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its study can not, therefore, it is evident, supply us with any means of obviating those illusions from which it is itself exempt. The contrast of mathematics and philosophy, in this respect, is an interesting object of speculation ; but, as imitation is impossible, one of no practical result.
3. I nrespect of the matter : - Mathematics afford us no assistance, either in conquering the difficulties, or in avoiding the dangers which we encounter in the great field of probabilities wherein we live and move.
As to the difficulties :-Mathematical demonstration is solely occupied in deducing conclusions; probable reasoning, principally concerned in looking out for premises.-All mathematical reasoning flows from, and-admitting no tributary streams can be traced back to its original source : principle and conclusion are convertible. The most eccentric deduction of the science is only the last ring in a long chain of reasoning, which descends, with adamantine necessity, link by link, in one simple series, from its original dependence.-In contingent matter, on the contrary, the reasoning is comparatively short; and as the conclusion can seldom be securely established on a single antecedent, it is necessary, in order to realize the adequate amount of evidence, to accumulate probabilities by multiplying the media of inference; and thus to make the same conclusion, as it were, the apex of many convergent arguments. In general reasoning, therefore, the capacities mainly requisite, and mainly cultivated, are the prompt acuteness which discovers what materials are wanted for our premises, and the activity, knowledge, sagacity, and research able competently to supply them.-In demonstration, on the contrary, the one capacity cultivated is that patient habit of suspending all intrusive thought, and of continuing an attention to the unvaried evolution of that perspicuous evidence which it passively recognizes, but does not actively discover. Of Observation, Experiment, Induction, Analogy, the mathematician knows nothing. What Mr. Whewell, therefore, alleges in praise of demonstration—" that the mixture of various grounds of conviction, which is so common in other men's minds, is rigorously excluded from the mathematical student's,” is precisely what mainly contributes to render it useless as an exercise of reasoning. In the practical business of life the geometer is proverbially but a child : and for the theory of science ?-the subtlety of mind, the multiformity of matter, lie far beyond calculus and demonstration ; mathematics are not the net in which Psyche may be caught, nor the chain by which Proteus can be fettered.
As to the dangers :- How important soever may be the study of general logic, in providing us against the fallacies which originate both in the form and in the vehicle of reasoning, the error of our conclusions is, in practice, far less frequently occasioned by any vice in our logical inference from premises, than by the sin of a rash assumption of premises materially false. Now if mathematics, as is maintained, do constitute the true logical catharticon, the one practical propædeutic of all reasoning, it must of course enable us to correct this the most dangerous and prevalent of our intellectual failings. But, among all our rational pursuits, mathematics stand distinguished, not merely as affording us no aid toward alleviating the evil, but as actually inflaming the disease. The mathematician, as already noticed, is exclusively engrossed with the deduction of in. evitable conclusions, from data passively received; while the cultivators of the other departments of knowledge, mental and physical, are for the most part, actively occupied in the quest and scrutiny, in the collection and balancing of probabilities, in order to obtain and purify the facts on which their premises are to be established.
HISTORICAL DEVELOPMENT OF CLASSICAL STUDIES.. The Greek and Latin tongues, with the literature to which these tongues are the keys, obtained their foothold in the schools of Christian nations, not because the study of a dead language was the best mental discipline for young students, or the only means of their acquiring a masterly freedom in the use of their own tongue, but because at the time they were introduced into schools, as branches of study, they were the languages of educated men, and were employed for public business, literature, philosophy, science and religion. Once introduced, they have retained their position partly for the same reasons, and partly by the influence of endowments and the force of habit.
It arose from the relations in which the Greek and Latin languages have stood, in the past, to the whole higher life, intellectual and moral, literary and scientific, civil and religious, of Western Europe. Greeks and Romans, as well as Jews, are our spiritual ancestors. They left treasures of recorded thought, word, and deed, by the timely and judicious use of which their heirs have become the leaders of mankind. But they left them in custody of their nativo tongues.
After Alexander, the Greek tongue spread widely throngh the East, and became the means of blending Oriental with Western modes of thought. Commerce prepared the way for liberal intercourse. Ideas were exchanged freely with reciprocal advantage. But the Greek, offering new philosophy for old religion, obtained for Europe the more precious gift
Χρύσεα χαλκείων, εκατόμβοι έννεηβαίων. No faith attracted more attention than that of the Jews. Their sacred books were carefully translated into the Greek language, and afterwards, by fanciful adaptation, and by real insight, expressed in terms of Greek thought. Greek philosophy, meanwhile, embracing with reverence the long-sought wisdom of the East, went beyond the measure of Pythagoras, Socrates, or Plato, and often beyond the guidance of sober reason, in ascetic abstraction from the things of sense, and ardent longing after spiritual truth.
Christianity itself had Greek for its mother-tongue. St. Paul, a Roman citizen, writes in Greek to the Christians of Rome. The Epistle to the Hebrews is Greek, and so is that of St. James " to the twelve tribes scattered abroad.”
