The Legacy of Greece. Various

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СКАЧАТЬ of the University of Strasbourg. When his researches are complete, the continuity of Greek and modern philosophy will be plainly seen, and the part played by Platonism in the making of the modern European mind will be made manifest. We shall then understand better than ever why Greek philosophy is a subject of perennial interest.

      The history of Greek philosophy is, in fact, the history of our own spiritual past, and it is impossible to understand the present without taking it into account. In particular, the Platonist tradition underlies the whole of western civilization. It was at Rome, as has been pointed out, that Plotinus taught, and it was in certain Latin translations of the writings of his school that St. Augustine found the basis for a Christian philosophy he was seeking. It was Augustine’s great authority in the Latin Church that made Platonism its official philosophy for centuries. It is a complete mistake to suppose that the thinking of the Middle Ages was dominated by the authority of Aristotle. It was not till the thirteenth century that Aristotle was known at all, and even then he was studied in the light of Platonism, just as he had been by Plotinus and his followers. It was only at the very close of the Middle Ages that he acquired the predominance which has made so strong an impression on the centuries that followed. It was from the Platonist tradition, too, that the science of the earlier Middle Ages came. A considerable portion of Plato’s Timaeus had been translated into Latin in the fourth century by Chalcidius with a very elaborate commentary based on ancient sources, while the Consolation of Philosophy, written in prison by the Roman Platonist Boethius in A. D. 525, was easily the most popular book of the Middle Ages. It was translated into English by Alfred the Great and by Chaucer, and into many other European languages. It was on these foundations that the French Platonism of the twelfth century, and especially that of the School of Chartres, was built up, and the influence of that school in England was very great indeed. The names of Grosseteste and Roger Bacon may just be mentioned in this connexion, and it would not be hard to show that the special character of the contribution which English writers have been able to make to science and philosophy is in large measure attributable to this influence.

      But the interest of Greek philosophy is not only historical; it is full of instruction for the future too. Since the time of Locke, philosophy has been apt to limit itself to discussions about the nature of knowledge, and to leave questions about the nature of the world to specialists. The history of Greek philosophy shows the danger of this unnatural division of the province of thought, and the more we study it, the more we shall feel the need of a more comprehensive view. The ‘philosophy of things human’, as the Greeks called it, is only one department among others, and the theory of knowledge is only one department of that. If studied in isolation from the whole, it must inevitably become one-sided. From Greek philosophy we can also learn that it is fatal to divorce speculation from the service of mankind. The notion that philosophy could be so isolated would have been wholly unintelligible to any of the great Greek thinkers, and most of all perhaps to the Platonists who are often charged with this very heresy. Above all, we can learn from Greek philosophy the paramount importance of what we call the personality and they called the soul. It was just because the Greeks realized this that the genuinely Hellenic idea of conversion played so great a part in their thinking and in their lives. That, above all, is the lesson they have to teach, and that is why the writings of their great philosophers have still the power to convert the souls of all that will receive their teaching with humility.

      J. Burnet.

MATHEMATICS AND ASTRONOMY

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      It has been well said that, if we would study any subject properly, we must study it as something that is alive and growing and consider it with reference to its growth in the past. As most of the vital forces and movements in modern civilization had their origin in Greece, this means that, to study them properly, we must get back to Greece. So it is with the literature of modern countries, or their philosophy, or their art; we cannot study them with the determination to get to the bottom and understand them without the way pointing eventually back to Greece.

      When we think of the debt which mankind owes to the Greeks, we are apt to think too exclusively of the masterpieces in literature and art which they have left us. But the Greek genius was many-sided; the Greek, with his insatiable love of knowledge, his determination to see things as they are and to see them whole, his burning desire to be able to give a rational explanation of everything in heaven and earth, was just as irresistibly driven to natural science, mathematics, and exact reasoning in general, or logic.

      To quote from a brilliant review of a well-known work: ‘To be a Greek was to seek to know, to know the primordial substance of matter, to know the meaning of number, to know the world as a rational whole. In no spirit of paradox one may say that Euclid is the most typical Greek: he would know to the bottom, and know as a rational system, the laws of the measurement of the earth. Plato, too, loved geometry and the wonders of numbers; he was essentially Greek because he was essentially mathematical. … And if one thus finds the Greek genius in Euclid and the Posterior Analytics, one will understand the motto written over the Academy, μηδεις αγεωμετρητος εισιτω. To know what the Greek genius meant you must (if one may speak εν αινιγματι) begin with geometry.’

      Mathematics, indeed, plays an important part in Greek philosophy: there are, for example, many passages in Plato and Aristotle for the interpretation of which some knowledge of the technique of Greek mathematics is the first essential. Hence it should be part of the equipment of every classical student that he should have read substantial portions of the works of the Greek mathematicians in the original, say, some of the early books of Euclid in full and the definitions (at least) of the other books, as well as selections from other writers. Von Wilamowitz-Moellendorff has included in his Griechisches Lesebuch extracts from Euclid, Archimedes and Heron of Alexandria; and the example should be followed in this country.

      Acquaintance with the original works of the Greek mathematicians is no less necessary for any mathematician worthy of the name. Mathematics is a Greek science. So far as pure geometry is concerned, the mathematician’s technical equipment is almost wholly Greek. The Greeks laid down the principles, fixed the terminology and invented the methods ab initio; moreover, they did this with such certainty that in the centuries which have since elapsed there has been no need to reconstruct, still less to reject as unsound, any essential part of their doctrine.

      Consider first the terminology of mathematics. Almost all the standard terms are Greek or Latin translations from the Greek, and, although the mathematician may be taught their meaning without knowing Greek, he will certainly grasp their significance better if he knows them as they arise and as part of the living language of the men who invented them. Take the word isosceles; a schoolboy can be shown what an isosceles triangle is, but, if he knows nothing of the derivation, he will wonder why such an apparently outlandish term should be necessary to express so simple an idea. But if the mere appearance of the word shows him that it means a thing with equal legs, being compounded of ισος, equal, and σκελος, a leg, he will understand its appropriateness and will have no difficulty in remembering it. Equilateral, on the other hand, is borrowed from the Latin, but it is merely the Latin translation of the Greek ισοπλευρος, equal-sided. Parallelogram again can be explained to a Greekless person, but it will be far better understood by one who sees in it the two words παραλληλος and γραμμη and realizes that it is a short way of expressing that the figure in question is contained by parallel lines; and we shall best understand the word parallel itself if we see in it the statement of the fact that the two straight lines so described go alongside one another, παρ’ αλληλας, all the way. Similarly a mathematician should know that a rhombus is so called from its resemblance to a form of spinning-top (ῥομβος from ῥεμβω, to spin) and that, just as a parallelogram is a figure formed by two pairs of parallel straight lines, so a parallelepiped СКАЧАТЬ