1898 - On the Foundations of GeometryPoincare herein discusses Euclidean and non-euclidean geometry, and the nature of how a system of geometry is selected for use. Unlike Kant who said that the use of Euclidian geometry is a priori, Poincare conjects that either system could be chosen based on a combination of synthetic a priori knowledge and human experience. To establish this point, Poincare uses a thought experiment now called “Sphereland”. This is the basis of the conventionalist thesis often attributed to him.
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1902 - Science and HypothesisIn this published work Poincare points out that classical mechanics and physics may have empirical origins, but the process of turning individual experimental results into a theory or principle causes that empirical data to be shaped by the mind. Humans are prone to making generalizations, and will simplify data sets in order to produce a usable theory. Poincare describes this method of though as being between empirical and a priorism
1902 La science et l’hypothèse,(Science and hypothesis, 1905)
1905 - Mathematics and Logic I-IIIPlease see text box in assignment submission. Entry was over 500 words.