For neither can things dissimilar be similar, nor things similar be dissimilar … If, therefore, it is impossible that dissimilars should be similar, and similars dissimilar, is it not impossible that many things should have a subsistence? For, if there were many, they would suffer impossibilities? Is it not then the sole intention of your discourses to evince, by contesting through all things, that the many has no subsistence?’
[Here, Socrates implies that Zeno’s purpose is show that ‘the many is not’ – to disprove Heraclitus’ idea of change.]
Socrates then addresses Parmenides, that ‘Zeno, in a certain respect, has written the same as yourself … For you, in your poems assert that the universe is one … but Zeno says that the many is not’.
And Zeno answers, that ‘these writings were composed for the purpose of affording a certain assistance to the doctrine of Parmenides, against those who endeavor to defame it by attempting to show that if The One is, many ridiculous consequences must attend such an opinion; and that things contrary to the assertion must ensue. This writing, therefore, contradicts those who say that the many is, and opposes this and many other opinions; as it is desirous to evince that the hypothesis which defends the subsistence of the many is attended with more ridiculous consequences than that which vindicates the subsistence of The One, if both are sufficiently examined.’
So, Parmenides asserts that if we were to accept the idea of The One (the monad of Pythagoras) then, there cannot be many – that there cannot be any change (of Heraclitus). And, conversely, Zeno asserts that if we accept the idea of many (of change) then, there cannot be the one.
The attack against Pythagoras’ idea of the monad (the creative cause) was the attempt to assert that the monad cannot be known, since something cannot be created out of nothing. The attack against Heraclitus’ idea of change, was the attempt to assert that nothing could be known, since everything is constantly changing.
But, can we really know the truth? Or, are we only left to decide between one doctrine that leads to many ridiculous consequences, and another doctrine that leads to more ridiculous consequences?
In fact, after the ‘operose’ deductive logic of the discourse, we are left with the final result that ‘whether the One is or is not, both itself, as it appears, and others, both with respect to themselves and to others, are entirely all things, and at the same time are not at all, and appear to be, and at the same time do not appear.’
And this was put into the mind of a young Socrates (and the minds of ourselves too), to try to figure out a solution to this Eleatic paradox.
If we go back and read another of Plato’s dialogue, the Sophist, we are introduced to a Guest ‘who is an Elean by birth, but very different from the associates of Parmenides and Zeno’ and who is in a dialogue with Theaetetus.
In their attempt to define a sophist, they are led back to the words of Parmenides, and to his assertion that ‘non-beings can never, nor by any means, be. But do thou, when inquiring, restrain thy conceptions from this path’
They decide – ‘not for the sake of contention, therefore, nor jesting, but seriously’ – that ‘it will be necessary for us to examine with our opponents the discourse of our father Parmenides, and to compel non-being in a certain respect to be, and again being, in a certain respect not to be’. In order to do this, they must ‘adduce for this purpose a certain paradigm’ in order to resolve the paradox.
And thus, by changing one of the necessary conditions of Parmenides’ argument (that is, by changing necessity) they adduced – not deduced or induced – but adduced a new paradigm (that is, by hypothesizing a new idea) they were able to prove Socrates’ original assertion ‘that if beings are many, it is requisite that the same things should be both similar and dissimilar?’ and were able to solve their problem of discovering the essence of the sophist.
(The following is from Lyndon LaRouche – ‘SDI & Mars Colonization: Examples of the Way in Which Science Performs as an Expression of The Absolute Good’, August 1986)
‘The first rule in the method of Plato’s Socratic dialogues, is that any deductive reasoning is nothing but a giant tautology, from beginning to end. The only kind of mental activity which is possible within the limits of deductive reasoning, is to prove that a particular theorem is logically consistent with the original axiomatic assumptions of that deductive system. Therefore, within the bounds of deductive reasoning, it is impossible to prove, adequately, whether or not the system as a whole is sane or insane.
Thinking deductively, is not insanity in and of itself. On the contrary, as long as you limit deductive thinking to the business of checking the consistency of theorems, you would be as insane as a typical liberal, if you did not employ deductive rigor. Deductive reasoning becomes paranoid, only if you carry it to the extreme, of rejecting Plato’s Socratic method. The essence of Socratic reasoning, is the recognition, that the best deductive reasoning can do no better than to generate gigantic tautologies. In Socratic method, we use deductive reasoning; but we stand outside it. We look at the entirety of any deductive reasoning as a gigantic tautology; we take the entirety of that tautology as a single object of thought. You may be asking yourself, how is it possible to see an entire system of deductive thinking as an indivisible unit of thought? The answer is a simple one. Take two equally consistent systems of deductive thinking. Ask yourselves: What is it, which distinguishes one of these two systems from the other? The answer is, “a difference of the axiomatic assumptions of the one, from the set of axioms upon which the other is premised”.’
Let us end Part One with a poem written by Callimachus, a poet and scholar who worked at the Library of Alexandria. (The following was translated by William Johnson Cory.)
They told me, Heraclitus, they told me you were dead,
They brought me bitter news to hear and bitter tears to shed.
I wept as I remember’d how often you and I
Had tired the sun with talking and sent him down the sky.
And now that thou art lying, my dear old Carian guest,
A handful of grey ashes, long, long ago at rest,
Still are thy pleasant voices, thy nightingales, awake;
For Death, he taketh all away, but these he cannot take.
For more information on the poetic principle, read Why the Poetic Principle is Imperative for Statecraft, and watch the Rising Tide Lecture Series ‘Towards an Age of Creative Reason‘
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