Pythagoras was the first to call the pursuit of wisdom philosophy and to prefer to be called philosophos: for previously philosophers had been called sophoi, that is, wise men. Fitly indeed did he call the seekers of truth not the wise men but lovers of wisdom, for certainly the whole truth lies so deeply hidden that the mind, however much it may ardently yearn toward it or however much it may struggle to acquire it, can nonetheless comprehend only with difficulty the truth as it is. (Hugh of St Victor, Didascalion, book 1).
‘Suppose there were men who had always lived underground … but had learned by report and hearsay that there was a divine spirit and power. Suppose that then, at some time, the jaws of the earth opened, and they were able to escape and make their way from those hidden dwellings into those regions which we inhabit. When they suddenly saw earth and seas and skies, when they learned the grandeur of clouds and the power of winds, when they saw the sun and realized not only its grandeur and beauty but also its power, by which it fills the sky with light and makes the day; when, again, night darkened the lands and they saw the whole sky picked out and adorned with stars, and the varying light of the moon as it waxes and wanes, and the risings and settings of all these bodies, and their courses settled and immutable to all eternity; when they saw those things, most certainly would they have judged that there are gods and that these great works are the works of gods.’ (Aristotle, fragment. 12.)
The True is thus the Bacchanalian revel in which no member is not drunk Das Wahre ist so der bacchantische Taumel, an dem kein Glied nicht trunken ist Hegel, G.W.F. (1977) Phenomenology of Spirit, trans. Miller, Oxford: Oxford University Press, p. 27.
I gave a thorough examination to this person – I need not mention his name, but it was one of our politicians … and in conversation with him I formed the impression that although in many people’s opinion, and especially in his own, he appeared to be wise, in fact he was not. The when I began to try to show him that he only thought he was wise and was not really so, my efforts were resented both by him and by many of the other people present. However, I reflected as I walked away: ‘Well, I am certainly wiser than this man. It is only too likely that neither of us has any knowledge to boast of; but he thinks that he knows something which he does not know, when I am quite conscious of my ignorance. At any rate it seems that I am wiser than he is to this smallest extent, that I do not think that I know what I do not know.’ …
Are you not ashamed that you give your attention to acquiring as much money as possible, and similarly with reputation and honour, and give no attention or thought to truth and understanding and the perfection of your soul? …
Life without this sort of examination is not worth living. Socrates, from The Apology (trans. H Tredennick)
Plato and the Cave
This is probably the most famous model of education and enlightenment in the Western tradition.
‘He imagines men in an underground cave, which has a broad entrance open to the light. They have been chained down there since childhood, by their legs and neck, so that they cannot move, and cannot turn round and look behind.
They have their backs to the entrance. Above and beyond them, some distance off, a fire is burning: its rays fall above the heads of the prisoners on the back wall of the cave, towards which they are looking.
Between them and the fire there is a road, along which runs a low wall, like the stage of a marionette-theatre, upon which conjurors show their puppets. Behind the wall there are people carrying along all sorts of objects and figures made of word and stone, some talking and others silent. The objects show above the wall, and the fire throws their shadows onto the back wall.
The prisoners cannot turn round, so that they have never seen anything all their lives except the shadows. They naturally take the shadows for reality, and the echoes of the voices for the speech of the shadow-figures.
Now, if one of them were released from his chains, and compelled to climb up and look towards the light, he would not be able, because of the dazzling brightness, to see the things whose shadows he used to look at: and would not believe it if anyone told him everything he had seen hitherto was all nonsense, while he was now looking at a world of higher reality.
Instead, he would be quite convinced that the shadow-pictures he used to see were the true reality, and he would turn away with smarting eyes into the cave once more…’
(Plato’s cave, from Jaeger, W. (1986) Paideia: the ideals of Greek culture, vol. II, Oxford; Oxford University Press, pp. 291-2.)
See, for example: [the cave]
Great indeed is the admiration aroused by an eloquent and wise speaker, who hearers judge him wiser, and more understanding too, than the rest. And if in such a speech there is also a weightiness blended with modesty, then no achievement can be more admirable (Cicero, On Duties, Book II).
