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Profile: Paola Cantù
  1. Paola Cantù (forthcoming). Il sorgere di nuove geometrie nell'Ottocento: alcune riflessioni storico-filosofiche sui fondamenti della matematica. Rivista di Storia Della Filosofia.
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  2. Paola Cantù (2014). The Right Order of Concepts: Graßmann, Peano, Gödel and the Inheritance of Leibniz's Universal Characteristic. Philosophia Scientiæ 18:157-182.
    This paper tackles the question of whether the order of concepts was still a relevant aspect of scientific rigour in the 19th and 20th centuries, especially in the case of authors who were deeply influenced by the Leibnizian project of a universal characteristic. Three case studies will be taken into account: Hermann Graßmann, Giuseppe Peano and Kurt Gödel. The main claim will be that the choice of primitive concepts was not only a question of convenience in modern hypothetico-deductive investigations, but (...)
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  3. Paola Cantù (2013). Geometry and Measurement in Otto Hölder's Epistemology. Philosophia Scientiæ 17 (17-1):131-164.
    L’article a pour but d’analyser la conception de la géométrie et de la mesure présentée dans Intuition et Raisonnement [Hölder 1900], « Les axiomes de la grandeur et la théorie de la mensuration » [Hölder 1901] et La Méthode mathématique [Hölder 1924]. L’article examine les relations entre a) la démarcation introduite par Hölder entre géométrie et arithmétique à partir de la notion de ‘concept donné’, b) sa position philosophique par rapport à l’apriorisme kantien et à l’empirisme et c) le choix (...)
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  4. Paola Cantù & Schlaudt (2013). General Introduction. Philosophia Scientiæ 17 (17-1).
    1 The epistemology of Otto Hölder This special issue is devoted to the philosophical ideas developed by Otto Hölder (1859-1937), a mathematician who made important contributions to analytic functions and group theory. Hölder’s substantial work on the foundations of mathematics and the general philosophical conception outlined in this work are, however, still largely unknown. Up to the present, philosophical interest in Hölder’s work has been limited to his axiomatic formulation of a theory of..
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  5. Paola Cantu & Oliver Schlaudt (2013). Intuition and Reasoning in Geometry Inaugural Academic Lecture Held on July 22, 1899. With Supplements and Notes: Otto Hölder (1859-1937). [REVIEW] Philosophia Scientiae 17 (1):15-52.
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  6. Paola Cantu, Italian Epistemology at the End of the XIXth Century.
    At the beginning of the xxth century the high rate of analphabetism and the recent unification of the country, achieved only in 1870, had required a vast program of school and university reforms which were accompanied by a debate on two fundamental questions: whether the university should depend on public funds or become autonomous, and whether the curriculum should be specialized or remain general as in the modern era. The 1859 Casati reform had separated the faculty for literature and philosophy (...)
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  7. Paola Cantù, Bolzano Versus Kant: Mathematics as a Scientia Universalis. Philosophical Papers Dedicated to Kevin Mulligan.
    The paper discusses some changes in Bolzano's definition of mathematics attested in several quotations from the Beyträge, Wissenschaftslehre and Grössenlehre: is mathematics a theory of forms or a theory of quantities? Several issues that are maintained throughout Bolzano's works are distinguished from others that were accepted in the Beyträge and abandoned in the Grössenlehre. Changes are interpreted as a consequence of the new logical theory of truth introduced in the Wissenschaftslehre, but also as a consequence of the overcome of Kant's (...)
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  8. Paola Cantù (2010). Aristotle's Prohibition Rule on Kind-Crossing and the Definition of Mathematics as a Science of Quantities. Synthese 174 (2):225 - 235.
    The article evaluates the Domain Postulate of the Classical Model of Science and the related Aristotelian prohibition rule on kind-crossing as interpretative tools in the history of the development of mathematics into a general science of quantities. Special reference is made to Proclus’ commentary to Euclid’s first book of Elements , to the sixteenth century translations of Euclid’s work into Latin and to the works of Stevin, Wallis, Viète and Descartes. The prohibition rule on kind-crossing formulated by Aristotle in Posterior (...)
