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low craft, fit only for carpenters and wheelwrights. The office of geometry, he said, was to discipline the mind, not to minister to the base wants of the body. His interference was successful; and from that time, according to Plutarch, the science of mechanics was considered as unworthy of the attention of a philosopher.

Archimedes in a later age imitated and surpassed Archytas. But even Archimedes was not free from the prevailing notion that geometry was degraded by being employed to produce anything useful. It was with difficulty that he was induced to stoop from speculation to practice. He was half ashamed of those inventions which were the wonder of hostile nations, and always spoke of them slightingly as mere amusements, as trifles in which a mathematician might be suffered to relax his mind after intense application to the higher parts of his science.

The opinion of Bacon on this subject was diametrically opposed to that of the ancient philosophers. He valued geometry chiefly, if not solely, on account of those uses, which to Plato appeared so base. And it is remarkable that the longer Bacon lived the stronger this feeling became. When in 1605 he wrote the two books on the Advancement of Learning, he dwelt on the advantages which mankind derived from mixed mathematics; but he at the same time admitted that the beneficial effect produced by mathematical study on the intellect, though a collateral advantage, was "no less worthy than that which was principal and intended." But it is evident that his views underwent a change. When, near twenty years later, he published the De Augmentis, which is the Treatise on the Advancement of Learning, greatly expanded and carefully corrected, he made important alterations in the part which related to mathematics. He condemned with severity the high, pretensions of the mathematicians, "delicias et fastum mathematicorum." Assuming the well-being of the human race to be the end of knowledge, [Usui et commodis hominum consulimus.] he pronounced that mathematical science could claim no higher rank than that of an appendage or auxiliary to other sciences. Mathematical science, he says, is the handmaid of natural philosophy; she ought to demean herself as such; and he declares that he cannot conceive by what ill chance it has happened that she presumes to claim precedence over her mistress. He predicts- a prediction which would have made Plato shudder-that as more and more discoveries are made in physics, there will be more and more branches of mixed mathematics. Of that collateral advantage the value of which, twenty years before, he rated so highly, he says not one word. This omission cannot have been the effect of mere inadvertence. His own treatise was before him. From that treatise he deliberately expunged whatever was favourable to the study of pure mathematics, and inserted several keen reflections on the ardent votaries of that study. This fact, in our opinion, admits of only one explanation. Bacon's love of those pursuits which directly tend to improve the condition of mankind, and his jealousy of all pursuits merely curious, had grown upon him, and had, it may be, become immoderate. He was afraid of using any expression which might have the effect of inducing any man of talents to employ in speculations, useful only to the mind of the speculator, a single hour which might be employed in extending the empire of man over matter. [Compare the passage relating to mathematics in the Second Book of the Advancement of Learning with the De Augmentis Lib. iii. Cap. 6.] If Bacon erred here, we must acknowledge that we greatly prefer his error to the opposite error of Plato. We have no patience with a philosophy which, like those Roman matrons who swallowed abortives in order to preserve their shapes, takes pains to be barren for fear of being homely.

Let us pass to astronomy. This was one of the sciences which Plato exhorted his disciples to learn, but for reasons far removed from common habits of thinking. "Shall we set down astronomy," says Socrates, "among the subjects of study?" [Plato's Republic, Book vii.] "I think so," answers his young friend Glaucon: "to know something about the seasons, the months, and the years is of use for military purposes, as well as for agriculture and navigation." "It amuses me," says Socrates, "to see how afraid you are, lest the common herd of people should accuse you of recommending useless studies." He then proceeds, in that pure and magnificent diction which, as Cicero said, Jupiter would use if Jupiter spoke Greek, to explain, that the use of astronomy is not to add to the vulgar comforts of life, but to assist in raising the mind to the contemplation of things which are to be perceived by the pure intellect alone. The knowledge of the actual motions of the heavenly bodies Socrates considers as of little value. The appearances which make the sky beautiful at night are, he tells us, like the figures which a geometrician draws on the sand, mere examples, mere helps to feeble minds. We must get beyond them; we must neglect them; we must attain to an astronomy which is as independent of the actual stars as geometrical truth is independent of the lines of an ill-drawn diagram. This is, we imagine, very nearly if not exactly, the astronomy which Bacon compared to the ox of Prometheus, [De Augmentis, Lib. iii. Cap. 4] a sleek, well-shaped hide, stuffed with rubbish, goodly to look at, but containing nothing to eat. He complained that astronomy had, to its great injury, been separated from natural philosophy, of which it was one of the noblest provinces, and annexed to the domain of mathematics. The world stood in need, he said, of a very different astronomy, of a living astronomy, [Astronomia viva.] of an astronomy which should set forth the nature, the motion, and the influences of the heavenly bodies, as they really are. [Quae substantiam et motum et influxum ecelestium, prout re vera sunt proponat." Compare this language with Plato's "ta d'en to ourano easomen."]

