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 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, Why space with three dimensions – Analysis Situs (Topology)

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Geometers usually distinguish two kinds of geometries, which they call the first of metric and the second of projective; metric geometry is based on the notion of distance; two figures are regarded as equivalent when they are “equal” in the … Read More

Propositional logic

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Propositional logic (propositional calculus, statement logic, sentential calculus, sentential logic, or sometimes zeroth-order logic) is part of the mathematical logic. Its purpose is the study of the logical relations between “propositions” and defines the formal laws according to which the … Read More