Mathematicians From Greece

"As man loses touch with his 'inner being', his instinctive depths, he finds himself trapped in the world of consciousness, that is to say, in the world of other people. Any poet knows this truth; when other people sicken him, he turns to hidden resources of power inside himself, and he knows then that other people don't matter a damn. He knows the 'secret life' inside him is the reality; other people are mere shadows in comparison. but the 'shadows' themselves cling to one another. 'Man is a political animal', said Aristotle, telling one of the greatest lies in human history. Man has more in common with the hills, or with the stars, than with other men."

"Aristotle especially, both by speculation and observation... reached something like the modern idea of a succession of higher organizations from lower, and made the fruitful suggestion of "a perfecting principle" in Nature. With the coming in of Christian theology this tendency toward a yet truer theory of evolution was mainly stopped, but the old crude view remained..."

"We've got to purge Aristotle from our system." "I've never read him so why do I have to purge him from my system?" "It's proof of his grip on Western Man that he dominates the thinking of people who have never heard of him."

"It is an age of Intellectual slaveries; If they meet any thing extraordinary, they prune it with distinctions, or dawb it with false Glosses, til it looks like the Traditions of Aristotle. His followers are so confident of his principles they seek not to understand what others speak, but to make others speak what they understand... Their Aristotle is a Poet in text, his principles are but Fancies, and they stand more on our Concessions, then his Bottom. Hence it is that his followers, notwithstanding the Assistance of so many Ages, can fetch nothing out of him but Notions: And these indeed they use, as He sayeth Lycophron did his Epithets, Non ut Condimentis, sed ut Cibis, Their Compositions are a meer Tympanie of Terms... It is better then a Fight in Quixot, to observe what Duels, and Digladiations they have about Him. One will make him speak Sense another Non-sense and a third both, Aquinas palps him gently, Scotus makes him winch and he is taught like an ape to shew severall tricks. If we look on his adversaries the least amongst them hath foyld him, but Telesius knocked him in the head, and Campanella hath quite discomposed him... Aristotle thrives by scuffles and the world cryes him up, when trueth cryes him down."

"Aristotle's works are full of platitudes in much the same way that Shakespeare's Hamlet is full of quotations."

"Thus to the plain man there may be no metaphor in Aristotle's "substance", Descartes' "machine of nature," Newtonian "force" and "attraction," Thomas Young's "kinetic energy" and Michelangelo's figure of Leda. Placed in their customary contexts these present nothing to him but the face of literal truth. To the initiated, however, who are aware of the "gross original" senses as well as the now literal senses , they may become metaphors. There are no metaphors per se...."

"In matter-theory, as in astronomy, the Church's commitment to Aristotle was in due course to prove an embarassment. In both branches of science his speculative distinction between terrestrial and celestial matter was insecure from the very beginning. His own most loyal commentator, ... had already dreamt of a theory unifying all things, and John Philoponos... had rejected the distinction between terrestrial and celestial matter outright. Nevertheless, it was still an axiom of almost a thousand years later."

"The metaphysical doctrine of 'permanent essences' drew empirical support from the success of Aristotle's zoological theory of fixed species, which was its most convincing application to our actual experience of the world. ...[T]he doctrine of fixed organic species simply exemplified, in the special sphere of biology, the permanent character of all 'rationally intelligible' entities. Conversely, Darwin demonstrated that Aristotle's most favored examples failed to support... the metaphysical assumption on which orthodox Greek natural philosophy had been based. Species were not... permanent entities; the earlier 'typological' or 'essentialist' approach to taxonomy inherited from Aristotle misrepresented the long term history of living things. ...However irrelevant the empirical details of Darwin's work may be to general philosophy, the abstract form of his explanatory schema has a much broader significance. So, when Darwin and his successors showed that the whole zoological concepts of 'species' must be reanalysed in populational terms, their demonstration knocked away [a] prop from the traditional metaphysical debate."

"Aristotle... distinguished four sorts of explanatory factor... and in later centuries these came to be known as his 'four causes'. The name is unfortunate, since nowadays we usually restrict the term 'cause' to one of his four types... they would have been better called his 'four becauses'—since he was concerned to distinguish, not the different varieties of cause and effect, but rather the different senses in which the question 'Why?' can be asked... [W]e could give four different answers, whose relevance would depend on our precise interpretation of the question. We could refer to: (i) The material constitution... or 'From what?'... (ii) The form, essence, or 'What was it?'... (iii) The precipitating cause or 'By What?'... (iv) The end [destination or purpose], or 'In aid of what?'... These four types of explanation are not necessarily rivals. ...all four types can frequently be cited without inconsistency. Indeed, apart from a few phenomena... which have no function and so 'just happen', Aristotle thought all natural events called for explanation in all four ways."

