ONE:
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ONE:First I will notice that among our many books upon mechanical subjects there are none that seem to be directed to the instruction of apprentice engineers; at least, there are none directed to that part of a mechanical education most difficult to acquire, a power of analysing and deducing conclusions from commonplace matters."I am not very easily impressed," she said, "and as to that Spanish woman--eh, Dr. Bruce must have been taking lessons from Mr. Lawrence."
ONE:First I will notice that among our many books upon mechanical subjects there are none that seem to be directed to the instruction of apprentice engineers; at least, there are none directed to that part of a mechanical education most difficult to acquire, a power of analysing and deducing conclusions from commonplace matters."I am not very easily impressed," she said, "and as to that Spanish woman--eh, Dr. Bruce must have been taking lessons from Mr. Lawrence."
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ONE:As might be expected, the Parmenidean paradoxes provoked a considerable amount of contradiction and ridicule. The Reids and Beatties of that time drew sundry absurd consequences from the new doctrine, and offered them as a sufficient refutation of its truth. Zeno, a young friend and20 favourite of Parmenides, took up arms in his masters defence, and sought to prove with brilliant dialectical ability that consequences still more absurd might be deduced from the opposite belief. He originated a series of famous puzzles respecting the infinite divisibility of matter and the possibility of motion, subsequently employed as a disproof of all certainty by the Sophists and Sceptics, and occasionally made to serve as arguments on behalf of agnosticism by writers of our own time. Stated generally, they may be reduced to two. A whole composed of parts and divisible ad infinitum must be either infinitely great or infinitely little; infinitely great if its parts have magnitude, infinitely little if they have not. A moving body can never come to the end of a given line, for it must first traverse half the line, then half the remainder, and so on for ever. Aristotle thought that the difficulty about motion could be solved by taking the infinite divisibility of time into account; and Coleridge, according to his custom, repeated the explanation without acknowledgment. But Zeno would have refused to admit that any infinite series could come to an end, whether it was composed of successive or of co-existent parts. So long as the abstractions of our understanding are treated as separate entities, these and similar puzzles will continue to exercise the ingenuity of metaphysicians. Our present business, however, is not to solve Zenos difficulties, but to show how they illustrate a leading characteristic of Greek thought, its tendency to perpetual analysis, a tendency not limited to the philosophy of the Greeks, but pervading the whole of their literature and even of their art. Homer carefully distinguishes the successive steps of every action, and leads up to every catastrophe by a series of finely graduated transitions. Like Zeno, again, he pursues a system of dichotomy, passing rapidly over the first half of his subject, and relaxes the speed of his narrative by going into ever-closer detail until the consummation is reached. Such a poem as the Achilleis of modern critics21 would have been perfectly intolerable to a Greek, from the too rapid and uniform march of its action. Herodotus proceeds after a precisely similar fashion, advancing from a broad and free treatment of history to elaborate minuteness of detail. So, too, a Greek temple divides itself into parts so distinct, yet so closely connected, that the eye, after separating, as easily recombines them into a whole. The evolution of Greek music tells the same tale of progressive subdivision, which is also illustrated by the passage from long speeches to single lines, and from these again to half lines in the dialogue of a Greek drama. No other people could have created mathematical demonstration, for no other would have had skill and patience enough to discover the successive identities interposed between and connecting the sides of an equation. The dialectic of Socrates and Plato, the somewhat wearisome distinctions of Aristotle, and, last of all, the fine-spun series of triads inserted by Proclus between the superessential One and the fleeting world of sense,were all products of the same fundamental tendency, alternately most fruitful and most barren in its results. It may be objected that Zeno, so far from obeying this tendency, followed a diametrically opposite principle, that of absolutely unbroken continuity. True; but the Eleatic Palamedes fought his adversaries with a weapon wrested out of their own hands; rejecting analysis as a law of real existence, he continued to employ it as a logical artifice with greater subtlety than had ever yet been displayed in pure speculation.18Having assumed a certain work to do, the cutting of tooth racks ? in. pitch, and 3 in. face, the first thing to be considered will be, is the machine to be a special one, or one of general adaptation? This question has to do, first, with the functions of the machine in the way of adapting it to the cutting of racks of various sizes, or to performing other kinds of work, and secondly, as to the completeness of the machine; for if it were to be a standard one, instead of being adapted only to a special purpose, there are many expensive additions to be supplied which can be omitted in a special machine. It will be assumed in the present case that a special machine is to be constructed for a particular duty only.
