ONE:Owing to the slight importance which Aristotle attaches to judgments as compared with concepts, he does not go very deeply into the question, how do we obtain our premises? He says, in remarkably emphatic language, that all knowledge is acquired either by demonstration or by induction; or rather, we may add, in the last resort by the latter only, since demon388stration rests on generals which are discovered inductively; but his generals mean definitions and abstract predicates or subjects, rather than synthetic propositions. If, however, his attention had been called to the distinction, we cannot suppose that he would, on his own principles, have adopted conclusions essentially different from those of the modern experiential school. Mr. Wallace does, indeed, claim him as a supporter of the theory that no inference can be made from particulars to particulars without the aid of a general proposition, and as having refuted, by anticipation, Mills assertion to the contrary. We quote the analysis which is supposed to prove this in Mr. Wallaces own words:
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ONE:And the answer was:Mr. van Wersch denied this of course, but nevertheless they took him to Bilsen in the motor-car. There he was searched once more, the Netherland letters he had with him were taken away, as also 1,800 francs. But when he was released they gave him back the money.
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FORE:Returning to our more immediate subject, we must observe that the Pythagoreans did not maintain, in anticipation of modern quantitative science, that all things are determined by number, but that all things are numbers, or are made out of numbers, two propositions not easily distinguished by unpractised thinkers. Numbers, in a word, were to them precisely what water had been to Thales, what air was to Anaximenes, the absolute principle of existence; only with them the idea of a limit, the leading inspiration of Greek thought, had reached a higher degree of abstraction. Number was, as it were, the exterior limit of the finite, and the interior limit of the infinite. Add to this that mathematical studies, cultivated in Egypt and Phoenicia for their practical utility alone, were being pursued in Hellas with ever-increasing ardour for the sake of their own delightfulness, for the intellectual discipline that they supplieda discipline even12 more valuable then than now, and for the insight which they bestowed, or were believed to bestow, into the secret constitution of Nature; and that the more complicated arithmetical operations were habitually conducted with the aid of geometrical diagrams, thus suggesting the possibility of applying a similar treatment to every order of relations. Consider the lively emotions excited among an intelligent people at a time when multiplication and division, squaring and cubing, the rule of three, the construction and equivalence of figures, with all their manifold applications to industry, commerce, fine art, and tactics, were just as strange and wonderful as electrical phenomena are to us; consider also the magical influence still commonly attributed to particular numbers, and the intense eagerness to obtain exact numerical statements, even when they are of no practical value, exhibited by all who are thrown back on primitive ways of living, as, for example, in Alpine travelling, or on board an Atlantic steamer, and we shall cease to wonder that a mere form of thought, a lifeless abstraction, should once have been regarded as the solution of every problem, the cause of all existence; or that these speculations were more than once revived in after ages, and perished only with Greek philosophy itself.Machines and tools operating by percussive action, although they comprise a numerous class, and are applied in nearly all mechanical operations, have never received that amount of attention in text-books which the importance of the machines and their extensive use calls for. Such machines have not even been set off as a class and treated of separately, although the distinction is quite clear between machines with percussive action, and those with what may be termed direct action, both in the manner of operating and in the general plans of construction. There is, of course, no lack of formul? for determining the measure of force, and computing the dynamic effect of percussive machines acting against a measured or assumed resistance, and so on; but this is not what is meant. There are certain conditions in the operation of machines, such as the strains which fall upon supporting frames, the effect produced upon malleable material when struck or pressed, and more especially of conditions which may render percussive or positive acting machines applicable to certain purposes; but little explanation has been given which is of value to practical men.
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FORE:In the workshop, the objects of drawing are to communicate plans and dimensions to the workmen, and to enable a division of the labour, so that the several parts of a machine may be operated upon by different workmen at the same timealso to enable classification and estimates of cost to be made, and records kept.