"Aristotle...is the first man [Greek], so far as I know, to have collected books."

"Men often speak of virtue without using the word but saying instead "the quality of life" or "the great society" or "ethical" or even "square." But do we know what virtue is? Socrates arrived at the conclusion that it is the greatest good for a human being to make everyday speeches about virtue-apparently without ever finding a completely satisfactory definition of it. However, if we seek the most elaborate and least ambiguous answer to this truly vital question, we shall turn to Aristotle's Ethics. There we read among other things that there is a virtue of the first order called magnanimity—the habit of claiming high honors for oneself with the understanding that one is worthy of them. We also read there that sense of shame is not a virtue: sense of shame is becoming for the young who, due to their immaturity, cannot help making mistakes, but not for mature and well-bred men who simply always do the right and proper thing. Wonderful as all this is-we have received a very different message from a very different quarter."

"The old Greek philosophy, which in Europe in the later middle ages was synonymous with the works of Aristotle, considered motion as a thing for which a cause must be found: a velocity required a force to produce and to maintain it. The great discovery of Galileo was that not velocity, but acceleration requires a force. This is the law of inertia of which the real content is: the natural phenomena are described by differential equations of the second order."

"Aristotle, who foresaw so many things, never dreamed of the social truth. Cuvier, whose sagacity is so highly lauded, was constrained to yield homage to the genius of Aristotle in Natural History; for myself, who am at this date in full possession of social truth, in politics Aristotle only inspires me with profound pity."

"Aristotle's genius was for showing the ways in which we might construct the "best practicable state." This was not mere practicality; the goals of political life are not wholly mundane. The polity comes into existence for the sake of mere life, but it continues to exist for the sake of the good life. The good life is richly characterized, involving as it does the pursuit of justice, the expansion of the human capacities used in political debate, and the development of all the public and private virtues that a successful state can shelter—military courage, marital fidelity, devotion to the physical and psychological welfare of our children, and so on indefinitely."

"Justice is of two kinds, justice in distribution and justice in rectification. ... Aristotle thinks primarily of setting things straight, and denies that rectificatory justice contains an element of 'tit for tat'."

"Socrates and Plato had no time for Athenian democracy, and wanted a revived aristocratic government for their city. But both were moral radicals; they thought ordinary morality was radically misguided, and that public opinion should be ignored when it was at odds with one's conscience or reason. Things are very different in Aristotle. Plato's concern for the balance of the soul was shared by Aristotle, but not his ethical radicalism."

"To modern educated people, it seems obvious that matters of fact are to be ascertained by observation, not by consulting ancient authorities. But this is an entirely modern conception, which hardly existed before the seventeenth century. Aristotle maintained that women have fewer teeth than men; although he was twice married, it never occurred to him to verify this statement by examining his wives' mouths. He said also that children would be healthier if conceived when the wind is in the north. One gathers that the two Mrs. Aristotles both had to run out and look at the weathercock every evening before going to bed. He states that a man bitten by a mad dog will not go mad, but any other animal will (Hiss. Am., 704a); that the bite of the shrewmouse is dangerous to horses, especially if the mouse is pregnant (ibid., 604b); that elephants suffering from insomnia can be cured by rubbing their shoulders with salt, olive oil, and warm water (ibid., 605a); and so on and so on. Nevertheless, classical dons, who have never observed any animal except the cat and the dog, continue to praise Aristotle for his fidelity to observation."

"Aristotle could have avoided the mistake of thinking that women have fewer teeth than men, by the simple device of asking Mrs Aristotle to keep her mouth open while he counted."

"Aristotle, so far as I know, was the first man to proclaim explicitly that man is a rational animal. His reason for this view was one which does not now seem very impressive; it was, that some people can do sums."

"I have gained this by philosophy ... I do without being ordered what some are constrained to do by their fear of the law."

"The roots of education ... are bitter, but the fruit is sweet."

"For the purposes of poetry a convincing impossibility is preferable to an unconvincing possibility."

"Homer has taught all other poets the art of telling lies skillfully."

"But the greatest thing by far is to have a command of metaphor. This alone cannot be imparted by another; it is the mark of genius, for to make good metaphors implies an eye for resemblances."

"διὸ εὐφυοῦς ἡ ποιητική ἐστιν ἢ μανικοῦ"

"διὸ καὶ φιλοσοφώτερον καὶ σπουδαιότερον ποίησις ἱστορίας ἐστίν: ἡ μὲν γὰρ ποίησις μᾶλλον τὰ καθόλου, ἡ δ᾽ ἱστορία τὰ καθ᾽ ἕκαστον λέγει."

"A whole is that which has beginning, middle, and end."