For great part of three centuries, the churches of the West were mostly “Greek religious colonies." 4 Their language, their organization, their liturgy, I their Scriptures, were Greek. The Apostolic Fathers, the apologists and historians of the early church, the great theologians, orthodox and heretic, wrote and spoke Greek. The proceedings of the first seven Councils were carried on, and the speculative form of the Christian faith defined, in that language. It
* This article is mainly from an " Essay on the History of Classical Education," in McMillan"s Essays on Liberal Studies. 1867, by Charles Stuart Parker. The author refers to Von Raumer, and Schmidt, for his material.
† Milman's Latin Christianity, i. 27.
1 It is significant that the word liturgy is Greek, as are hymn, psalm, homily, and catechism, baptist and eucharist, priest, bishop, and pope.
was hardly possible to bandle the profounder questions in any other. Augustine is at a loss for words to speak of them in Latin. Seven centuries later Anselm undertakes the task with diffidence; nor is it clear whether in his own judgment he succeeds or fails.
Thus, when Christianity became the State religion, and the emperor, in such broken language as he could command, took a modest part in the discussions of Nicæa, it was a last and signal spiritual triumph of captive Greece over Rome.
The ancient Church encouraged the study of heathen literature, but with a paramount regard to morality and Christian truth. Plato, Cicero, and Quintilian had pointed out the danger of using the poets indiscriminately as schoolbooks;
and the Father who slept with Aristopbanes under his pillow would not have placed him in the hands of boys. But even Tertullian allowed Christian boys to attend the public schools under pagan
Origen made the study of heathen poets and moralists preparatory to that of higher Christian truth. His master, Clement, tanght that philosophy was the testament or dispensation given to the Greeks, the schoolmaster to bring them, as the Mosaic law brought the Jews, to Christ. And his teaching was generally accepted. To this day " along the porticoes of Eastern churches, both in Greece and Russia, are to be seen portrayed on the walls the figures of Homer, Thucydides, Pythagoras, and Plato, as pioneers preparing the way for Christianity.” When Julian forbade the Christians to institute public schools of rhetorio and literature, in which pagan authors might be read, the bishops protested.
During this first Christian age, Greek was the common language of literature, while Latin, after Tacitus and Pliny, rapidly declined. The “Meditations" of the Emperor Marcus Aurelius are composed in the vernacular of the freedman Epictetus. No Latin names can be placed beside those of Lucian and Plutarch, Arrian and Dion Cassius, Ptolemy and Galen. At Athens and Alexandria, the great conservative and liberal universities, studies in grammar and criticism were conducted side by side with philosophy and science. In both alike the Greek tongue was employed. Of all the considerable intellectual production which went on throughout the Roman world, jurisprudence alone was Latin.
Latin Language. If Greek was the chosen language which carried literature, science, and wisdom, Christian, as well as heathen, to the highest pitch in the ancient world, Latin also was an appointed means of transferring them to Western Europe.
The imperial art of Rome laid the solid foundations on which, when the flood of barbarism began to subside, much of the old fabric was laboriously reconstructed, before the thoughts of man took a wider range. In Spain and Gaul Latin became the mother tongue. But in uneducated mouths it resumed that process of decay and regeneration, the natural life of a language spoken and not written, which only literature can arrest. Hence in time, Italians, as well as Spaniards and French, had to learn book-Latin as a foreign language. It was to them what the writings of our forefathers would be to us, if “ Englisc" literature excelled English as Roman did “Romance." But other than literary interests maintained the old Latin as a common language beside the provincial dialects of the new.
The laws of the Western Empire, the last and greatest produet of the an. cient Roman mind, were adopted by the Gothic, Lombard, and Carlovingian dynasties, and in the twelfth century the first great European school at Bologna was thronged by students of Roman law. At one time there were twenty thousand, from different countries, dividing their attention between civil and canon law, the Pandects and the Decretals. Both were studied with a view to advancement in life, but especially to Church preferment.
Indeed it may be said, with as much truth as is required in metaphor, that the ark which carried through the darkest age, together with its own sacred treasures, the living use of ancient Latin, and some tradition of ancient learn. ing, was the Christian Church.
What at first had been everywhere a Greek became in Western Europe a Latin religion. The discipline of Rome maintained the body of doctrine whiclı the thought of Greece had detined. A new Latin version, superseding alike the venerable Greek translation of the Old Testament and the original words of Evangelists and A postles, became the received text of Holy Scripture. The Latin Fathers acquired an authority scarcely less binding. The ritual, les. sous, and hymns of the Church were Latin. Ecclesiastics transacted the business of civil departments requiring education. Libraries were armories of the Church: grammar was part of her drill. The humblest scholar was enlisted in her service: she recruited her ranks by founding Latin schools. “Education in the rudiments of Latin," says Hallam, "was imparted to a greatur number of individuals than at present;" and, as they had more use for it than at present, it was longer retained. If a boy of humble birth had a taste for letters, or if a boy of high birth had a distaste for arms, the first step was to learn Latin. His foot was then on the ladder. He might rise by the good offices of his family to a bishoprie, or to the papacy itself by merit and the grace of God. Latin enabled a Greek from Tarsus (Theodore) to become the founder of learning in the English church; and a Yorkshireman (Alcuin) to organize the schools of Charlemagne. Without Latin, our English Winfrid (St. Boniface) could not have been apostle of Germany and reformer of the Frankish Church ; or the German Albert, master at Paris of Thomas Aquinas; or Nicholas Breakspeare, Pope of Rome. With it, Western Christendom was one vast field of labor: calls for self-sacrifice, or offers of promotion, might come from north or south, from east or west.
