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from which to borrow anything. The method of signal additions presents no such difficulty.

We have said little about the method of proving addition or subtraction, as in the proof the scholar is as much liable to error as in the operation. We dismiss from notice the method of

After a sufficient variety of the ordinary questions has been given, the pupil should be asked to take the subtrahend several times from the min-proof by casting out the nines, which fails always uend, e. g.―

6783
1265

5518
1265

4 25 3
1265

2988

If he be asked to take the smaller number away as often as is possible, and to note the number of times that this can be done, it will form a useful preparation for division.

where two errors are made, one in excess, another as much in defect. Here is an instance where this proof would not only fail to detect error, but pronounce the question correct :

5638543 = 7
3457360 = 1

2180283 6

Here the nines cast from the minuend leave 7,
from the subtrahend 1, and from the remainder 6,
which is the difference of these. In these circum-
stances we are assured that the result is correct.
If examined, it will be found that there are two
figures of it wrong. '
W. K.

EDUCATION IN THE PLATONIC REPUBLIC.*

HE great purpose of education is to Coming as they do from the better light, they turn a man round from his natural will, after a little temporary perplexity, be able position at the bottom of this dark to see the dim shadows better than those who cave, where he sees nothing but sha- have never looked at anything else. Having con+ dows to fix his eyes in the other templated the true and real Forms of the Just, direction, and to induce him to ascend into clear Beautiful, Good-they will better appreciate the daylight. Education does not, as some suppose, images of these Forms which come and go, pass either pour knowledge into an empty mind, or by and repass in the cave. They will indeed be impart visual power to blind persons. Men have very reluctant to undertake the duties or exercise good eyes, but these eyes are turned in the wrong the powers of government: their genuine delight direction. The clever among them see sharply is in philosophy; and if left to themselves, they enough what is before them; but they have no- would cultivate nothing else. But such reluc thing before them except shadows, and the sharper tance is in itself one proof that they are the fittest their vision the more mischief they do. What is persons to govern. If government be placed in required is, to turn them round and draw them the hands of men eager to possess it, there will up so as to face the real objects of daylight. be others eager to dispossess them, so that comTheir natural eyesight would then suffice to ena-petition and factions will arise. Those who come ble them to see these objects well. The task of our education must be, to turn round the men of superior natural aptitude, and to draw them up into the daylight of realities. Next, when they shall have become sufficiently initiated in truth and philosophy, we must not allow them to bury themselves permanently in such studies-as they will themselves be but too eager to do. We must compel them to come down again into the cave and exercise ascendancy among their companions, for whose benefit their superior mental condition will thus become available.

* From vol. iii. p. 95 of Plato, and the other Companions of Sokrates. By George Grote, F.R.S., &c. London: John Murray"

forward to govern, having no good of their own, and seeking to extract their own good from the exercise of power, are both unworthy of trust, and sure to be resisted by opponents of the like disposition. The philosopher alone has his own good in himself. He enjoys a life better than that of a ruler; which life he is compelled to forego when he accepts power and becomes a ruler.

The main purpose of education, I have said (continues Sokrates) is, to turn round the faces of the superior men, and to invite them upwards from darkness to light-from the region of perishable shadows to that of imperishable realities.

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Now what cognitions, calculated to aid such a purpose, can we find to teach? Gymnastic, music, the vulgar arts, are all useful to teach, but they do not tend to that which we are here seeking. Arithmetic does so to a certain extent, if properly taught which at present it is not. It furnishes a stimulus to awaken the dormant intellectual and reflective capacity. Among the variety of sensible phenomena, there are some in which the senses yield a clear and satisfactory judgment, leaving no demand in the mind for any thing beyond there are others in which the senses land us in apparent equivocation; puzzle, and contradiction-so that the mind is stung by this apparent perplexity, and instigated to find a solution by some intellectual effort. Thus, if we see or feel the fingers of our hand, they always appear to the sense, fingers: in whatever order or manner they may be looked at, there is no contradiction or discrepancy in the judgment of sense. But if we see or feel them as great or small, thick or thin, hard or soft, &c., they then appear differently according as they are seen or felt in different order or under different circumstances. The same object which now appears great, will at another time appear small: it will seem to the sense hard or soft, light or heavy, according as it is seen under different comparisons and relations. Here then, sense is involved in an apparent contradiction, declaring the same object to be both hard and soft, great and small, light and heavy, &c. The mind, painfully confounded by such a contradiction, is obliged to invoke intellectual reflection to clear it up. Great and small are presented by the sense as inhering in the same object. Are they one thing, or two separate things? Intellectual reflection informs us that they are two enabling us to conceive separately two things, which to our sense appeared confounded together. Intellectual (or abstract) conception is thus developed in our mind, as distinguished from sense, and as a refuge from the confusion and difficulties of sense, which furnish the stimulus whereby it is awakened.