ONE:As might be expected, the Parmenidean paradoxes provoked a considerable amount of contradiction and ridicule. The Reids and Beatties of that time drew sundry absurd consequences from the new doctrine, and offered them as a sufficient refutation of its truth. Zeno, a young friend and20 favourite of Parmenides, took up arms in his masters defence, and sought to prove with brilliant dialectical ability that consequences still more absurd might be deduced from the opposite belief. He originated a series of famous puzzles respecting the infinite divisibility of matter and the possibility of motion, subsequently employed as a disproof of all certainty by the Sophists and Sceptics, and occasionally made to serve as arguments on behalf of agnosticism by writers of our own time. Stated generally, they may be reduced to two. A whole composed of parts and divisible ad infinitum must be either infinitely great or infinitely little; infinitely great if its parts have magnitude, infinitely little if they have not. A moving body can never come to the end of a given line, for it must first traverse half the line, then half the remainder, and so on for ever. Aristotle thought that the difficulty about motion could be solved by taking the infinite divisibility of time into account; and Coleridge, according to his custom, repeated the explanation without acknowledgment. But Zeno would have refused to admit that any infinite series could come to an end, whether it was composed of successive or of co-existent parts. So long as the abstractions of our understanding are treated as separate entities, these and similar puzzles will continue to exercise the ingenuity of metaphysicians. Our present business, however, is not to solve Zenos difficulties, but to show how they illustrate a leading characteristic of Greek thought, its tendency to perpetual analysis, a tendency not limited to the philosophy of the Greeks, but pervading the whole of their literature and even of their art. Homer carefully distinguishes the successive steps of every action, and leads up to every catastrophe by a series of finely graduated transitions. Like Zeno, again, he pursues a system of dichotomy, passing rapidly over the first half of his subject, and relaxes the speed of his narrative by going into ever-closer detail until the consummation is reached. Such a poem as the Achilleis of modern critics21 would have been perfectly intolerable to a Greek, from the too rapid and uniform march of its action. Herodotus proceeds after a precisely similar fashion, advancing from a broad and free treatment of history to elaborate minuteness of detail. So, too, a Greek temple divides itself into parts so distinct, yet so closely connected, that the eye, after separating, as easily recombines them into a whole. The evolution of Greek music tells the same tale of progressive subdivision, which is also illustrated by the passage from long speeches to single lines, and from these again to half lines in the dialogue of a Greek drama. No other people could have created mathematical demonstration, for no other would have had skill and patience enough to discover the successive identities interposed between and connecting the sides of an equation. The dialectic of Socrates and Plato, the somewhat wearisome distinctions of Aristotle, and, last of all, the fine-spun series of triads inserted by Proclus between the superessential One and the fleeting world of sense,were all products of the same fundamental tendency, alternately most fruitful and most barren in its results. It may be objected that Zeno, so far from obeying this tendency, followed a diametrically opposite principle, that of absolutely unbroken continuity. True; but the Eleatic Palamedes fought his adversaries with a weapon wrested out of their own hands; rejecting analysis as a law of real existence, he continued to employ it as a logical artifice with greater subtlety than had ever yet been displayed in pure speculation.18Having assumed a certain work to do, the cutting of tooth racks ? in. pitch, and 3 in. face, the first thing to be considered will be, is the machine to be a special one, or one of general adaptation? This question has to do, first, with the functions of the machine in the way of adapting it to the cutting of racks of various sizes, or to performing other kinds of work, and secondly, as to the completeness of the machine; for if it were to be a standard one, instead of being adapted only to a special purpose, there are many expensive additions to be supplied which can be omitted in a special machine. It will be assumed in the present case that a special machine is to be constructed for a particular duty only.
