Science and Hypothesis

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Science Press, 1905 - Mathematics - 196 pages
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Page 132 - I have said above that probability is the ratio of the number of favorable cases to the number of possible cases.
Page 103 - ... it. The probability, however, is often so great that practically we may be content with it. It is far better to foresee even without certainty than not to foresee at all.
Page 39 - Is Euclidean geometry true? It has no meaning. We might as well ask if the metric system is true, and if the old weights and measures are false; if Cartesian co-ordinates are true and polar coordinates false. One geometry cannot be more true than another; it can only be more convenient. Now, Euclidean geometry is, and will remain, the most convenient...
Page 101 - Science / is built up with facts, as a house is with stones. But a collection , of facts is no more a science than a heap of stones is a house.
Page 114 - But these are merely names of the images we substituted for the real objects which Nature will hide for ever from our eyes. The true relations between these real objects are the only reality we can attain...
Page 12 - ... he may be, he will never prepare more than a finite number of them; if he applies his faculties to arithmetic, he will not be able to perceive its general truths by a single direct intuition ; to arrive at the smallest theorem he can not dispense with the aid of reasoning by recurrence, for this is an instrument which enables us to pass from the finite to the infinite. This instrument is always useful, for, allowing us to overleap at a bound as many stages as we wish, it spares us verifications,...
Page 1 - To be skeptical in this fashion is still to be superficial. To doubt everything and to believe everything are two equally convenient solutions; each saves us from thinking.
Page 180 - And in fact, they mark the same hour at the same physical instant, but on one condition, which is that the two stations are fixed In the contrary case the duration of the transmission will not be the same in the two senses, since the station A, for example, moves forward to meet the optical perturbation emanating from B, while the station B flies away before the perturbation emanating from A. The watches adjusted in that manner do not mark, therefore, the true time, they mark what one may call the...
Page 174 - Suppose we have before us any machine; the initial wheel work and the final wheel work alone are visible, but the transmission, the intermediary machinery by which the movement is communicated from one to the other, is hidden in the interior and escapes our view; we do not know whether the communication is made by gearing or by belts, by connecting-rods or by other contrivances.
Page 176 - I shall come back to it presently ; but there is something else. It is not alone the conservation of energy which is in question ; all the other principles are equally in danger, as we shall see in passing them successively in review. Let us commence with the principle of Carnot. This is the only one...

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