For like a queen with power over everything, she [Rhetoric] could drive any host of people where she wanted and draw them back from where she wanted; she could sway them to tears and whip them to a frenzy, and change the countenance and senses not only of cities but of armies in battle…
What countenance and voice she had as she spoke, what excellence and exaltation of speech! It was worth even the gods’ effort to hear such genius of argument, so rich a wealth of diction, so vast a store of memory and recollection. What order in structure, what harmonious delivery, what movement of gesture, what profundity of concept! She was light in treating small topics, ready with middling topics, and with exalted ones a firebrand. In discussion she made her whole audience attentive, in persuasion amenable, full of conflict in disagreements, full of pride in speeches of praise. But when she had, through the testimony of some public figure, proclaimed some matter of dispute, everything seemed to be in turbulence, confusion, and on fire.
(Martianus Capella, (1977) The Marriage of Philology and Mercury, New York: Columbia Press, pp. 156-7.)
Rhetoric is the master art of the trivium, for it presupposes and makes use of grammar and logic; it is the art of communicating through symbols about reality… The adaptation of language to circumstance, which is a function of rhetoric, requires the choice of a certain style and diction in speaking to adults, of a different style in presenting scientific ideas to the general public, and of another in presenting them to a group of scientists (Joseph, (2002) The Trivium, pp. 9-10.)
Rhetorical displays (of various quality)
You shall go out with joy
And be led forth with peace
And the mountains and the hills shall break forth into singing
And all the trees of the fields
Shall clap their hands
the heart neither proceeds to intellectual considerations not distracts our conscious attention to separate points of view, but is accustomed to live in deep feeling and undisclosed depths…it is precisely this sphere…which music takes for its own and which therefore brings movement into the seat of inner changes, into the heart and mind as this simple concentrated centre of the whole of human life
we finite creatures with infinite spirits are born only to suffer and to rejoice and one could almost say that the most excellent among us derive joy from suffering
Music is diffused through all the acts of our life if we before all else obey the commands of the creator and observe with pure hearts the rules which he has established. For whatever we say or whatever inward effect is caused by the beating of our pulse is joined by musical rhythms to the power of harmony. Music is indeed the science of proper modulation; and if we observe a good way of life we are always associated with this excellent science. When we sin, however, we no longer have music.
The sky and the Earth and everything which is accomplished in them by the supernal stewardship are not without the science of music; for Pythagoras is witness to the fact that this world was founded through the instrumentality of music and can be governed by it
(Cassiodorus, Secular Letters, c. 551CE).
Civilization or, to say the same thing, education is the taming or domestication of the soul’s raw passions—not suppressing or excising them, which would deprive the soul of its energy—but forming and informing them as art…
But rock music has one appeal only, a barbaric appeal, to sexual desire—not love, not eros, but sexual desire undeveloped and untutored. It acknowledges the first emanations of children’s emerging sensuality and addresses them seriously, eliciting them and legitimating them, not as little sprouts that must be carefully tended in order to grow into gorgeous flowers, but as the real thing. Rock gives children, on a silver platter, with all the public authority of the entertainment industry, everything their parents always used to tell them they had to wait for until they grew up and would understand later.
Young people know that rock has the beat of sexual intercourse. That is why Ravel’s Bolero is the one piece of classical music that is commonly known and like by them.
(Bloom, A, (1987) The Closing of the American Mind, New York: Simon & Schuster, pp. 71-3.)
The power of the judgement of the ear ‘so apprehends settlements that it not only judges them and knows their differences, but is often delighted when the modes are sweet and well-ordered, and pained when disordered and incoherent ones offended the sense.
From this it follows that, of the for mathematical disciplines, the others are concerned with the pursuit of truth, but music is related not only to speculation but to morality as well. Nothing is more characteristic of human nature than to be soothed by sweet modes and stirred up by their opposites… From this may be discerned the truth of what Plato not idly said, that the soul of the universe is united by musical Concorde. For when, by means of what in ourselves is well and fitly ordered, we apprehend what in sounds is well and fitly combined, and takes pleasure in it, we recognise that we ourselves are united by this likeness’
(Boethius, De Institutione musica, C6th CE)
There is a chain of being that comprises the celestial hierarchy and an ecclesiastical hierarchy, and the musician plays the essential role of receiving the hymns sung in heaven and transmitting these, making them audible to mortal man
(Karp, in Wagner, The Seven Liberal Arts in the Middle Ages, p. 176)
The Pythagoreans, as they are called, devoted themselves to mathematics; they were the first to advance this study, and having been brought up in it they thought its principles were the principles of all things.