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ONE:To understand Descartes aright, we must provisionally disregard the account given in his work on Method of the process by which he arrived at a new theory of the world; for, in truth, there was nothing new about it except the pro388portion in which fragments taken from older systems were selected and recombined. As we have already noticed, there is no such thing as spinning philosophies out of ones own head; and, in the case of Descartes, even the belief that he was so doing came to him from Plato; for, along with Aristotles dogmatic errors, his sound teaching with regard to the derivation of knowledge had fallen into oblivion. The initial doubt of the Discourse on Method and the Meditations is also Platonic; only it is manifested under an individual and subjective, instead of a universal and objective form. But to find the real starting-point of Descartes enquiries we must look for it in his mathematical studies. A geometrician naturally conceives the visible world under the aspect of figured extension; and if he thinks the figures away, nothing will remain but extension as the ultimate material out of which all determinate bodies are shaped. Such was the result reached by Plato in his Timaeus. He identified matter with space, viewing this as the receptacle for his eternal and self-existent Ideas, or rather the plastic medium on which their images are impressed. The simplest spatial elements are triangles; accordingly it is with these that he constructs his solid bodies. The theory of triangular elements was probably suggested by Atomism; it is, in fact, a compromise between the purely mathematical and the materialistic methods. Like all Platos fancies, this theory of matter was attacked with such convincing arguments by Aristotle that, so long as his physics remained in the ascendent, it did not find a single supporter; although, as we saw in the last chapter, Plotinus very nearly worked his way back to it from the Peripatetic definition. Even now, at the moment of Aristotles fall, it might have failed to attract attention, had not the conditions under which it first arose been almost exactly repeated. Geometrical demonstration had again become the type of all reasoning; there was again a sceptical spirit abroad, forcing men to fall back on the most elementary and universal con389ceptions; an atomistic materialism again threatened to claim at least the whole field of physical enquiry for its own. That Descartes followed the Timaeus in identifying matter with extension cannot be doubted; especially when we see that he adopts Platos analysis of body into elementary triangles; but the theory agreed so well with his intellectual predispositions that he may easily have imagined it to be a necessary deduction from his own priori ideas. Moreover, after the first two steps, he parts company with Plato, and gives himself up, so far as his rejection of a vacuum will permit, to the mechanical physics of Democritus. Much praise has recently been bestowed on his attempt to interpret all physical phenomena in terms of matter and motion, and to deduce them from the unaided operation of natural causes; but this is no more than had been done by the early Greek thinkers, from whom, we may observe, his hypothesis of an initial vortex was also derived. His cosmogony is better than theirs, only in so far as it is adapted to scientific discoveries in astronomy and physiology not made by Descartes himself; for where his conjectures go beyond these they are entirely at fault.
ONE:To understand Descartes aright, we must provisionally disregard the account given in his work on Method of the process by which he arrived at a new theory of the world; for, in truth, there was nothing new about it except the pro388portion in which fragments taken from older systems were selected and recombined. As we have already noticed, there is no such thing as spinning philosophies out of ones own head; and, in the case of Descartes, even the belief that he was so doing came to him from Plato; for, along with Aristotles dogmatic errors, his sound teaching with regard to the derivation of knowledge had fallen into oblivion. The initial doubt of the Discourse on Method and the Meditations is also Platonic; only it is manifested under an individual and subjective, instead of a universal and objective form. But to find the real starting-point of Descartes enquiries we must look for it in his mathematical studies. A geometrician naturally conceives the visible world under the aspect of figured extension; and if he thinks the figures away, nothing will remain but extension as the ultimate material out of which all determinate bodies are shaped. Such was the result reached by Plato in his Timaeus. He identified matter with space, viewing this as the receptacle for his eternal and self-existent Ideas, or rather the plastic medium on which their images are impressed. The simplest spatial elements are triangles; accordingly it is with these that he constructs his solid bodies. The theory of triangular elements was probably suggested by Atomism; it is, in fact, a compromise between the purely mathematical and the materialistic methods. Like all Platos fancies, this theory of matter was attacked with such convincing arguments by Aristotle that, so long as his physics remained in the ascendent, it did not find a single supporter; although, as we saw in the last chapter, Plotinus very nearly worked his way back to it from the Peripatetic definition. Even now, at the moment of Aristotles fall, it might have failed to attract attention, had not the conditions under which it first arose been almost exactly repeated. Geometrical demonstration had again become the type of all reasoning; there was again a sceptical spirit abroad, forcing men to fall back on the most elementary and universal con389ceptions; an atomistic materialism again threatened to claim at least the whole field of physical enquiry for its own. That Descartes followed the Timaeus in identifying matter with extension cannot be doubted; especially when we see that he adopts Platos analysis of body into elementary triangles; but the theory agreed so well with his intellectual predispositions that he may easily have imagined it to be a necessary deduction from his own priori ideas. Moreover, after the first two steps, he parts company with Plato, and gives himself up, so far as his rejection of a vacuum will permit, to the mechanical physics of Democritus. Much praise has recently been bestowed on his attempt to interpret all physical phenomena in terms of matter and motion, and to deduce them from the unaided operation of natural causes; but this is no more than had been done by the early Greek thinkers, from whom, we may observe, his hypothesis of an initial vortex was also derived. His cosmogony is better than theirs, only in so far as it is adapted to scientific discoveries in astronomy and physiology not made by Descartes himself; for where his conjectures go beyond these they are entirely at fault.