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master sets before his pupils numbers in the concrete, that is, embodied in visible and tangible objects-so many balls or pebbles. Each of these balls he enumerates as One, though they be unequal in magnitude, and whatever be the magnitude of each. If you remark that the balls are unequal-and that each of them is Many as well as One, being divisible into as many parts as you please he will laugh at the objection as irrelevant. He will tell you that the units to which his numeration refers are each Unum per se, indivisible and without parts; and all equal among themselves without the least shade of difference. He will add that such units cannot be exhibited to the senses, but can only be conceived by the intellect; that the balls before you are not such units in reality, but serve to suggest and facilitate the effort of abstract conception. In this manner arithmetical teaching conducts us to numbers in the abstract-to the real, intelligible, indivisible unit the Unum per se.

Geometrical teaching conducts the mind to the same order of contemplation; leading it away from variable particulars to unchangeable universal essence. Some persons extol geometry chiefly on the ground of its usefulness in applications to practice. But this is a mistake: its real value is in conducing to knowledge, and to elevated contemplations of the mind. It does, however, like arithmetic, yield useful results in practice: and both of them are farther valuable as auxiliaries to other studies.

After geometry-the measurement of lines and superficial areas-the proper immediate sequel is Stereometry, the measurement of solids. But this latter is nowhere properly honoured and cultivated; though from its intrinsic excellence, it forces its way partially even against public neglect and discouragement. Most persons omit it, and treat astronomy as if it were the immediate sequel to geometry: which is a mistake, for astronomy relates to solid bodies in a state of rotatory movement, and ought to be preceded by the treatment of solid bodies generally. Assuming stereometry, therefore, as if it existed, we proceed to astronomy.

Now arithmetic, besides its practical usefulness for arrangements of war, includes difficulties and furnishes a stimulus of this nature. We see the same thing both as One and as infinite in multi- Certainly (remarks Glaukon) astronomy, besides tude as definite and indefinite in number. We its usefulness in regard to the calendar and the can emerge from these difficulties only by intel- seasons, must be admitted by every one to carry lectual and abstract reflection. It is for this pur- the mind upwards, to the contemplation of things pose, and not for purposes of traffic, that our not below but on high. I do not admit this at intended philosophers must learn arithmetic. all (replies Sokrates), as astronomy is now culti Their minds must be raised from the confu-vated: at least in my sense of the words, looking sion of the sensible world to the clear daylight upwards, and looking downwards. If a man lies of the intelligible. In teaching arithmetic, the on his back, contemplating the ornaments of the

ceiling, he may carry his eyes upward, but not his mind. To look upwards, as I understand it, is to carry the mind away from the contemplation of sensible things, whereof no science is attainable -to the contemplation of intelligible things, entities invisible and unchangeable, which alone are the objects of science. Observation of the stars. such as astronomers now teach, does not fulfil any such condition. The heavenly bodies are the most beautiful of all visible bodies and the most regular of all visible movements, approximating most nearly, though still with a long interval of inferiority, to the ideal figures and movements of genuine and self-existent forms-quickness, slow. ness, number, figure, &c., as they are in themselves, not visible to the eye, but conceivable only by reason and intellect. The movements of the heavenly bodies are exemplifications, approaching nearest to the perfection of these ideal movements, but still falling greatly short of them They are like visible circles or triangles drawn by some very exact artist; which, however beautiful as works of art, are far from answering to the conditions of the idea and its definition, and from exhibiting exact equality and proportion So about the movements of the sun and stars they are comparatively regular, but they are yet bodily and visible, never attaining the perfect sameness and unchangeableness of the intelligible world and its forms. We cannot learn truth by observation of phenomena constantly fluctuating and varying. We must study astronomy as we do geometry, not by observation, but by mathematical theorems and hypotheses: which is a far more arduous task than astronomy as taught at present. Only in this way can it be made available to improve and strengthen the intellectual organ of the mind.

cursive power which deals exclusively with these
intelligible forms, carrying on ratiocination by
means of them only, with no reference to sensible
objects. He will attain at length the last goal of
the dialectician-the contemplation of bonum per
se (the highest perfection and elevation of the in-
telligible) with intellect per se in its full purity:
the best part of his mind will have been raised to
the contemplation and knowledge of the best and
purest entity.

