Paola Cantu
- Centre National de la Recherche Scientifique (CNRS)
- Aix Marseille Université (AMU)
- Centre Gilles-Gaston Granger (CGGG)
Présentation
Ma recherche actuelle concerne principalement les thèmes suivants: 1) le rôle de l’argumentation en mathématiques, soit en rapport avec la question des éléments idéaux soit en rapport avec la notion d’algorithme et de comptabilité ; 2) l’analyse des notions de grandeur, quantité, mesure, soit en rapport avec la définition des mathématiques soit en relation aux différentes notions de fonction et d’égalité utilisées ;
3) la théorie des concepts de Kurt Gödel et Bernard Bolzano, et particulièrement la signification des concepts vides en mathématiques et l’héritage de la mathesis universalis leibnizien;
4) les difficultés et les avantages liés à l’introduction des différents symbolismes et à de nouvelles procédures de démonstration en mathématiques;
5) l’analyse des approches interdisciplinaires par rapport à la recherche sur les fondements des mathématiques et de la logique, sur la base de plusieurs exemples que j’ai trouvé dans l’œuvre de Hermann Graßmann, dans les travaux des membres de l’école de Peano (Giuseppe Peano, Giovanni Vailati, Alessandro Padoa, Rodolfo Bettazzi), mais aussi dans certains auteurs français comme Louis Rougier.
Domaines de recherche
Compétences
Publications
Publications
L'objectivité en mathématiques / Objectivity in mathematics38, 2022 |
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The Peano School: Logic, Epistemology and DidacticsPhilosophia Scientiae, 2021, ⟨10.4000/philosophiascientiae.2786⟩ |
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The Peano School: Logic, Epistemology and DidacticsPhilosophia Scientiae, 25-1, 2021, ⟨10.4000/philosophiascientiae.2786⟩ |
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The Epistemological Thought of Otto HölderPhilosophia Scientiae, 17 (1), pp.189, 2013, The Epistemological Thought of Otto Hölder, ⟨10.4000/philosophiascientiae.811⟩ |
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An Epistemological View of the Peano School AxiomaticsPiccolomini d'Aragona, Antonio. Perspectives on Deduction: Contemporary Studies in the Philosophy, History and Formal Theories of Deduction, 481, Springer International Publishing, pp.323-343, 2024, Synthese Library, 978-3-031-51405-0. ⟨10.1007/978-3-031-51406-7_15⟩ |
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Russell and Carnap or Bourbaki? Two Ways Towards StructuresPaola Cantù; Georg Schiemer. Logic, Epistemology, and Scientific Theories - From Peano to the Vienna Circle, 29, Springer Nature Switzerland, pp.193-216, 2023, Vienna Circle Institute Yearbook, 978-3-031-42189-1. ⟨10.1007/978-3-031-42190-7_9⟩ |
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Introduction. Symbolic logic and scientific philosophyPaola Cantù; Georg Schiemer. Logic, Epistemology, and Scientific Theories - From Peano to the Vienna Circle, 29, Springer Nature Switzerland, pp.3-10, 2023, Vienna Circle Institute Yearbook, ⟨10.1007/978-3-031-42190-7_1⟩ |
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The Social Constitution of Mathematical Knowledge. Objectivity, Semantics, and AxiomaticsBharath Sriraman. Handbook of the History and Philosophy of Mathematical Practice, Springer International Publishing, pp.1-31, 2023, 978-3-030-19071-2. ⟨10.1007/978-3-030-19071-2_57-1⟩ |
Langage et cognition mathématiqueAlexandre Gefen. Un monde commun. Les savoirs des sciences humaines et sociales, CNRS EDITIONS, pp.326--329, 2023, EAN : 9782271147530 |
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Syllogism and beyond in the Peano SchoolVerburgt, Lukas M. and Cosci, M. Aristotle's Syllogism and the Creation of Modern Logic: Between Tradition and Innovation, Bloomsbury, 2023, 9781350228863 |
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Peano's Philosophical Views between Structuralism and LogicismFrancesca Boccuni; Andrea Sereni. Origins and Varieties of Logicism. On the Logico-Philosophical Foundations of Mathematics, 1, Routledge, 2021, ⟨10.4324/9780429277894-11⟩ |
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Grassmann’s Concept StructuralismThe Prehistory of Mathematical Structuralism, Oxford University Press, pp.21-58, 2020, ⟨10.1093/oso/9780190641221.003.0002⟩ |
