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: 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

Logic

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(Allegory of logic) The logic, from the Greek λογική / logikê, is a term derived from λόγος / lógos – meaning at the same time “reason”, “language”, and “reasoning” – is, in a first approach, the study of the formal … Read More