On the greatest and most useful of all human inventions, the invention of alphabetical writing, Plato did not look with much complacency. He seems to have thought that the use of letters had operated on the human mind as the use of the go-cart in learning to walk, or of corks in learning to swim, is said to operate on the human body. It was a support which, in his opinion, soon became indispensable to those who used it, which made vigorous exertion first unnecessary and then impossible. The powers of the intellect would, he conceived, have been more fully developed without this delusive aid. Men would have been compelled to exercise the understanding and the memory, and, by deep and assiduous meditation, to make truth thoroughly their own. Now, on the contrary, much knowledge is traced on paper, but little is engraved in the soul. A man is certain that he can find information at a moment's notice when he wants it. He therefore suffers it to fade from his mind. Such a man cannot in strictness be said to know anything. He has the show without the reality of wisdom. These opinions Plato has put into the mouth of an ancient king of Egypt. [Plato's Phaedrus.] But it is evident from the context that they were his own; and so they were understood to be by Quinctilian. [Quinctilian, xi.] Indeed they are in perfect accordance with the whole Platonic system.

Bacon's views, as may easily be supposed, were widely different. [De Augmentis, Lib. v. Cap. 5.] The powers of the memory, he observes, without the help of writing, can do little towards the advancement of any useful science. He acknowledges that the memory may be disciplined to such a point as to be able to perform very extraordinary feats. But on such feats he sets little value. The habits of his mind, he tells us, are such that he is not disposed to rate highly any accomplishment, however rare, which is of no practical use to mankind. As to these prodigious achievements of the memory, he ranks them with the exhibitions of rope-dancers and tumblers. "These two performances," he says, "are much of the same sort. The one is an abuse of the powers of the body; the other is an abuse of the powers of the mind. Both may perhaps excite our wonder; but neither is entitled to our respect."

To Plato, the science of medicine appeared to be of very disputable advantages. [Plato's Republic, Book iii.] He did not indeed object to quick cures for acute disorders, or for injuries produced by accidents. But the art which resists the slow sap of a chronic disease, which repairs frames enervated by lust, swollen by gluttony, or inflamed by wine, which encourages sensuality by mitigating the natural punishment of the sensualist, and prolongs existence when the intellect has ceased to retain its entire energy, had no share of his esteem. A life protracted by medical skill he pronounced to be a long death. The exercise of the art of medicine ought, he said, to be tolerated, so far as that art may serve to cure the occasional distempers of men whose constitutions are good. As to those who have bad constitutions, let them die; and the sooner the better. Such men are unfit for war, for magistracy, for the management of their domestic affairs, for severe study and speculation. If they engage in any vigorous mental exercise, they are troubled with giddiness and fulness of the head, all which they lay to the account of philosophy. The best thing that can happen to such wretches is to have done with life at once. He quotes mythical authority in support of this doctrine; and reminds his disciples that the practice of the sons of Aeculapius, as described by Homer, extended only to the cure of external injuries.

Far different was the philosophy of Bacon. Of all the sciences, that which he seems to have regarded with the greatest interest was the science which, in Plato's opinion, would not be tolerated in a well-regulated community. To make men perfect was no part of Bacon's plan. His humble aim was to make imperfect men comfortable. The beneficence of his philosophy resembled the beneficence of the common Father, whose sun rises on the evil and the good, whose rain descends for the just and the unjust. In Plato's opinion man was made for philosophy; in Bacon's opinion philosophy was made for man; it was a means to an end; and that end was to increase the pleasures and to mitigate the pains of millions who are not and cannot be philosophers. That a valetudinarian who took great pleasure in being wheeled along his terrace, who relished his boiled chicken, and his weak wine and water, and who enjoyed a hearty laugh over the Queen of Navarre's tales, should be treated as a caput lupinum because he could not read the Timaeus without a headache, was a notion which the humane spirit of the English school of wisdom altogether rejected. Bacon would not have thought it beneath the dignity of a philosopher to contrive an improved garden chair for such a valetudinarian, to devise some way of rendering his medicines more palatable, to invent repasts which he might enjoy, and pillows on which he might sleep soundly; and this though there might not be the smallest hope that the mind of the poor invalid would ever rise to the contemplation of the ideal beautiful and the ideal good. As Plato had cited the religious legends of Greece to justify his contempt for the more recondite parts of the heart of healing, Bacon vindicated the dignity of that art by appealing to the example of Christ, and reminded men that the great physician of the soul did not disdain to be also the physician of
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