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Logica impura. Un contrappunto epistemologicoE. Montuschi and P.D. Omodeo. Ordinare il mondo. Prospettive logiche ed epistemologiche su scienza, natura e società, Armando, pp.71--95, In press |
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Mathematics. Systematical conceptsRobert Theis; Alexander Aichele. Handbuch Christian Wolff, Springer VS, pp.357—379, 2018, 978-3-658-14736-5. ⟨10.1007/978-3-658-14737-2_17⟩ |
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Peano and GödelGabriella Crocco and Eva-Maria Engelen. Kurt Gödel: Philosopher-Scientist, Presses Universitaires de Provence, pp.107—126, 2016, 9782853999762 |
Louis Rougier’s reception of the Peano SchoolFréderic Brechenmacher, Guillaume Jouve, Laurent Mazliak and Rossana Tazzioli. Images of Italian Mathematics in France. The Latin Sisters, from Risorgimento to Fascism, , pp.213--254, 2016, Series "New trends in history of science", 978-3-319-40080-8. ⟨10.1007/978-3-319-40082-2_8⟩ |
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Bolzano versus Kant: mathematics as a scientia universalisREBOUL Anne. MInd, Values and Metaphysics. Philosophical Papers Dedicated to Kevin Mulligan, 1, Springer International Publishing, pp.295--316, 2014, 9783319041988 |
An Argumentative Approach to Ideal Elements in Mathematics.Andrew Aberdein et Ian J. Dove. The argument of Mathematics, Springer, p., 2012, ⟨10.1007/978-94-007-6534-4_6⟩ |
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Life and Works of Giovanni VailatiClaudia Arrighi; Paola Cantú; Mauro de Zan; Patrick Suppes. Logic and Pragmatism. Selected Writings of Giovanni Vailati., 198, CSLI Publications, pp.xxi-lxvii, 2009, CSLI Lecture Notes, 9781575865904 |
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La svolta argomentativa. 50 anni dopo Perelman e Toulmin : 1958-2008.Consento e dissenso., Loffredo, Napoli., pp. 87-96, 2009 |
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Prospettiva e immaginazione metafisicaRino Genovese et Italo Testa. Ragione impura. Una Jam Session su metafisica e immaginazione, Bruno Mondadori, pp. 171-175, 2006 |
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Propositions et états de choses.J. Benoist. Bolzano et les propositions en soi : une théorie objective des vérités., Vrin, pp. 51-66, 2006 |
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La matematica da scienza delle grandezze a teoria delle forme. L'Ausdehnungslehre de H. GrassmannHistory, Philosophy and Sociology of Sciences. Università degli Studi di Genova, 2003. Italian. ⟨NNT : ⟩ |
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Philosophie de l'axiomatiqueSciences de l'Homme et Société. Ecole Normale Superieure de Paris - ENS Paris, 2022 |
E. Paganini, La vaghezza.2009, p |
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Venezia : le due città.2008, pp. 10-30 |
The librarian as an antidote: recognizing the misinformation online to improve the educational reference for patients12th International Congress on Medical Librarianship and the 2017 EAHIL Workshop, Jun 2017, Dublin, Ireland |
Logic and interaction. Pragmatics and Argumentation TheoryLet’s prove it. CIVIS Summer School, National and Kapodistrian University of Athens, Jul 2025, Athens, Greece |
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Can definitions play an epistemological role in axiomatics?International Workshop, Mathematical Concepts: Analysis, Definitions and Explications, IUSS, Istituto Universitario di Studi Superiori, Jun 2025, Pavia, Italy |
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Definitions by abstraction in the Peano SchoolVienna-IUSS Workshop: Axiomatic Definitions and Abstraction, a Century After Frege, University of Vienna, Department of Philosophy, Feb 2025, Vienna, Austria |
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Variétés de métamathématiques : que peut-on étudier de l’intérieur ?Journées d'étude Autour de la métamathématique, Centre Gilles Gaston Granger, Aix-Marseille Université, Nov 2025, Marseille, France |
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Mathematical understanding and mathematical translation(s), International Workshop “Mathematics, history and philosophy of mathematics: Which interactions?”, International Center of Mathematical Research (CIRM), Nov 2025, Marseille, France |