"A tragedy, then, is the imitation of an action that is serious and also, as having magnitude, complete in itself; in language ... not in a narrative form; with incidents arousing pity and fear, wherewith to accomplish its catharsis of such emotions."

"It is simplicity that makes the uneducated more effective than the educated when addressing popular audiences."

"Wit is cultured insolence."

"The young have exalted notions, because they have not been humbled by life or learned its necessary limitations; moreover, their hopeful disposition makes them think themselves equal to great things—and that means having exalted notions. They would always rather do noble deeds than useful ones: Their lives are regulated more by moral feeling than by reasoning.... All their mistakes are due to excess and vehemence and their neglect of the maxim of Chilon [The maxim was Μηδὲν ἄγαν, Ne quid nimis, Never go to extremes.]. They overdo everything; they love too much, hate too much, and the same with everything else. And they think they know everything, and confidently affirm it, and this is the cause of their excess in everything."

"Thus every action must be due to one or other of seven causes: chance, nature, compulsion, habit, reasoning, anger, or appetite."

"Evils draw men together."

"It is absurd to hold that a man ought to be ashamed of being unable to defend himself with his limbs but not of being unable to defend himself with reason when the use of reason is more distinctive of a human being than the use of his limbs."

"Rhetoric is the counterpart of Dialectic. Both alike are concerned with such things as come, more or less, within the general ken of all men and belong to no definite science. Accordingly, all men make use, more or less, of both; for to a certain extent all men attempt to discuss statements and to maintain them, to defend themselves and to attack others."

"For well-being and health, again, the homestead should be airy in summer, and sunny in winter. A homestead possessing these qualities would be longer than it is deep; and its main front would face the south."

"Misfortune shows those who are not really friends."

"Now the activity of the practical virtues is exhibited in political or military affairs, but the actions concerned with these seem to be unleisurely. Warlike actions are completely so (for no one chooses to be at war, or provokes war, for the sake of being at war; any one would seem absolutely murderous if he were to make enemies of his friends in order to bring about battle and slaughter); but the action of the statesman is also unleisurely, and-apart from the political action itself—aims at despotic power and honours, or at all events happiness, for him and his fellow citizens—a happiness different from political action, and evidently sought as being different. So if among virtuous actions political and military actions are distinguished by nobility and greatness, and these are unleisurely and aim at an end and are not desirable for their own sake, but the activity of reason, which is contemplative, seems both to be superior in serious worth and to aim at no end beyond itself, and to have its pleasure proper to itself (and this augments the activity), and the self-sufficiency, leisureliness, unweariedness (so far as this is possible for man), and all the other attributes ascribed to the supremely happy man are evidently those connected with this activity, it follows that this will be the complete happiness of man, if it be allowed a complete term of life."

"And happiness is thought to depend on leisure; for we are busy that we may have leisure, and make war that we may live in peace."

"After these matters we ought perhaps next to discuss pleasure. For it is thought to be most intimately connected with our human nature, which is the reason why in educating the young we steer them by the rudders of pleasure and pain; it is thought, too, that to enjoy the things we ought and to hate the things we ought has the greatest bearing on virtue of character. For these things extend right through life, with a weight and power of their own in respect both to virtue and to the happy life, since men choose what is pleasant and avoid what is painful; and such things, it will be thought, we should least of all omit to discuss, especially since they admit of much dispute."

"The best friend is he that, when he wishes a person's good, wishes it for that person's own sake."

"When people are friends, they have no need of justice, but when they are just, they need friendship in addition."

"ἄνευ γὰρ φίλων οὐδεὶς ἕλοιτ᾽ ἂν ζῆν, ἔχων τὰ λοιπὰ ἀγαθὰ πάντα"

"μεταβολὴ δὲ πάντων γλυκύ"

"What it lies in our power to do, it lies in our power not to do."

"Therefore only an utterly senseless person can fail to know that our characters are the result of our conduct."

"κατὰ τὸν δεύτερον, φασί, πλοῦν τὰ ἐλάχιστα ληπτέον τῶν κακῶν"

"οὕτω δὲ καὶ τὸ μὲν ὀργισθῆναι παντὸς καὶ ῥᾴδιον, καὶ τὸ δοῦναι ἀργύριον καὶ δαπανῆσαι· τὸ δ᾽ ᾧ καὶ ὅσον καὶ ὅτε καὶ οὗ ἕνεκα καὶ ὥς, οὐκέτι παντὸς οὐδὲ ῥᾴδιον"

"In cases of this sort, let us say adultery, rightness and wrongness do not depend on committing it with the right woman at the right time and in the right manner, but the mere fact of committing such action at all is to do wrong."

"The vices respectively fall short of or exceed what is right in both passions and actions, while virtue both finds and chooses that which is intermediate."