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13Giuseppe Peano and his School: Axiomatics, Symbolism and RigorPhilosophia Scientiae 25 3-14. 2021.Peano’s axioms for arithmetic, published in 1889, are ubiquitously cited in writings on modern axiomatics, and his Formulario is often quoted as the precursor of Russell’s Principia Mathematica. Yet, a comprehensive historical and philosophical evaluation of the contributions of the Peano School to mathematics, logic, and the foundation of mathematics remains to be made. In line with increased interest in the philosophy of mathematics for the investigation of mathematical practices, this them...
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13Introduction: Symbolic Logic and Scientific PhilosophyIn Paola Cantù & Georg Schiemer (eds.), Logic, Epistemology, and Scientific Theories – From Peano to the Vienna Circle, Springer Nature Switzerland. pp. 3-10. 2023.The turn of the last century was a key transitional period for the development of symbolic logic and scientific philosophy. The Peano school, the editorial board of the Revue de Métaphysique et de Morale, and the members of the Vienna Circle are generally mentioned as champions of this transformation of the role of logic in mathematics and in the sciences. The articles contained in this volume aim to contribute to a richer historical and philosophical understanding of these groups and research a…Read more
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13Geometry and Measurement in Otto Hölder’s EpistemologyPhilosophia Scientiae 17 (1): 131-164. 2012.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…Read more
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9Louis Rougier’s reception of the Peano SchoolIn F. Brechenmacher, G. Jouve, L. Mazliak & R. Tazzioli (eds.), Images of Italian Mathematics in France . Trends in the History of Science, . pp. 213-254. 2016.Among the numerous influences and reciprocal interactions between France and Italy at the beginning of the 20th century, it is interesting to investigate the complex case of Louis Rougier’s reception of Italian mathematical logic (including in particular the contributions by some members of the Peano school: Giuseppe Peano, Giovanni Vailati, Alessandro Padoa, and Mario Pieri). This paper aims to investigate the role and the influence of the Peano school on the inversion of this French tendency o…Read more
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6An Epistemological View of the Peano School AxiomaticsIn Antonio Piccolomini D'Aragona (ed.), Perspectives on Deduction: Contemporary Studies in the Philosophy, History and Formal Theories of Deduction, Springer Verlag. pp. 323-343. 2024.The paper advocates an epistemological interpretation of the Peano School axiomatics. The construction of axiom systems is presented as a cognitive enterprise unveiling the internal dynamics, evolution, and architecture of axiomatic systems as well as connections to applications. This approach reveals that the study of the relation between axioms and theorems not only serves to reduce a theory to a minimum number of principles and increase the certainty or justification of the latter, but also t…Read more
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4F. Barone, Logica formale e logica trascendentale, Milano, Unicopli, 1999-2000Rivista di Storia Della Filosofia 57 (4): 701-704. 2002.
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1The Social Constitution of Mathematical Knowledge: Objectivity, Semantics, and AxiomaticsIn Bharath Sriraman (ed.), Handbook of the History and Philosophy of Mathematical Practice, Springer. pp. 2847-2877. 2024.The philosophy of mathematical practice sometimes investigates the social constitution of mathematics but does not always make explicit the philosophical-normative framework that guides the discussion. This chapter investigates some recent proposals in the philosophy of mathematical practice that compare social facts and mathematical objects, discussing similarities and differences. An attempt will be made to identify, through a comparison with three different perspectives in social ontology, th…Read more
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Geometry and geometries in the 19th century-Report on the history of mathematics conference held in Rende (Cosenza), Italy, June 29-July 3, 1998 (review)Rivista di Storia Della Filosofia 53 (4): 745-748. 1998.
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Life and Works of Giovanni VailatiIn Cantù Paola & De Zan Mauro (eds.), Logic and Pragmatism: Selected Essays ofGiovanni Vailati, Csli Publications. 2009.
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""David Rabouin, Mathesis universalis. L'idée de" mathématique universelle" d'Aristote à Descartes (review)Rivista di Storia Della Filosofia 65 (3): 605. 2010.
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Logic and Pragmatism: Selected Essays by Giovanni VailatiCenter for the Study of Language and Inf. 2010._Logic and Pragmatism_ features a number of the key writings of Giovanni Vailati, the Italian mathematician and philosopher renowned for his work in mechanics, geometry, logic, and epistemology. The selections in this book—many of which are available here for the first time in English—focus on Vailati’s significant contributions to the field of pragmatism. Accompanying these pieces are introductory essays by the volume’s editors that outline the traits of Vailati’s pragmatism and provide insight…Read more
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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. 2013.
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Proceedings of the International Conference: Dissensus & The Search for Common GroundOntario Society for the Study of Argumentation. 2007.
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Centre National de la Recherche ScientifiqueCentre D'Epistemologie Gilles Gaston Granger, Université Aix-MarseilleRegular Faculty
Areas of Specialization
Epistemology |
Philosophy of Mathematics |