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Axiomatisation, formalisation et mesureSéminaire « Approches historiques, philosophiques et anthropologiques des nombres, de la mesure et de la mesurabilité » 2024 – 2025, IHSS / Laboratoire SPHERE UMR 7219, Université Paris Cité, Feb 2025, Paris, France |
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The Social Constitution of Mathematical Knowledge: Objectivity, Semantics and AxiomaticsSTS Colloquium, ETH Zürich, Mar 2025, Zurich (CH), Switzerland |
Les structures : concepts ou objets épistémiques ?Journée Bourbaki et le structuralisme, ANR BANANA, Feb 2025, Paris, France |
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Practical rationality and structuralism. Peano’s remarks on the principle of permanenceSéminaire PhilMath | IHPST, Jan 2024, Paris, France |
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Axiomatic definitions in the Peano SchoolThe Lesson of Peano and Russell. Logical Tools for the Computational Approach to Legal Theory, Sep 2024, Genova, Italy |
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Veronese's non-Archimedean ContinuityOn Giuseppe Veronese and non-Archimedean mathematics, Dec 2024, Paris, France |
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Peano's Axiomatic definitions1st AXDEF WORKSHOP Implicit Definitions, May 2024, Marseille, France |
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Axiomatic Definitions in the Peano SchoolSymposium “Geometry to Logic and Back: History, Philosophy, and Foundations”, 17th International Congress on Logic, Methodology and Philosophy of Science and Technology, CMPLST and University of Buenos Aires, Jul 2023, Buenos Aires, Argentina |
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L'objectivité et la constitution sociale des pratiques mathématiques, Table ronde Objectivité mathématiqueECOLE THEMATIQUE MATHEMATIQUES ET PHILOSOPHIE CONTEMPORAINES X « Grothendieck, Vuillemin, l’Objectivité mathématique », GDR PHILMATH, Université de Toulouse, Jun 2023, Saint-Ferreol, France |
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What role does (can) axiomatics play today?FPMW15 15th French PhilMath Workshop, Université Paris 1 Panthéon-Sorbonne et Université Paris-Cité, Oct 2023, Paris, France |
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Information scientifique et désinformation : arguments, émotions et fake newsSéminaire du Cycle HiPhiS 2023 "Communication scientifique : certitudes, incertitudes et prise de décision", Université de Montpellier, May 2023, Montpellier, France |
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What role do definitions play in axiomatics?6th Arthur Pap Lecture, Vienna Circle Institute, Dec 2023, Vienna, Austria |
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Granger, le style et l’épistémologieSéminaire Commun du Centre Gilles Gaston Granger, Université Aix-Marseille, Feb 2023, Marseille, France |
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Axiomatisation, formalisation et mesure dans l’œuvre de G. G. Granger : constitution de l’objectivité scientifique et praxisTable Ronde « Quelles mathématisations pour quelles mesures ? Cheminement à travers les disciplines », Université Paris-Cité, Dec 2023, Paris, France |
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Formalism in the Peano GroupInternational Workshop "The Formal Turn in Twentieth-Century Thought", University of Vienna, Feb 2023, Vienna, Austria |
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Intuition and Axiomatics. The case of non-Archimedean continuityInternational Workshop "Intuition in mathematics. Historical, epistemological, cognitive and phenomenological aspects", University of Liège, Nov 2023, Liège, Belgium |
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Actualité du structuralisme dans la philosophie de la pratique mathématique et son rapport au pragmatismeTable ronde "Actualité du structuralisme", Workshop of the network PHILMATHMED (Philosophie, Histoire et Didactique des Mathématiques en Méditerranée) "Les structures, et après ?", Université Côte d'Azur, May 2023, Nice, France |
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Practical rationality, formalism and structuralism. Peano’s remarks on the principle of permanenceInternational Workshop "From Permanence to Conservativity – Metatheoretic Ideals in Early Formalism", University of Vienna, Dec 2023, Vienna, Austria |