I know not whether I ought to admit your doc-
trine, Sokratęs (observes Glaukon). There are
difficulties both in admitting and denying it.
However, let us assume it for the present. Your
next step must be to tell us what is the charac-
teristic function of this dialectic power-what are
its different varieties and ways of proceeding? I
would willingly do so (replies Sokrates), but you
would not be able to follow me.
I would lay
before you not merely an image of the truth, but
the very truth itself; as it appears to me at least,
whether I am correct or not-for I ought not to
be sure of my own correctness.

But I am sure that the dialectic power is something of the nature which I have described. It is the only force which can make plain the full truth to students who have gone through the preliminary studies that we have described. It is the only study which investigates rationally real forms and essences-what each thing is, truly in itself. Other branches of study are directed either towards the opinions and preferences of men-or towards generation and combination of particular results-or towards upholding of combinations already produced or naturally springing up: while even as to geometry and the other kindred studies, we have seen that as to real essence they have nothing better than dreams-and that they cannot see it as it is, so long as they take for their principle or point of departure certain assumptions or hypotheses of which they can render no account. The principle being thus unknown, and the conclusion as well as the intermediate items being After going through all these different studies, spun together out of that unknown, how can such the student will have his mind elevated so as to a convention deserve the name of Science? Purperceive the affinity of method and principle which suant to custom, indeed, we call these by the pervades them all. In this state he will be pre- name of Sciences. But they deserve no higher pared for entering on dialectic, which is the final title than that of Intellectual Cognitions, lower consummation of his intellectual career. He will than Science, yet higher than mere Opinion. It then have ascended from the cave into daylight. is the Dialectician alone who discards all assumpHe will have learnt to see real objects, and ulti- tions, ascending at once to real essence as his mately the sun itself, instead of the dim and tran- principle and point of departure: defining, and sitory shadows below. He will become qualified discriminating by appropriate words, each variety to grasp the pure intelligible form with his pure of real essence-rendering account of it to others intellect alone, without either aid or disturbance and carrying it safely through the cross-examfrom sense. He will acquire that dialectical dis-ining process of question and answer.

In like manner (continues Sokrates), acoustics or harmonics must be studied, not by the ear, listening to and comparing various sounds, but by the contemplative intellect, applying arithmetical relations and theories.

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cannot discriminate in this way the Idea or Form of Good from every thing else, will have no proper cognition of Good itself, but only, at best, opinions respecting the various shadows of Good. Dialectic-the capacity of discriminating real forms and maintaining them in cross-examining dialogue-is thus the coping-stone, completion, or consummation, of all the other sciences.

The preliminary sciences must be imparted to our guardians during the earlier years of life, together with such bodily and mental training as may test their energy and perseverance of character. After the age of twenty, those who have distinguished themselves in the juvenile studies and gymnastics must be placed in a select class of honour above the rest, and must be initiated in a synoptic view of the affinity pervading all the separate cognitions which have been imparted to them. They must also be introduced to the view of real essence and its nature. This is the test of aptitude for dialectics: it is the synoptic view only which constitutes the dialectician.

In these new studies they will continue until thirty years of age: after which a farther selection must be made of those who have most distinguished themselves. The men selected will be enrolled in a class of yet higher honour, and will be tested by dialectic cross-examination: so that we may discover who among them are competent to apprehend true, pure, and real essence, renouncing all visual and sensible perceptions. It is important that such dialectic exercises should be deferred until this advanced age, and not imparted, as they are among us at present to immature youths who abuse the licence of in

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terrogation, find all their homegrown opinions uncertain, and end by losing all positive convictions. Our students will remain under such dialectic tuition for five years, until they are thirtyfive years of age, after which they must be brought again down into the cave, and constrained to acquire practical experience by undertaking military and administrative functions. In such employ ments they will spend fifteen years, during which they will undergo still farther scrutiny, to ascer tain whether they can act up to their previous training, in spite of all provocations and temptations. Those who well sustain all these trials will become, at fifty years of age, the finished elders or chiefs of the republic. They will pass their remaining years partly in philosophical contemplations, partly in application of philo sophy to the regulation of the city. It is these elders whose mental eye will have been s trained as to contemplate the real essence of good, and to copy it as an archetype in all their ordinances and administration. They will be the moderators of the city, but they will perform this function as a matter of duty and necessity-not being at all ambitious of it as a matter of honour.

What has here been said about the male guardians and philosophers must be understood to apply equally to the female. We recognise no difference in this respect between the two sexes. Those females who have gone through the same education, and have shewn themselves capable of enduring the same trials as males, will partici pate, after fifty years of age, in the like philosophical contemplations, and in superintendence of the city.