Thus in the Middle Ages Latin was made the groundwork of education; not for the beauty of its classical literature, nor because the study of a dead lan. guage was the best mental gympastic, or the only means of acquiring a masterly freedom in the use of living tongues, but because it was the language of educated men throughout Western Europe, employed for public business, literature, philosophy, and science; above all, in God's providence, essential to the unity, and therefore enforced by the authority, of the Western Church.
But the Latin of the Middle Ages was not classical, and in the West Greek became an unknown tongue. Cicero did less to form style than Jerome; Plato was forgotten in favor of Augustine; Aristotle alone, translated out of Greek into Syriac, out of Syriac into Arabic, out of Arabic into Latin, and in Latin purged of every thing offensive to the medieval mind, had become in the folios of Thomas Aquinas a buttress, if not a pillar, of the Christian Church.
Prof. Max MÜLLER, Taylorian Professor of Modern Languages at Oxford, remarks on the study of these languages :
The experience of German schools, as well as of English, as generally constituted, is this : fluency in speaking is never acquired. The time spared from other studies is only' sufficient to give the pupil a good grounding in grammar, and the mastery of a sufficient number of words to enable him to read a newspaper or an historical author.
Some boys have no ear for accents at all, just as some have no ear for music, and, although they may bear a word pronounced by a Frenchman, they cannot imitate it.
Much more might be saved in the teaching French at public schools if it was grafted on the knowledge of Latin which most of the boys possess. There is no feature of French grammar which does not find its explanation in Latin, and if the connecting links were clearly put before the pupil, he would find that his knowledge of Latin enables him at once to understand the apparently new parts of French grammar that come before him. The experiment was made in France in 1852, under the recommendation of the Minister, and in a text-book prepared by M. Egger, a member of the Institute.
In a public school, French should be taught by an Englishman properly instructed in the language, assisted by a French teacher, who should have charge of the pronunciation and idiomatic part of the language.
The study of French and German has increased in Oxford — nearly all its good scholars try to learn German, because it opens a vast literature.
Socially and educationally; I think the study of Latin and Greek is of the highest importance. Frederick the Great said to his tea, hers: do, do not let a boy grow up without knowing Latin.”
Prof. GOLDWIN Smith distinguishes between the earlier and the later motives for the excessive devotion to classical studies thus :
Then (in the period of the Tudors and earlier Stuarts) education was classical, but classical learning was then, not a gymnastic cxercise of the mind in philology, but a deep draught from what was the great and almost the only spring of philosophy, science, history, and poetry at that time. It introduced the student to a great treasure of wisdom and knowledge, and not to philological niceties and beautics. Latin was then the language of literary, ecclesiastic, diplomatic, loyal, academic Europe; and familiarity with it was the first and most indispensable accomplishment, not only of the gentlemen, but of the high born ladies of the time.
In choosing the subjects of boys studies, you may use your own discretion ; in choosing the subjects of a man's studies, if you desire any worthy and fruitful effect, you must choose such as the world values, and such as may receive the allegiance of a manly mind. It has been said that six months study of the language of Schiller and Goethe, will now open to the student more enjoyment than six years study of the language of Greece and Rome. It is certain that six months study of French will now open to the student more of Europe, than six years of that which was once the European tongue.
Baron Houghton (Richard Monckton Milnes, raised to the peerage in 1862), in an Essay on the Social Results of Classical Education (published in 1867), advocates the more frank recognition of the worth and use of translations into modern languages, which represent, as truly as may be, the graces of form, and the essential merits of the original writers : versions, not merely accurate, but sympathetic with the matter and style they are handling - of poetry, by poets, of oratory, by orators, of history and philosophy, by affectionate students of the emotions and reflections of mankind. These should, by right, be the most effective material of school training, instead of being prohibited, and regarded as substitutes for severe study and inducements to juvenile indolence. But the true encouragement to a more general and unpedantic cultivation of what is universal and enduring in classic literature and life, beyond the mechanism of language, would result from such an alteration of the habitual methods of instruction as would strive, first and foremost, to fill the mind of each pupil with the realities of the past, and to make the thoughts and deeds of their old excellencies as intelligible to him as the events of his own time in the working of his own observation."