It is remarkable that Aristotle, after repeatedly speaking of induction as an ascent from particulars to generals, when he comes to trace the process by which we arrive at the most general notions of any, does not admit the possibility of such a movement in one direction only. The universal and the individual are, according to him, combined in our most elementary sense-impressions, and the business of scientific393 experience is to separate them. Starting from a middle point, we work up to indivisible predicates on the one hand and down to indivisible subjects on the other, the final apprehension of both extremes being the office, not of science, but of Nous. This theory is equally true and acute. The perception of individual facts is just as difficult and just as slowly acquired as the conception of ultimate abstractions. Moreover, the two processes are carried on pari passu, each being only made possible by and through the other. No true notion can be framed without a firm grasp of the particulars from which it is abstracted; no individual object can be studied without analysing it into a group of common predicates, the idiosyncrasy of whichthat is, their special combinationdifferentiates it from every other object. What, however, we wish to remark is the illustration incidentally afforded by this striking aper?u of Aristotles analytical method, which is also the essentially Greek method of thought. We saw that, for our philosopher, syllogism was not the subsumption of a particular case under a general law, but the interpolation of a mean between two extremes; we now see that his induction is not the finding of a law for the particular phenomenon, but its analysis into two elementsone universal and the other individuala solution of the mean into the extremes. And the distinctive originality of his whole system was to fix two such extremes for the universea self-thinking thought in absolute self-identity at one end of the scale, and an absolutely indeterminate matter at the other; by combining which in various proportions he then re-constructed the whole intermediate phenomenal reality. In studying each particular class of facts, he follows the same method. The genus is marked by some characteristic attribute which one speciesthe prerogative species, so to speakexhibits in its greatest purity, while the others form a graduated scale by variously combining this attribute with its opposite or privation. Hence his theory, since revived by Goethe, that394 the colours are so many different mixtures of light and darkness.
ONE:In Rome, as well as in Greece, rationalism took the form of disbelief in divination. Here at least the Epicurean, the Academician, and, among the Stoics, the disciple of Panaetius, were all agreed. But as the sceptical movement began at a much later period in Rome than in the country where it first originated, so also did the supernaturalist reaction come later, the age of Augustus in the one corresponding very nearly with the age of Alexander in the other. Virgil and Livy are remarkable for their faith in omens; and although the latter complains of the general incredulity with which narratives of such events were received, his statements are to be taken rather as an index of what people thought in the age immediately preceding his own, than as an accurate description of contemporary opinion. Certainly nothing could be farther from the truth than to say that signs and prodigies were disregarded by the Romans under the empire. Even the cool and cautious Tacitus feels himself obliged to relate sundry marvellous incidents which seemed to accompany or to prefigure great historical catastrophes; and the more credulous Suetonius has transcribed an immense number of such incidents from the pages of older chroniclers, besides informing us of the extreme attention paid even to trifling omens by Augustus.341In making up the time charged to different machines during their construction, a good plan is to supply each workman with a slate and pencil, on which he can enter his time as so many hours or fractions of hours charged to the respective symbols. Instead of interfering with his time, this will increase a workman's interest in what he is doing, and naturally lead to a desire to diminish the time charged to the various symbols. This system leads to emulation among workmen where any operation is repeated by different persons, and creates an interest in classification which workmen will willingly assist in.
TWO:My stories are not exaggerated or touched up, but are true to reality. That is the reason why the German authorities have driven me away from Belgium, and tried to get hold of me to punish me. On that side they are afraid that the truth be known.That when the ship sinks we no longer may be!
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ONE:On the other hand, a theory of reasoning based on the relations of concepts, instead of on the relations of judgments, necessarily leaves out of account the whole doctrine of hypothetical and disjunctive propositions, together with that of the syllogisms based on them; since the elements of which they are composed are themselves propositions. And this inevitable omission is the more remarkable because alterna381tive and, to a less extent, hypothetical arguments form the staple of Aristotles own dialectic; while categorical reasoning never occurs in it at all. His constant method is to enumerate all possible views of a subject, and examine them one after the other, rejecting those which are untenable, and resting content with the remainder. In other words, he reaches his positive conclusions through a series of negative premises representing a process of gradual elimination. The First Analytics is itself an admirable instance of his favourite method. Every possible combination of terms is discussed, and the valid moods are sifted out from a much greater number of illegitimate syllogisms. The dialectic of Socrates and Plato followed the same procedure. It was essentially experimentala method of trial, elimination, and selection. On going back still further, we find that when there is any reasoning at all in Homer, it is conducted after the same fashion. Hector, in his soliloquy before the Scaean Gate, imagines three alternative courses, together exhausting the possibilities of the situation. He may either retreat within the walls, or offer terms of peace to Achilles, or fight. The first two alternatives being rejected, nothing remains but the third. This is the most elaborate example; but on many other occasions Homers actors are represented as hesitating between two courses, and finally deciding on one of them.
