Henri Poincaré, Reports on Matter and Ether

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(Conference at the French Society of Physics, April 11, 1912.) When Mr. Abraham came to ask me to close the series of lectures organized by the French Society of Physics, I was at first about to refuse; it seemed to … Read More

Philosophical Aspects of Big Data

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Big Data can generate, through inferences, new knowledge and perspectives. The paradigm that results from using Big Data creates new opportunities. One of the major concerns in the Big Data case is that data scientists tend to work with data … Read More

Henri Poincaré, Quanta hypothesis: Quanta of action

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The new design is seductive by a certain side; for some time the tendency has been to atomism, matter appears to us as formed of indivisible atoms, and the electricity is no longer continuous, it is no longer divisible to … Read More

Henri Poincaré, Quanta hypothesis

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One wonders if Mechanics is not on the eve of a new upheaval; recently a meeting was held at Brussels, attended by some twenty physicists of various nationalities, and at each moment they might have been heard to speak of … Read More

Henri Poincaré, The logic of infinity: The use of infinity

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Is it possible to reason about objects that can notbe defined in a finite number of words? Is it even possible to talk about it knowing what one is talking about, and by saying something other than empty words? Or … Read More

Henri Poincaré, The logic of infinity: Axiom of reducibility

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Russell introduces a new axiom which he calls axiom of reducibility. As I’m not sure I fully understood his thought, I will let him speak. “We assume, that every function is équivalent, for ail its value to some predicative function … Read More

Henri Poincaré, The logic of infinity: The memory of Mr. Russel

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Russell published in the American Journal of Mathematics, vol. XXX, under the title Mathematical Logics as Based on the Theory of Types, a memoir in which he relies on considerations quite similar to those which precede. After recalling some of … Read More

Henri Poincaré, The logic of infinity: The cardinal number

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We must not forget the preceding considerations when defining the cardinal number. If we consider two collections, we may seek to establish a law of correspondence between the objects of these two collections, so that any object of the first … Read More

Henri Poincaré, The logic of infinity: What a classification must be

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Can the ordinary rules of logic be applied without change, as soon as we consider collections taking an infinite number of objects? This is a question we did not ask at first, but we were led to examine when the … Read More

Henri Poincaré, Why space with three dimensions – Analysis Situs and intuition

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I would like to add a remark which relates only indirectly to the foregoing; we have seen above the importance of the Analysis Situs and I explained that this is the real domain of geometric intuition. Does this intuition exist? … Read More

Henri Poincaré, Why space with three dimensions – Space and Nature

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But the question can be asked from a completely different point of view. We have so far placed ourselves in a purely subjective, purely psychological or, if you will, physiological point of view; we have only considered the relations of … Read More

Henri Poincaré, Why space with three dimensions – Space and movements

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It seems, therefore, that space cannot be constructed by considering sets of simultaneous sensations, which must be considered as sequences of sensations. Always go back to what I said before. Why do certain changes appear to us as changes of … Read More

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