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Social ontology and mathematical practiceInternational Workshop on Mathematical Practice, Paola Cantù, Centre Gilles Gaston Granger, Aix-Marseille Université and CNRS, Oct 2019, Aix-en-Provence, France |
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The Peano’s School Epistemology and Frege's Logicism II2nd Prague Workshop on Frege's Logic, Joan Bertran-San Millán, Institute of Philosophy, Czech Academy of Sciences, Jul 2019, Prague, Czech Republic |
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Théorie de l’argumentation et empirisme logique à la base du naturalisme scientifique en sciences socialesSéminaire commun du Centre Gilles Gaston Granger 2018-2019, Gabriella Crocco and Philippe Abgrall, Centre Gilles Gaston Granger, Aix-Marseille Université, Jan 2019, Marseille, France |
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The Peano’s school epistemology and Frege’s logicism IIIERC International Conference “Origins of Structuralism”, Georg Schiemer, Department of Philosophy, University of Vienna, Aug 2019, Vienna, Austria |
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Épistémologie historique et architecture du savoirIII PHILMATHMED Workshop L’épistémologie historique, hier et aujourd’hui, Sébastien Maronne, Institut de Mathématiques de Toulouse UMR 5219, Université Toulouse III Paul Sabatier, Jun 2019, Toulouse, France |
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The Peano’s School Epistemology and Frege's Logicism I2nd International INTEREPISTEME Workshop, Paola Cantù, Georg Schiemer and Erika Luciano, Dipartimento di Matematica, Università di Torino, May 2019, Torino, Italy |
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Logica impura: perdita dell'unità e contrappunto epistemologicoInternational Workshop. "Mettere ordine al mondo: prospettive logiche ed epistemologiche su scienza, natura, società", Eleonora Montuschi e Pietro Daniel Omodeo, Dipartimento di Filosofia, Università di Venezia, May 2019, Venezia, Italy |
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Mathematical practice and social ontologySeminario interdisciplinare di epistemologia delle scienze sociali, Francesco Guala, Dipartimento di Filosofia, Università degli Studi di Milano; Paola Cantù, Centre Gilles Gaston Granger, Université Aix-Marseille; Matteo Bianchin, Dipartimento delle Scienze Umane, Università Milano-Bicocca; Italo Testa, Dipartimento di discipline umanistiche, sociali e delle imprese culturali, Università di Parma, Oct 2019, Milano, Italy |
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Bolzano’s requirement of a correct ordering of concepts and its inheritance in modern axiomaticsSymposium : Bolzano’s Mathematics and the General Methodology of the Sciences, 16th International Congress on Logic, Methodology and Philosophy of Science and Technology (CLMPST), Bridging across academic cultures, CLMPS and Steve Russ (Symposium Organizer), Aug 2019, Prague, Czech Republic |
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The role of implicit definitions in the Peano School12th International Conference of the International Society for the History of Philosophy of Science (HOPOS), Jul 2018, Groningen, Netherlands |
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Language and metatheory in the Peano SchoolInternational Workshop “Modern Axiomatics and Early Metatheory”, Feb 2018, Vienna, Austria |
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Grassmann’s conceptual structuralism. Particular thought forms and concepts’ underdeterminacyInternational Workshop “Mathematics and its Philosophy between the 18th and the 19th Century”, Jul 2018, Amsterdam, Netherlands |
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L'introduction des éléments idéaux en mathématiques : une définition correlative.PhilMathMed Workshop “Regards croisés sur les mathématiques. Philosophie, Histoire et Didactique”, Jun 2017, Nice, France |
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Épistémologies interdisciplinaires au début du XXe siècleAssises du CEPERC, Feb 2017, Aix-en-Provence, France |
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Grassmann’s proto-structuralismInternational Workshop “Structuralist Methods in Modern Mathematics”, Apr 2017, Vienna, Austria |
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Philosophie et mathématiques : opposition et croisement disciplinaireAssises du Ceperc, Jun 2016, Aix-en-Provence, France |