TWO:"Because it wasn't there when he passed, Prout," said a quick voice that caused the detective to turn with a start. "There was a confederate, of course. Nothing easier than for the confederate to listen for the officer's footsteps and put out the gas till he had gone by. Other people didn't matter."Meanwhile Atomism continued to exercise a powerful influence on the method even more than on the doctrines of science. The analytical mode of treatment, applied by Galileo to dynamics, was applied, with equal success, by other mathematicians, to the study of discrete and continuous quantity. It is to the division of numbers and figures into infinitesimal partsa direct contravention of Aristotles teachingthat we owe logarithms, algebraic geometry, and the differential calculus. Thus was established a connexion between spiritualism and materialism, the philosophy of Plato and the philosophy of Democritus. Out of these elements, together with what still survived of Aristotelianism, was constructed the system of Descartes.
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ONE:
TWO:Mayst Thou from baneful Ignorance
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TWO:"It can't be as bad as my news," Leona said, gloomily. "They have traced the rest of the missing notes directly to my possession."
FORE:Water-wheels, or water-power, as a mechanical subject, is apparently quite disconnected with shop manipulation, but will serve as an example for conveying general ideas of force and motion, and, on these grounds, will warrant a more extended notice than the seeming connection with the general subject calls for.
FORE:The next day, Sunday, August 16th, I was already about at five o'clock in the morning, and soon witnessed some historical shots. In the park on one of the boulevards the Germans had been digging for two days, and prepared a firm foundation upon which big guns might be mounted. I saw one of these guns that morning, and at about half-past five three shots were fired from it at short intervals, by which Fort Loncin was completely destroyed, as was indicated by the terrific explosions which followed the third shot. After these shots I was quite benumbed for several minutes; in all the streets63 of Lige they caused the greatest commotion, which became all the greater because large numbers of cavalry happened to ride through the town, and all the horses started rearing.
FORE:According to Bacon, the object of science is to analyse the complex of Forms making up an individual aggregate into its separate constituents; the object of art, to superinduce one or more such Forms on a given material. Hence his manner of regarding them differs in one important respect from Aristotles. The Greek naturalist was, before all things, a biologist. His interest lay with the distinguishing characteristics of animal species. These are easily discovered by the unassisted eye; but while they are comparatively superficial, they are also comparatively unalterable. The English experimenter, being primarily concerned with inorganic bodies, whose properties he desired to utilise for industrial purposes, was led to consider the attributes of an object as at once penetrating its inmost texture, and yet capable of being separated from it, like heat and colour for instance. But, like every other thinker of the age, if he escapes from the control of Aristotle it is only to fall under the dominion of another Greek masterin this instance, Democritus. Bacon had a great admiration for the Atomists, and although his inveterate Peripatetic proclivities prevented him from embracing their theory as a whole, he went along with it so far as to admit the dependence of the secondary on the primary qualities of matter; and on the strength of this he concluded that the way to alter the properties of an object was to alter the arrangement of its component particles.
FORE:
FORE:Invention, as applied to mechanical improvements, should not mean chance discovery. Such a meaning is often, if not generally, attached to the term invention, yet it must be seen that results attained by a systematic course of reasoning or experimenting can have nothing to do with chance or even discovery. Such results partake more of the nature of demonstrations, a name peculiarly suitable for such inventions as are the result of methodical purpose.
FORE:There is a story that Plato used to thank the gods, in what some might consider a rather Pharisaic spirit, for having made him a human being instead of a brute, a man instead of a woman, and a Greek instead of a barbarian; but more than179 anything else for having permitted him to be born in the time of Socrates. It will be observed that all these blessings tended in one direction, the complete supremacy in his character of reason over impulse and sense. To assert, extend, and organise that supremacy was the object of his whole life. Such, indeed, had been the object of all his predecessors, and such, stated generally, has been always and everywhere the object of philosophy; but none had pursued it so consciously before, and none has proclaimed it so enthusiastically since then. Now, although Plato could not have done this without a far wider range of knowledge and experience than Socrates had possessed, it was only by virtue of the Socratic method that his other gifts and acquisitions could be turned to complete account; while, conversely, it was only when brought to bear upon these new materials that the full power of the method itself could be revealed. To be continually asking and answering questions; to elicit information from everybody on every subject worth knowing; and to elaborate the resulting mass of intellectual material into the most convenient form for practical application or for further transmission, was the secret of true wisdom with the sage of the market-place and the workshop. But the process of dialectic investigation as an end in itself, the intense personal interest of conversation with living men and women of all classes, the impatience for immediate and visible results, had gradually induced Socrates to restrict within far too narrow limits the sources whence his ideas were derived and the purposes to which they were applied. And the dialectic method itself could not but be checked in its internal development by this want of breadth and variety in the topics submitted to its grasp. Therefore the death of Socrates, however lamentable in its occasion, was an unmixed benefit to the cause for which he laboured, by arresting (as we must suppose it to have arrested) the popular and indiscriminate employment of his cross-examining method,180 liberating his ablest disciple from the ascendency of a