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32An Examination of Counterexamples in Proofs and RefutationsPhilosophia Scientiae 13 (2): 3-20. 2009.Dans son influent Proofs and Refutations (Preuves et Réfutations), Lakatos introduit les méthodes de preuves et de réfutations en discutant l’histoire et le développement de la formule V — E+F = 2 d’Euler pour les polyèdres en 3 dimensions. Lakatos croyait, en effet, que l’histoire du polyèdre présentait un bon exemple pour sa philosophie et sa méthodologie des mathématiques, incluant la géométrie. Le présent travail met l’accent sur les propriétés mathématiques et topologiques qui sont incorpor…Read more
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24An Examination of Counterexamples in Proofs and RefutationsPhilosophia Scientiae 13 3-20. 2009.Dans son influent Proofs and Refutations (Preuves et Réfutations), Lakatos introduit les méthodes de preuves et de réfutations en discutant l’histoire et le développement de la formule V — E+F = 2 d’Euler pour les polyèdres en 3 dimensions. Lakatos croyait, en effet, que l’histoire du polyèdre présentait un bon exemple pour sa philosophie et sa méthodologie des mathématiques, incluant la géométrie. Le présent travail met l’accent sur les propriétés mathématiques et topologiques qui sont incorpor…Read more
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4The Meno and the Second Problem of Geometry at 86ePhilosophia: International Journal of Philosophy (Philippine e-journal) 17 (1): 45-68. 2016.The aim of this paper is two-fold: firstly, to argue for the claim that the two problems of geometry presented in the Meno seem to be connected to each other, and secondly, to offer, in connection with the first claim, a conjecture concerning the nature of the second problem of geometry brought up in the dialogue at 86e. This paper offers, in particular, a historical reconstruction of how we should understand this problem of construction in geometry.
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The Meno and the Second Problem of Geometry At 86e1Φιλοσοφια: International Journal of Philosophy 17 (1). 2016.The aim of this paper is two-fold: firstly, to argue for the claim that the two problems of geometry presented in the Meno seems to be connected to each other, and secondly, to offer, in connection with the first claim, a conjecture concerning the nature of the second problem of geometry brought up in the dialogue at 86e. This paper offers, in particular, a historical reconstruction of how we should understand this problem of construction in geometry.
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170Reichenbach on the relative a priori and the context of discovery/justification distinctionSynthese 181 (1). 2011.Hans Reichenbach introduced two seemingly separate sets of distinctions in his epistemology at different times. One is between the axioms of coordination and the axioms of connections. The other distinction is between the context of discovery and the context of justification. The status and nature of each of these distinctions have been subject-matter of an ongoing debate among philosophers of science. Thus, there is a significant amount of works considering both distinctions separately. However…Read more
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A study on the heuristic of Saccheri's euclides: A methodological-cum-historical approachBoston Studies in the Philosophy of Science 244 137-150. 2005.