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Updated: May 26, 2025
The inductions of arithmetic are of two sorts: first, those which we have just expounded, such as One and one are two, Two and one are three, etc., which may be called the definitions of the various numbers, in the improper or geometrical sense of the word Definition; and secondly, the two following axioms: The sums of equals are equal, The differences of equals are equal.
Chicot had reached so far in his reasonings, his inductions, and his philosophy, which had consumed a good hour and a half altogether, when he was drawn from his train of thought by the arrival of a litter proceeding from the direction of the inn of the "Brave Chevalier." This litter stopped at the threshold of the mysterious house.
At all events, the theory of evolution is in perfect, unquestionable harmony with the inductions of socialism and, or the contrary, it flatly contradicts the hypothesis of the absoluteness and immutability of the "natural" laws of economies, etc. III., fasc. 5.
"Let the earth bring forth" is just as much an outspoken law of nature, and one as inexorably obeyed, as that unerring force of gravity which led Leverrier, in the faith of his inductions, to indicate the precise point in the heavens where the far-off planet, now bearing his name, might be seen by the required telescope. Dr. Cooke, quoting Mr.
In this relation, of course, the derivative truths of every deductive science must stand to the inductions, or assumptions, on which the science is founded, and which, whether true or untrue, certain or doubtful in themselves, are always supposed certain for the purposes of the particular science.
Then, with that science of vision which gives to a libertine, as it does to a sculptor, the fatal power of disrobing, if we may so express it, a woman, and divining her shape by inductions both rapid and sagacious, he beheld one of those masterpieces of Nature whose creation appears to demand as its right all the happiness of love.
1. Thus, where there is an ambiguous middle, or a term used in different senses in the premisses and in the conclusion, the argument proceeds as though there were evidence to the point, when, in fact, there is none. This error does not occur much in direct inductions, since the things themselves are there present to the senses or memory; but chiefly, in Ratiocination, where we are deciphering our own or others' notes. The ambiguity arises very often from assuming that a word corresponds precisely in meaning with the root itself (e.g. representative), or with cognate words from the same root, called paronymous words (as, artful, with art). Other examples of ambiguities are; 'Money, which, meaning both the currency and also capital seeking investment, is often thought to be scarce in the former sense, because scarce in the latter; 'Influence of Property, which, signifying equally the influence of respect for the power for good, and of fear of the power for evil, which is possessed by the rich, is represented as being assailed under its former form when attacked really only under the latter; 'Theory, which, because applied popularly to the accounting for an effect apart from facts, is ridiculed, even when expressing, as it properly does, the result of philosophical induction from experience; 'The Church, which refers (as in the question of the inviolability of Church property) sometimes to the clergy alone, sometimes to all its members; 'Good, in the Stoic argument that virtue, as alone good (in the Stoic sense), must therefore include freedom and beauty, because these are good (in the popular sense). So, the meaning of 'I' shifts from the laws of my nature to my will, in Descartes'
In order to a better understanding of the problem which the logician must solve if he would establish a scientific theory of Induction, let us compare a few cases of incorrect inductions with others which are acknowledged to be legitimate. Some, we know, which were believed for centuries to be correct, were nevertheless incorrect.
The substance before us is only seen to come within one of these inductions; but by means of this one, it is brought within the other.
It will appear, I think, from the subsequent part of our inquiry, that there is no logical fallacy in this mode of proceeding; but we may see already that any other mode is rigorously impracticable: since it is impossible to frame any scientific method of induction, or test of the correctness of inductions, unless on the hypothesis that some inductions deserving of reliance have been already made.
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