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  1. Space and Geometry.Henri Poincaré - forthcoming - Foundations of Science.
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  2. Kierkegaard‘s Philosophical Fragments.Irfan Ajvazi - 2022 - Tesla Books 1 (Kierkegaard philosophy):10.
    Kierkegaard, like Plato, though using different methods and conclusions, sought to ground knowledge in the ineffability of subjectivity. For Plato, knowledge comes subjectively (internally); for Kierkegaard, it comes by God's grace through faith. Socrates becomes the facilitator for the slave in the /Meno/, as does God for the man of faith. Again, Kierkegaard is also concerned with passion. "...the paradox is the passion of thought, and the thinker without the paradox is like the lover without passion; a mediocre fellow" (p. (...)
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  3. Arithmetic, Logicism, and Frege’s Definitions.Timothy Perrine - 2021 - International Philosophical Quarterly 61 (1):5-25.
    This paper describes both an exegetical puzzle that lies at the heart of Frege’s writings—how to reconcile his logicism with his definitions and claims about his definitions—and two interpretations that try to resolve that puzzle, what I call the “explicative interpretation” and the “analysis interpretation.” This paper defends the explicative interpretation primarily by criticizing the most careful and sophisticated defenses of the analysis interpretation, those given my Michael Dummett and Patricia Blanchette. Specifically, I argue that Frege’s text either are inconsistent (...)
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  4. 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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  5. 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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  6. 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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  7. 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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  8. Mathematics in Victorian Britain. [REVIEW]Joan Richards - 2013 - Isis 104:853-855.
  9. Different senses of finitude: An inquiry into Hilbert’s finitism.Sören Stenlund - 2012 - Synthese 185 (3):335-363.
    This article develops a critical investigation of the epistemological core of Hilbert's foundational project, the so-called the finitary attitude. The investigation proceeds by distinguishing different senses of 'number' and 'finitude' that have been used in the philosophical arguments. The usual notion of modern pure mathematics, i.e. the sense of number which is implicit in the notion of an arbitrary finite sequence and iteration is one sense of number and finitude. Another sense, of older origin, is connected with practices of counting (...)
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  10. 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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  11. Prova, Explicação e Intuição em Bernard Bolzano.Humberto de Assis Clímaco - 2008 - Anais Do XII Encontro Brasileiro de Pós Graduação Em Educação Matemática.
  12. Introduction: The Empirical and the Formal - Tensions in Scientific Knowledge.Gregor Schiemann & Friedrich Steinle - 2008 - Centaurus 50 (3):211-213.
  13. The Empirical and the Formal – Tensions in Scientific Knowledge (Centaurus 50/3).Gregor Schiemann & Friedrich Steinle (eds.) - 2008
  14. 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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  15. From Kant to Hilbert: A Source Book in the Foundations of Mathematics. [REVIEW]Antoni Kosinski - 2003 - Isis 94:345-347.
  16. The Foundations of Geometry and the Concept of Motion: Helmholtz and Poincaré.Gerhard Heinzmann - 2001 - Science in Context 14 (3):457-470.
    ArgumentAccording to Hermann von Helmholtz, free mobility of bodies seemed to be an essential condition of geometry. This free mobility can be interpreted either as matter of fact, as a convention, or as a precondition making measurements in geometry possible. Since Henri Poincaré defined conventions as principles guided by experience, the question arises in which sense experiential data can serve as the basis for the constitution of geometry. Helmholtz considered muscular activity to be the basis on which the form of (...)
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  17. For science and for the Pope-king: writing the history of the exact sciences in nineteenth-century Rome.Massimo Mazzotti - 2000 - British Journal for the History of Science 33 (3):257-282.
    This paper analyses the contents and the style of the Bullettino di bibliografia e di storia delle scienze matematiche e fisiche , the first journal entirely devoted to the history of mathematics. It is argued that its innovative and controversial methodological approach cannot be properly understood without considering the cultural conditions in which the journal was conceived and realized. The style of the Bullettino was far from being the mere outcome of the eccentric personality of its editor, Prince Baldassarre Boncompagni. (...)
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  18. 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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  19. ‘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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  20. 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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  21. Philosophy of Geometry from Riemann to Poincaré.Nicholas Griffin - 1981 - Philosophical Quarterly 31 (125):374.
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  22. The metaphysical foundations of critical personalism.William Stern - 1936 - Pacific Philosophical Quarterly 17 (3):238.
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  23. On Poincaré’s “Mathematical Creation”.Lucien Arréat - 1910 - The Monist 20 (4):615-617.
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