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International Logic Workshop 'Logic in Question' - Université Paris-SorbonneA pragmatic conception of logic., May 2012, Paris, France |
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Senza misura niente grandezzaWorkshop Is It Wrong to Measure?, Jun 2012, Urbino, Italy |
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EPSA 2011 Third conference of the European Philosophy of Science Association - Dept of Philosophy and History of Science University of AthensKant and 20th century philosophy of mathematics, Oct 2011, Athènes, Greece |
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12th MidWest PhilMath Workshop - Notre Dame UniversityAn argumentative analysis of the method of ideal elements in mathematics, Nov 2011, France |
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Sur les fondements d'une théorie des grandeurs au XIXème siècle, Workshop - Lille University, Department of MathematicThe axioms of geometry in the 20th century, Nov 2011, Lille, France |
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Alla ricerca delle fallacie nei discorsi pubbliciGuanxinet, Valdagno (PD), Apr 2010, Italy |
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Le fallacie dell'argomentazioneNoesis, Apr 2010, Treviglio, Italy |
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Changes in Bolzano's definition of mathematics9th National Conference of the Italian Society for Analytic Philosophy, Sep 2010, Padoue, Italy |
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The Italian debate on the analytical definition of real number at the end of the 19th centuryInternational Workshop Algèbre et géométrie au XIX siècle, Jun 2010, Paris, France |
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Le fallacie argomentative nel discorso filosofico e scientificoDipartimento di Filosofia, Università di Bologna, Apr 2010, Bologna, Italy |
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Algorithms and arguments7th Conference on Argumentation of the International Society for the Study of Argumentation, Jun 2010, Amsterdam, Netherlands |
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Algoritmi e argomenti Algorithms and argumentsWorkshop Linguaggio, mente e logica, Sep 2010, Milano, Italy |
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Theory of Magnitudes and Theory of MeasurementInternational Workshop Hoelder, Archives Poincaré, Université de Nancy2, Mar 2010, France |
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The epistemological conception of Hermann Günther GrassmannCongresso Internazionale della Società Italiana di Logica e Filosofia delle Scienze (SILFS), Dec 2010, Bergamo, Italy |
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Changes in Bolzano's definition of mathematicsInternational Conference Philosophy and Mathematics in the Work of Bernard Bolzano, Apr 2010, Prague, Czech Republic |
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A Theory-relative notion of IdealityIP Fellow Seminar, Apr 2009, Nancy, France |
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Ideal magnitudes and numbers: a matter of degree?IP Fellow Seminar, Jan 2009, Paris, France |
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La conception épistémologique de Hermann GrassmannSéminaire de Philosophie des Mathématiques, Sep 2009, Marseille, France |
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Caffè Filosofico.Vailati : Logica e Pragmatismo., Mar 2009, Crema, Italy |
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Vailati: Logica e PragmatismoCaffè Filosofico, Crema, Mar 2009, Crema, Italy |
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Geometry as a theory of extensive magnitudesInternational Workshop Ontological Shifts in Geometry, Paris, Université Paris Diderot, Jun 2009, Paris, France |
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On the foundations of a theory of magnitudes in the XIXth centuryInternational Workshop Quantité et mesure, Paris, Université Paris Diderot (Paris 7), Mar 2009, France |
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Giovanni Vailati and the Peano school. On the analysis of scientific premises and languageInternational Conference Rethinking Pragmatism, Università degli Studi di Milano, Oct 2009, Milano, Italy |