Since of these principles numbers are by nature the first, and in numbers they seemed to see many resemblances to the things that exist and come into being [including numbers being justice, and being soul and reason]; since, again, they saw that the attributes and the ratios of the musical scales were expressible in numbers; since, then, all other things seemed in their whole nature to be modelled after numbers, and numbers seemed to be the first things in the whole of nature, they supposed the elements of numbers to be the elements of all things, and the whole heaven to be a musical scale and a number.
(Aristotle, Metaphysics, I.5.)
Masculine and Feminine Numbers
Odd numbers were considered masculine; even numbers feminine because they are weaker than the odd. When divided they have, unlike the odd, nothing in the center. Further, the odds are the master, because odd + even always give odd. And two evens can never produce an odd, while two odds produce an even.
Since the birth of a son was considered more fortunate than birth of a daughter, odd numbers became associated with good luck. “The gods delight in odd numbers,” wrote Virgil (Calter, Squaring the Circle, p. 5-6; see also the wonderful website of Calter’s book: [link]
Numbers were [ ] at the basis of many medieval conceptions of the beautiful. According to the aesthetics of number theory, the parts of a work of art are determined in their size, proportions, and relationships in terms of numerical ratios. These proportions are ratios among the parts of a cathedral, for example, have nothing at all to do with the engineering aspects of the structure. Instead, they order the parts of the whole according to an abstract notion of intellectual beauty, one which speaks not to the senses which in all likelihood are not even able to perceive the ratios and proportions, but to the mind, which, on a close examination of the relationships between aisle and transept, width and height of nave, or sizes and distribution in a row of arches, is able to perceive a higher order and so arrive at an intellectual notion of the beautiful in that work.
But the function of numerical order and proportion in cathedrals is more than a matter of aesthetics. The ratio of numbers is the philosopher’s guide to the divine order in the nature of the universe and by transmitting these orders to the structure of the cathedral, the architect brought the design of his church into accord with the structure of the macrocosm and responded to the order of the numbers determined by the Divine Intellect.
(Masi, M. ‘Arithmetic’ in Wagner, D. (ed.) (1983) The Seven Liberal Arts in the Middle Ages, Bloomington: Indiana university Press, pp. 157-8.)
In this mnemonic about the seven liberal arts, grammar has priority over the others:
Gram loquitur; Dia vera docet; Rhet verba colorat;
Mus canit; Ar numerat; Ge ponderat; Asti colit astra.
Grammar speaks; dialectic teaches truth; rhetoric adorns words;
Music sings; arithmetic counts; geometry measures; astronomy studies stars.
‘Grammar is skill in the art of cultivated speech—skill acquired from famous writers of poetry and of prose; its end is to please through skill in finished speech and blameless writing’
(Cassiodorus, c. 551AD).
…grammar is the foundation, gate and source of all the other liberal arts, without which such arts cannot be known… By the knowledge of grammar justice is cultivated and the property of the estate of humanity is increased
(Foundation Deed of Winchester College, from Leach, (1911) Educational Charters 598-1909, p. 321).
One of the pupils of Dame Logic
Was sent to Grammar;
He bore letters to make peace.
Now I simply cannot refrain from telling this,
That when he arrived at his destination
He did not know the sense
Of the presents nor the preterits;
And that there where he had been brought up,
He had dwelt on them but little.
He had not learned thoroughly
Which are most difficult to inflect,
Adverbs and parts of speech,
Articles and declensions,
Genders and nominatives
Supines and imperatives,
Cases, figures, formations,
Singulars, plurals, a thousand terms;
For in the court of Grammar are more corners
Thank in all of Logic’s prattlings.
The boy did not know how to come to the point;
And came back in shame.
Henry d’Andeli, ‘The Battle of the Arts,’ 13th century
(From Ross, JB, and McLaughlin, MM, (1977) The Portable Medieval Reader, New York: Penguin, p. 592.)
‘About a quarter of an hour after five in the morning we were called up by one of the monitors of the chamber; and after Latin prayers we went into the cloysters to wash, and thence in order, two by two, to the schoole, where we were to be by six of the clock at furthest. Between six and eight we repeated our grammar parts (Latin and Greek); 14 or 15 of us being selected and called out to stand in a semi- circle before the Mr. and other scholars and their repeated four or five leaves in either… At dinner and supper time are read some portion of the Latin Bible….
(Westminster School, 17th century, from Monroe, 1905, pp. 525-6).
