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  1. added 2018-10-18
    Poincaré's Thesis of the Translatability of Euclidean and Non-Euclidean Geometries.David Stump - 1991 - Noûs 25 (5):639-657.
    Poincaré's claim that Euclidean and non-Euclidean geometries are translatable has generally been thought to be based on his introduction of a model to prove the consistency of Lobachevskian geometry and to be equivalent to a claim that Euclidean and non-Euclidean geometries are logically isomorphic axiomatic systems. In contrast to the standard view, I argue that Poincaré's translation thesis has a mathematical, rather than a meta-mathematical basis. The mathematical basis of Poincaré's translation thesis is that the underlying manifolds of Euclidean and (...)
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  2. added 2018-10-17
    Is There Any Room for Spatial Intuition in Riemann’s Philosophy of Geometry?Dinçer Çevik - 2015 - Beytulhikme An International Journal of Philosophy 5 (1):81.
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  3. added 2018-10-17
    The Two Dozen Pages That Changed the Space (Geometry). Notes in the Margins to the Absolute Science of Space by Janos Bolyai.Paolo Valore - 2010 - Rivista di Storia Della Filosofia 65 (1):131-134.
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  4. added 2018-10-17
    The Foundations of Geometry and the Concept of Motion: Helmholtz and Poincaré.Gerhard Heinzmann - 2001 - Science in Context 14 (3).
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  5. added 2018-10-17
    Poincaré on Mathematical Intuition. A Phenomenological Approach to Poincaré's Philosophy of Arithmetic.Jairo José Da Silva - 1996 - Philosophia Scientiae 1 (2):87-99.
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  6. added 2018-10-17
    Philosophy of Geometry From Riemann to Poincare.Nicholas Griffin & Roberto Torretti - 1978 - Philosophical Quarterly 31 (125):374.
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  7. added 2018-10-17
    On Poincaré's “Mathematical Creation”.Lucien Arréat - 1910 - The Monist 20 (4):615-617.
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  8. added 2018-10-16
    Space and Geometry.Henri Poincaré - forthcoming - Foundations of Science.
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  9. added 2018-10-16
    The Metaphysical Foundations of Critical Personalism.William Stern - 1936 - Pacific Philosophical Quarterly 17 (3):238.
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  10. added 2018-06-06
    De Morgan on Euclid’s Fourth Postulate.John Corcoran & Sriram Nambiar - 2014 - Bulletin of Symbolic Logic 20 (2):250-1.
    This paper will annoy modern logicians who follow Bertrand Russell in taking pleasure in denigrating Aristotle for [allegedly] being ignorant of relational propositions. To be sure this paper does not clear Aristotle of the charge. On the contrary, it shows that such ignorance, which seems unforgivable in the current century, still dominated the thinking of one of the greatest modern logicians as late as 1831. Today it is difficult to accept the proposition that Aristotle was blind to the fact that, (...)
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  11. added 2018-06-06
    Mathematics, Explanation and Reductionism: Exposing the Roots of the Egyptianism of European Civilization.Arran Gare - 2005 - Cosmos and History 1 (1):54-89.
    We have reached the peculiar situation where the advance of mainstream science has required us to dismiss as unreal our own existence as free, creative agents, the very condition of there being science at all. Efforts to free science from this dead-end and to give a place to creative becoming in the world have been hampered by unexamined assumptions about what science should be, assumptions which presuppose that if creative becoming is explained, it will be explained away as an illusion. (...)
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  12. added 2018-06-06
    ‘The Emergency Which Has Arrived’: The Problematic History of Nineteenth-Century British Algebra – a Programmatic Outline.Menachem Fisch - 1994 - British Journal for the History of Science 27 (3):247-276.
    More than any other aspect of the Second Scientific Revolution, the remarkable revitalization or British mathematics and mathematical physics during the first half of the nineteenth century is perhaps the most deserving of the name. While the newly constituted sciences of biology and geology were undergoing their first revolution, as it were, the reform of British mathematics was truly and self-consciously the story of a second coming of age. ‘Discovered by Fermat, cocinnated and rendered analytical by Newton, and enriched by (...)
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  13. added 2018-02-03
    Prova, Explicação e Intuição em Bernard Bolzano.Humberto de Assis Clímaco - 2008 - Anais Do XII Encontro Brasileiro de Pós Graduação Em Educação Matemática.
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  14. added 2017-08-31
    Poincaré on the Foundations of Arithmetic and Geometry. Part 2: Intuition and Unity in Mathematics.Katherine Dunlop - 2017 - Hopos: The Journal of the International Society for the History of Philosophy of Science 7 (1):88-107.
    Part 1 of this article exposed a tension between Poincaré’s views of arithmetic and geometry and argued that it could not be resolved by taking geometry to depend on arithmetic. Part 2 aims to resolve the tension by supposing not merely that intuition’s role is to justify induction on the natural numbers but rather that it also functions to acquaint us with the unity of orders and structures and show practices to fit or harmonize with experience. I argue that in (...)
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  15. added 2017-01-31
    Beyond Quantities and Qualities: Frege and Jevons on Measurement.Raphaël Sandoz - 2016 - Hopos: The Journal of the International Society for the History of Philosophy of Science 6 (2):212-238.
    On which philosophical foundations is the attribution of numerical magnitudes to qualitative phenomena based? That is, what is the philosophical basis for attributing, through measurement operations, numbers to empirical qualities that our senses perceive in the outside world? This question, nowadays rarely addressed in such a way, actually refers to an old debate about the quantification of qualities. A historical analysis reveals that it was a major issue in the “context of discovery” of the first attempts to mathematize new fields (...)
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