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  9. Paola Cantù (2010). David Rabouin, Mathesis universalis. L'idée de" mathématique universelle" d'Aristote à Descartes. Rivista di Storia Della Filosofia 3:605.
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  10. Paola Cantù (2010). Grassmann’s Epistemology: Multiplication and Constructivism. In Hans-Joachim Petsche (ed.), From Past to Future: Graßmann's Work in Context.
    The paper aims to establish if Grassmann’s notion of an extensive form involved an epistemological change in the understanding of geometry and of mathematical knowledge. Firstly, it will examine if an ontological shift in geometry is determined by the vectorial representation of extended magnitudes. Giving up homogeneity, and considering geometry as an application of extension theory, Grassmann developed a different notion of a geometrical object, based on abstract constraints concerning the construction of forms rather than on the homogeneity conditions required (...)
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  11. Paola Cantù (2010). The Role of Epistemological Models in Veronese's and Bettazzi's Theory of Magnitudes. In M. D'Agostino, G. Giorello, F. Laudisa, T. Pievani & C. Sinigaglia (eds.), New Essays in Logic and Philosophy of Science. College Publications.
    The philosophy of mathematics has been accused of paying insufficient attention to mathematical practice: one way to cope with the problem, the one we will follow in this paper on extensive magnitudes, is to combine the `history of ideas' and the `philosophy of models' in a logical and epistemological perspective. The history of ideas allows the reconstruction of the theory of extensive magnitudes as a theory of ordered algebraic structures; the philosophy of models allows an investigation into the way epistemology (...)
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  12. Paola Cantù (2009). Le Concept d'Espace Chez Veronese. Philosophia Scientiae 13 (2):129-149.
    Giuseppe Veronese (1854-1917) est connu pour ses études sur les espaces à plusieurs dimensions ; moins connus sont les écrits « philosophiques », qui concernent les fondements de la géométrie et des mathématiques et qui expliquent les raisons pour la construction d’une géométrie non-archimédienne (une dizaine d’années avant David Hilbert) et la formulation d’un concept de continu, qui contient des éléments infinis et infiniment petits. L’article esquissera quelques traits saillants de son épistémologie et analysera le rapport entre géométrie et intuition (...)
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  13. Paola Cantù & De Zan Mauro (2009). Life and Works of Giovanni Vailati. In Arrighi Claudia, Cantù Paola, De Zan Mauro & Suppes Patrick (eds.), Life and Works of Giovanni Vailati. CSLI Publications.
    The paper introduces Vailati’s life and works, investigating Vailati’s education, the relation to Peano and his school, and the interest for pragmatism and modernism. A detailed analysis of Vailati’s scientific and didactic activities, shows that he held, like Peano, a a strong interest for the history of science and a pluralist, anti-dogmatic and anti-foundationalist conception of definitions in mathematics, logic and philosophy of language. Vailati’s understanding of mathematical logic as a form of pragmatism is not a faithful interpretation of Peano’s (...)
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  14. Paola Cantù (2007). Is Common Ground a Word or Just a Sound? In H. V. Hanson (ed.), Proceedings of the International Conference: Dissensus & The Search for Common Ground. Ontario Society for the Study of Argumentation. 1--9.
    The paper analyses the role played by the concept of ‘common ground’ in argumentation theories. If a common agreement on all the rules of a discursive exchange is required, either at the beginning or at the end of an argumentative practice, then no violation of the rules is possible. The paper suggests an alternative understanding of ‘common ground’ as something that can change during the development of the argumentative practice, and in particular something that can change without the practice being (...)
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  15. Paola Cantù (2007). Proceedings of the International Conference: Dissensus & The Search for Common Ground. Ontario Society for the Study of Argumentation.
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  16. Paola Cantù (2006). Benjamin Schnieder, Substanz und Adhärenz. Bolzanos Ontologie des Wirklichen, Sankt Augustin, Academia Verlag, 2002, 269 pages.Benjamin Schnieder, Substanz und Adhärenz. Bolzanos Ontologie des Wirklichen, Sankt Augustin, Academia Verlag, 2002, 269 pages. [REVIEW] Philosophiques 33 (1):306-308.
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