The causal theory of reference

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John Stuart Mill argued that names can be divided into two types: connotative and non-connotative. Proper names are the only names of objects that are not connotative and do not have a strictly meaning. (Mill 1882) John Searle argues that … 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

A natural extension of the methodology of the scientific research programmes of Imre Lakatos

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Both general relativity and quantum mechanics are paradigms in Kuhn’s sense[1]. Both coexist simultaneously. But in Kuhn’s scheme there is no such situation in which two simultaneous paradigms coexist peacefully. Kuhn’s paradigm is defined primarily from a sociological point of … 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, Mathematics and logic

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A few years ago, I had the opportunity to expose some ideas about the logic of the infinite; on the use of the infinite in Mathematics, on the use made of it since Cantor; I explained why I did not … Read More

Henri Poincaré, The logic of infinity: An overview

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The antinomies to which certain logicians have been led come from the fact that they could not avoid certain vicious circles. It happened to them when they considered finite collections, but it happened to them much more often when they … 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: The memory of Mr. Zermelo

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It is in a totally different direction that Mr. Zermelo is seeking the solution of the difficulties we have pointed out. He tries to establish a system of axioms a priori, which must allow him to establish all the mathematical … 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

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