revered master, and inducing him to reconsider the whole question of human knowledge and action from a remoter point of view. For, be it observed that Plato did not begin where Socrates had left off; he went back to the germinal point of the whole system, and proceeded to reconstruct it on new lines of his own. The loss of those whom we love habitually leads our thoughts back to the time of our first acquaintance with them, or, if these are ascertainable, to the circumstances of their early life. In this manner Plato seems to have been at first occupied exclusively with the starting-point of his friends philosophy, and we know, from the narrative given in the Apologia, under what form he came to conceive it. We have attempted to show that the account alluded to cannot be entirely historical. Nevertheless it seems sufficiently clear that Socrates began with a conviction of his own ignorance, and that his efforts to improve others were prefaced by the extraction of a similar confession of ignorance on their part. It is also certain that through life he regarded the causes of physical phenomena as placed beyond the reach of human reason and reserved by the gods for their own exclusive cognisance, pointing, by way of proof, to the notorious differences of opinion prevalent among those who had meddled with such matters. Thus, his scepticism worked in two directions, but on the one side it was only provisional and on the other it was only partial. Plato began by combining the two. He maintained that human nescience is universal and necessary; that the gods had reserved all knowledge for themselves; and that the only wisdom left for men is a consciousness of their absolute ignorance. The Socratic starting-point gave the centre of his agnostic circle; the Socratic theology gave the distance at which it was described. Here we have to note two thingsfirst, the breadth of generalisation which distinguishes the disciple from the master; and, secondly, the symptoms of a strong181 religious reaction against Greek humanism. Even before the end of the Peloponnesian War, evidence of this reaction had appeared, and the Bacchae of Euripides bears striking testimony to its gloomy and fanatical character. The last agony of Athens, the collapse of her power, and the subsequent period of oligarchic terrorism, must have given a stimulus to superstition like that which quite recently afflicted France with an epidemic of apparitions and pilgrimages almost too childish for belief. Plato followed the general movement, although on a much higher plane. While looking down with undisguised contempt on the immoral idolatry of his countrymen, he was equally opposed to the irreligion of the New Learning, and, had an opportunity been given him, he would, like the Reformers of the sixteenth century, have put down both with impartial severity. Nor was this the only analogy between his position and that of a Luther or a Calvin. Like them, and indeed like all great religious teachers, he exalted the Creator by enlarging on the nothingness of the creature; just as Christianity exhibits the holiness of God in contrast and correlation with the sinfulness of unregenerate hearts; just as to Pindar mans life seemed but the fleeting shadow in a dream when compared with the beauty and strength and immortality of the Olympian divinities; so also did Plato deepen the gloom of human ignorance that he might bring out in dazzling relief the fulness of that knowledge which he had been taught to prize as a supreme ideal, but which, for that very reason, seemed proper to the highest existences alone. And we shall presently see how Plato also discovered a principle in man by virtue of which he could claim kindred with the supernatural, and elaborated a scheme of intellectual mediation by which the fallen spirit could be regenerated and made a partaker in the kingdom of speculative truth.
FORE:"You don't mean to say he's in it!" Isidore cried, grimly amused. "The cunningest fox in all Europe. Truly the Lalage is a wonderful woman! But I see our friend Dr. Bruce is burning to tell me a story. Pray go on."Castings are of course sprung by the action of unequal strains, caused by one part cooling or 'setting' sooner than another. That far all is clear, but the next step takes us into the dark. What are the various conditions which induce irregular cooling, and how is it to be avoided?
TWO:It may be assumed that the same conditions apply to the standards of a common planing machine, but the case is different; the upright framing is easily made strong enough by increasing its depth; but the strain upon running joints is as the distance from them at which a force is applied, or to employ a technical phrase, as the amount of overhang. With a moving platen the larger and heavier a piece to be planed, the more [132] firmly a platen is held down; and as the cross section of pieces usually increases with their depth, the result is that a planing machine properly constructed will act nearly as well on thick as thin pieces.
TWO:He paused in some confusion. He had the profoundest respect for the cunning and audacity of the people with whom he had to deal. Was this some startling new plot that they had been working on him?Dick, Larry and Sandy were silent.
You go. Dick was generous to the friend he admired, and who was almost a year older. It would need a cool, quick head to handle whatever you might find in the swamp. You go."But it is no disguise. My wife's companion was a Spanish blonde."By assuming this or any other well-proved example, and estimating larger or smaller shafts by keeping their diameters as the cube root of the power to be transmitted, the distance between bearings as the diameter, and the speed inverse as the diameter, the reader will find his calculations to agree approximately with the modern practice of our best engineers. This is not mentioned to give proportions for shafts, so much as to call attention to accidental strains, such as winding belts, and to call attention to a marked discrepancy between actual practice and such proportions as would be given by what has been called the measured or determinable strains to which shafts are subjected.And here it was all out in the lurid light of day. Dramatic arrest of the Countess. The suicide and confession. It was flaring in the evening papers--the boys were yelling at the top of their voices in the street. The din of it filled Bruce's ears. "Confession of the crime." "The confession of the murder." "The mystery of the motor explained." "Dr. Bruce cleared of the cruel charge." It seemed strange to Gordon to hear his name yelled out like this in his own ears. He had a paper thrust into his hands.
TWO:
