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 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