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ONE:"Dr. Bruce is here," he whispered. "That little fool of a governess of yours took it in her head to call him on the telephone. Of course, she knows nothing, but if Bruce and our friend Maitrank meet, goodness knows what will happen."
ONE:"Dr. Bruce is here," he whispered. "That little fool of a governess of yours took it in her head to call him on the telephone. Of course, she knows nothing, but if Bruce and our friend Maitrank meet, goodness knows what will happen."
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ONE:We have said that the founder of Neo-Platonism contrived to blend the systems of his two great authorities in such a manner as to eliminate much of the relative truth which is contained in each of them taken by itself. It has been reserved for modern thought to accomplish the profounder synthesis which has eliminated their errors in combining their truths. Yet, perhaps, no other system would have satisfied the want of the time so well as that constructed by Plotinus out of the materials at his disposal. Such as it was, that system held its ground as the reigning philosophy until all independent thinking was suppressed by Justinian, somewhat more than two and a half centuries after its authors death. Even then it did not become extinct, but reappeared in Christian literature, in the writings attributed to Dionysius the Areopagite, and again in the daring speculations of Erigena, the father of mediaeval philosophy, to pass under more diluted forms into the teaching of the later Schoolmen, until the time arrived for its renewed study in the original sources as an element of the Platonic revival in the fifteenth century. All this popularity proves, as we say, that Plotinus suited his own age and other ages which reproduced the same general intellectual tendencies. But the important thing was that he made Plato and Aristotle more interesting, and thus led men to study their writings more eagerly than before. The true reign of those philosophers does not begin until we reach the Middle Ages, and the commanding position which they then enjoyed was due, in great measure, to the revolution effected by Plotinus.
ONE:We have said that the founder of Neo-Platonism contrived to blend the systems of his two great authorities in such a manner as to eliminate much of the relative truth which is contained in each of them taken by itself. It has been reserved for modern thought to accomplish the profounder synthesis which has eliminated their errors in combining their truths. Yet, perhaps, no other system would have satisfied the want of the time so well as that constructed by Plotinus out of the materials at his disposal. Such as it was, that system held its ground as the reigning philosophy until all independent thinking was suppressed by Justinian, somewhat more than two and a half centuries after its authors death. Even then it did not become extinct, but reappeared in Christian literature, in the writings attributed to Dionysius the Areopagite, and again in the daring speculations of Erigena, the father of mediaeval philosophy, to pass under more diluted forms into the teaching of the later Schoolmen, until the time arrived for its renewed study in the original sources as an element of the Platonic revival in the fifteenth century. All this popularity proves, as we say, that Plotinus suited his own age and other ages which reproduced the same general intellectual tendencies. But the important thing was that he made Plato and Aristotle more interesting, and thus led men to study their writings more eagerly than before. The true reign of those philosophers does not begin until we reach the Middle Ages, and the commanding position which they then enjoyed was due, in great measure, to the revolution effected by Plotinus.
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ONE:Between a running motion of the dies, or a running motion of the blanks, there are the following points which may be noticed.
ONE:Between a running motion of the dies, or a running motion of the blanks, there are the following points which may be noticed.
THREE:"Seems pretty bad," said the policeman gruffly, as he flashed his lantern down on the white still face. "This here's a job for the ambulance."
THREE:The combination of several functions in one machine, although it may not seem an important matter to be considered here, is nevertheless one that has much to do with the manufacture of machines, and constitutes what may be termed a principle of construction.Without ceremony she darted into Countess Lalage's bedroom. The lights were still up, and the mistress of the house was brushing out her long black hair. She was cool and collected enough now.