‘The Greek teacher presented grammar in a more philosophical way. When it was explained to Johannes that the accusative case, for example, is an extension in time and space, that the preposition does not govern the case but that the relation does, everything expanded before him. The preposition vanished; the extension in time and space became like an enormous empty picture for intuition.’(Kierkegaard, S. (1985) Johannes Climacus, Princeton: Princeton University Press, p. 121.)
“What really alarms me about President Bush’s ‘War on Terrorism’ is the grammar. How do you wage war on an abstract noun? How is ‘Terrorism’ going to surrender? It’s well known, in philological circles, that it’s very hard for abstract nouns to surrender.”
‘We go about our daily lives understanding almost nothing of the world. We give little thought to the machinery that generates the sunlight that makes life possible, to the gravity that glues us to an earth that would otherwise send us spinning off into space, or the atoms of which we are made and on whose stability we fundamentally depend. Except for children (who don’t know enough not to ask the important questions), few of us spend much time wondering why nature is the way it is; where the cosmos came from, or whether it was always here; if time will one day flow back backward and effects precede causes; or whether there are ultimate limits to what humans can know. There are even children, and I have met some of them, who want to know what a black hole looks like; what is the smallest piece of matter; why we remember the past and not the future; how it, if there was chaos early, that there is, apparently, order today; and why there is a universe.
In our society it is still customary for parents and teachers to answer most of these questions with a shrug, or with an appeal to vaguely recalled religious precepts. Some are uncomfortable with issues like these, because they so vividly expose the limitations of human understanding.
But much of philosophy and science has been driven by such enquiries’
(Carl Sagan, Introduction to Stephen Hawking’s a Brief History of Time.)
‘Up to now, most scientists have been too occupied with the development of new theories that describe what the universe is to ask the question why. On the other hand, the people whose business it is to ask why, the philosophers, have not been able to keep up with the advance of scientific theories …
However, if we do discover a complete theory, it should in time be understandable in broad principle by everyone, not just a few scientists. Then we shall all, philosophers, scientists and just ordinary people, be able to take part in the discussion of the question of why it is that we and the universe exist. If we find the answer to that, it would then be the ultimate triumph of human reason – for then we would know the mind of God.’
‘Can any person imagine that this overall pattern of constellations, this massive embellishment of the heavens, can have been the outcome of atoms careering at random in various chance directions? Or that any other natural process devoid of intelligence or reason could have achieved a creation which not merely required the use of reason, but whose working cannot be understood without its utmost application?’
(Cicero, The Nature of the Gods, book 2).
By far the best way I know to engage the religious sensibility, the sense of awe, is to look up on a clear night. I believe that it is very difficult to know who we are until we understand where and when we are. I think everyone in every culture has felt a sense of awe and wonder looking at the sky. This is reflected throughout the world in both science and religion. Thomas Carlyle said the wonder is the basis of worship. And Albert Einstein said, ‘I maintain that the cosmic religious feeling is the strongest and noblest motives for scientific research.
Some five or six or 7 billion years from now, the sun will become a red giant star and will engulf the orbits of Mercury and Venus and probably the Earth. The Earth then would be inside the sun, and some of the problems that face us on this particular day will appear, by comparison, modest. On the other hand, since it is 5000 or more million years away, it is not our most pressing problem. But it is something to bear in mind. It has theological implications.
(Carl Sagan, Gifford Lectures, 1985).
In the beginning to construct the body of the All, God was making it of fire and earth … [and] in the midst between fire and earth God set water and air [bestowing] upon them so far as possible a like ratio towards one another … out of these materials, such in kind and four in number, the body of the Cosmos was harmonized by proportion and brought into existence (31b-32c).
It is plain I presume to everyone that fire and earth and water and air are solid bodies; and the form of a body, in every case, possesses depth also. Further, it is absolutely necessary that depth should be bounded by a plane surface; and the rectilinear plane is composed of triangles … These we lay down as the principles of fire and all the other bodies, proceeding according to a method in which the probable is combined with the necessary; but the principles which are still higher than these are known only to God and the man who is dear to God (53c-e
The Platonic Solids
Marvel at the laws of geometry employed by Plato as described by Carl Sagan: [link]
In the human body the central point is naturally the navel. For if a man be placed flat on his back, with his hands and feet extended, and a pair of compasses centred at his navel, the fingers and toes of his two hands and feet will touch the circumference of a circle described therefrom. And just as the human body yields a circular outline, so too a square figure may be found from it. For if we measure the distance from the soles of the feet to the top of the head, and then apply that measure to the outstretched arms, the breadth will be found to be the same as the height, as in the case of plane surfaces which are perfectly square.