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DR TEMPLE ON UNIVERSITY EXTENSION.*

F all the plans proposed in the Hall | are, first, the abler men from a somewhat lower of Oriel College last week, there is but one which deserves the name of a plan for the extension of the University. It is that which was suggested by Professor Price. The present number of undergraduates is about 1,400. A new College would add 100 to this number. An enlargement of the existing Colleges might add 200. The addition might be valuable, but it would not meet the need, nor deserve to be called an extension.

There are two classes of men that now wish to come to the University, but cannot do so. There

* In a letter addressed o the Editor of the Times.

grade of society-men who have learnt to value a University education for its own sake, and who also know how much a University degree would aid them in their legitimate desire to rise in the world. To gain this, many who intend to practise medicine would come to study the science of their profession in the Oxford Museum. Many who intend to become solicitors would gladly avail themselves of the law which shortens the time of preparation for all who have passed the University examinations. If the School Inquiry Commission shall give, as it can hardly fail to give, a great stimulus to education, there will be a great demand for schoolmasters, and they will all be glad

to have a University degree. There is, in fact, no profession which will not supply students to the University, if the University be really opened to them. There cannot be the slightest doubt that Oxford could confer on all these men a boon of inestimable value, while she would find in them a body of very hardworking and, in many cases, very able students.

Again, there is a large class which has the strongest claim on the sympathies of Oxford-the sons of Oxford men who are too poor to do for their children what was done for themselves. It may safely be said that nine out of ten University men would send their sons to the University if they could afford it. They remember too well how much benefit they got, not to wish their children to have the same. This class would not, perhaps, be so able or so ambitious as the other, but it would have the advantage of possessing that refinement which is only to be obtained by passing childhood and boyhood in educated homes. It would, in fact, belong in every respect, except wealth, to the same grade of society as that which sends men to Oxford now.

There is one way of opening the University to all these men, and one way only, and that is to allow them to become undergraduates without belonging to any College or Hall. Demand the needful testimonials to character, ascertain before admitting them that they have reached a proper standard of knowledge, make regulations to insure duc discipline, require proper certificates before each examination to prove that they have resided the legal number of days in each term, and then let them live and study where and how they will.

No other plan holds out any real prospect of making Oxford cheap. In cases such as this there is, you may depend upon it, no economy like freedom. Even the workhouses administered by guardians jealous of the rates cannot keep paupers as cheaply as labourers can keep themselves; and the principle holds good for all ranks alike. A poor student left to himself can choose his own privations, and fit them to his own ability to bear; can choose his own society; can contract his expenditure if he find it too great,-can do all this without exciting unpleasant remark. The same man in a College is compelled to share some expenses which he would be quite willing to dispense with; is to a certain extent drawn into society, whether he likes it or not; always spends more money, and often finds less comfort.

I have no doubt that a very large number of men would get a University education on the open system for £50 a-year, and many for a good deal

less. No other system would make it much less than it is at present, except for a very small number. For the University students would need no College tutors, since they have the Professors. They might cut down their meals, the furniture of their rooms, the expenses of servants, as much as they chose; and, above all, they would be quite unfettered in their management of social expenses. For this plan would get rid of the objection commonly made to the admission of poor students, that they would have no society, and would therefore lose half, if not more than half, the benefits of the education; for they would soon come in sufficient numbers to make society for themselves. In many cases, such "poor" society as this would be as good as any society in the place. Poor men, sons of gentlemen, living in a humble way to complete their education, would certainly not be wanting in refinement; and even men of another kind would find it much easier to get society that would be really useful than if they were admitted to a College on such a footing as formerly the servitors of Christ Church. Poverty left to find its natural place has its discomforts; but poverty forced into invidious neighbourhood with wealth is not only uncomfortable, it is hurtful.

The common objection to an open system is that it would damage discipline and, therefore, morals. This objection would be undeniably fatal if it were well-founded, but I am convinced that it is groundless. The poor men who come to Oxford would be of a kind to raise, not to lower, the moral tone. The great bulk would come with an earnest desire for self-improvement, and even for distinction, and hard work would be sure to keep them out of mischief. Some rich men, no doubt, would prefer the apparent freedom of lodging in the town, and would perhaps be, or, at any rate, try to be, as idle and as noisy as they are at present; but I do not believe that it would be at all more difficult to control them than it is now. On the contrary, I believe that University officers would be less likely than College authorities at present to deal too leniently with disorderly youths of rank or wealth. The fact is that College discipline is exceedingly slight, and much of it merely formal. At all times in our history, the morality of Oxford has but reflected the morality of England, and the discipline of the Colleges never raised the tone of the University above that of the country at large. I believe that if there were no Colleges at all, the discipline would not fall below what it is. There would unquestionably be much loss, but not loss in that direction. Even now the discipline is chiefly in the hands of the proctors; and whatever further control is needed

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