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Quantité et mesure - International WorkshopOn the foundations of a theory of magnitudes in the XIXth century., Mar 2009, Paris, France |
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International Workshop Ontological Shifts in Geometry.Geometry as a theory of extensive magnitudes., Jun 2009, Paris, France |
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Bolzano's correspondence with Exner. An analysis of letters 4-9Facultair Colloquium, Faculteit der Wijsbegeertevrije, Amsterdam, Vrije Universiteit, May 2009, Amsterdam, Netherlands |
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La définition symbolique de l'égalité logique dans le cadre de l'école de PeanoSéminaire d'Epistemologie, IREM, May 2009, Paris, France |
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Séminaire d'Espistémologie IREM Institut Poincaré.La définition symbolique de l'égalité logique dans le cadre de l'école de Peano., May 2009, Paris, France |
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On real and ideal elements in mathematicsParis-Nancy PhilMath Workshop, Oct 2009, Nancy, France |
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Sul concetto di eguaglianza. Peano e la sua scuolaPeano e la sua scuola fra matematica, logica e interlingua., Oct 2008, Torino, Italy. pp.545-561 |
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The interest of Vailati's epistemologyInternational Workshop Pragmatism from Giovanni Vailati to contemporary epistemology., Oct 2009, Bologna, Italy |
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La Scuola di Peano fra matematica, logica e interlingua.Sul concetto di eguaglianza. Peano e la sua scuola., Oct 2008, Torino., Italy. p |
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Grassmann's epistemology: multiplication and constructivismFrom Past to Future: Grassmann's Work in Context. The Grassmann Bicentennial Conference, Sep 2009, Potsdam, Germany |
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Grassmann's epistemology : multiplication and constructivism.Grassmann's epistemology : multiplication and constructivism., Sep 2009, France. p |
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Facultaire Colloquium.Bolzano's correspondence with Exner. An analysis of letters 4-9., May 2009, Amsterdam, France |
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La théorie des représentations et des propositions en soiSéminaire des Archives Husserl, Ecole Normale Supérieure, Dec 2008, Paris, France |
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Sul concetto di eguaglianza. Peano e la sua scuola.Sul concetto di eguaglianza. Peano e la sua scuola., Sep 2008, Torino, Italy. p |
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Ontology, Mind and Language.Identity and Equality in Padoa's Works., Sep 2008, Bergamo, Italy |
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Facultair Colloquium.Bolzano'Criticism of Kant'Notion of Mathematics as the Science of Quantities., May 2008, Vrije, Netherlands |
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Séminaire des Archives Husserl 2008-2009.La théorie des représentations et des propositions en soi., Dec 2008, Paris, France |
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Internationalen Christian-Wolf-Kongresses.Mathématiques als Grobenlehre., Apr 2004, Saale, Germany. p. 13-24 |
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Seminario di teoria critica di Gallarate.Teorie dell'argomentazione., Nov 2006, Gallarate, Italy |
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Caffé Filosofico.Filosofia e le logiche del dialogo., Sep 2006, Crema, Italy |
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Seminari di Filosofia del Centro Studi Vailati.Jaakko Hintikka : il ruolo della logica nel ragionamento e nell'argomentazione., May 2006, Crema, Italy |
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Les mathématiques italiennes au XIXème siècle: Peano et son école.Alessandro Padoa and the concept of equality., Oct 2006, Aix-en-Provenve, France |
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Colloquium Logico-Philosophicum.Hermann Grassmanns extensive Grössen. La théorie des grandeurs extensives de Hermann Grassmann., Jan 2006, Nürnberg, Germany |
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Histoire de Géométries (séminaire).Giuseppe Veronese et les fondements de la géométrie., Mar 2006, Paris, France |