Vitruvius, Ten books on Architecture, trans. Hickey, chapter I, para. 3, at: [link]
“Philosophy [i.e., physics] is written in this grand book—I mean the universe—which stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometrical figures, without which it is humanly impossible to understand a single word of it; without these, one is wandering around in a dark labyrinth.”
Galileo Galilei, Il Saggiatore (The Assayer, 1623)
A reasonable conclusion from this might be that physics, astronomy, medicine, and all other disciplines which depend on the study of composite things, are doubtful; while arithmetic, geometry and other subjects of this kind, which deal only with the simplest and most general things, regardless of whether they really exist in nature or not, contain something certain and indubitable. For whether I am awake or asleep, two and three added together make five, and a square has no more than four sides. It seems impossible that such apparent truths should incur any suspicion of being false.
(Descartes, R. (1984) Meditations on First Philosophy, trans. Cottingham, Stoothoff and Murdoch, Cambridge: Cambridge university Press, p. 14).
Into the assembly of the Gods came Dialectic, a woman whose weapons are complex and knotty utterances. Without her, nothing follows, and likewise, nothing stands in opposition…
In her left hand she held a snake twined in immense coils; in her right-hand a set of patterns carefully inscribed on wax tablets, which were adorned with the beauty of contrasting colour, was held on the inside by a hidden hook; but since her left hand kept the crafty device of the snake hidden under her cloak, her right hand was offered to one and all. Then if anyone took one of those patterns, he was soon caught on the hook and dragged towards the poisonous coils of the hidden snake, which presently emerged and after first biting the man relentlessly with the venomous points of the sharp teeth then gripped him in its many coils and compelled into the intended position. If no one wanted to take any of the patterns, Dialectic confronted them with some questions; or secretly stirred the snake to creep up on them until its tight embrace strangled those who were caught and compelled them to accept the will of their interrogator.
(Martianus Capella, The Marriage of Philology and Mercury, pp. 106-7).
THEAETETUS: I think that someone knows something when he perceives it; my current impression, at any rate, is that knowledge and perception are the same.
SOCRATES: … this statement of yours about knowledge is a substantial one; it’s what Protagoras used to say as well, though he used different words to say the same thing. I mean, he says somewhere that ‘Man is the measure of all things…’ No doubt you’ve read this?
THEAETETUS: Yes, often.
SOCRATES: And doesn’t he mean by this that ‘Each and every event is for me as it appears to me, and is for you as it appears for you…?’
THEAETETUS: That’s what he says.
SOCRATES; … so, when the same wind is blowing, one of us might feel chilly, while the other doesn’t. Or one might feel slightly chilly, the other rather cold?
SOCRATES: So when that happens, are we to describe the wind per se as cold or not cold? Or should we follow Protagoras and say that it is cold for the one who feels cold, but not for the one who doesn’t?
THEAETETUS: That seems reasonable… but what are you getting at Socrates?
SOCRATES: I will tell you… I mean the view that nothing is a single, non-relative identity, and that you cannot correctly identify anything or describe what it is like. If you call something big it will also turn out to be small, and if you call something heavy, it will also turn out to be light, and so on for everything, on the grounds that nothing is single and you cannot say what it is or what it is like, In fact, everything which we describe as ‘being’ is actually in the process of being generated… (Plato, 1987, pp. 30-32).
(From the Platonic dialogue, Theaetetus, trans. R. Waterfield, Penguin.)
‘His father combined an irresistible dialectic with an omnipotent imagination. Whenever his father on occasion engaged in an argument with someone else, Johannes was all ears, all the more so because everything proceeded with an almost festive formality.
His father always let his opponent say everything he had to say and, as a precaution, always asked him if he had anything more to say before he began his response. Johannes, having followed the opponent’s case with keen attention, had in his own way a co-interest in the outcome.
Then came the pause; his father’s response followed, and—look!—in a twinkling everything was changed. How it happened remained a riddle to Johannes, but his soul delighted in this drama.
The opponent spoke again, and Johannes listened even more attentively, lest he lose the thread of thought. The opponent summed up his argument, and Johannes could almost hear his heart beating, so impatiently did he wait to see what would happen. —And it did happen. In an instant, everything was turned upside down; the explicable was made inexplicable, the certain doubtful, the opposite was made obvious.
(Kierkegaard, S. (1985) Johannes Climacus, Princeton: Princeton University Press, p. 122.)