Paola Cantu
CNRS Research Director (French National Center for Scientific Research)
Centre Gilles Gaston Granger
Aix-Marseille Université
114
Documents
Presentation
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.
My current research concerns:
* the role of argumentation in mathematics, either in relation to the question of ideal elements or in relation to the notion of algorithm and accounting ;
* the analysis of the notions of magnitude, quantity, measure, either in relation to the definition of mathematics or in relation to the different notions of function and equality used;
* the theory of concepts of Kurt Gödel and Bernard Bolzano, and particularly the meaning of empty concepts in mathematics and the heritage of the Leibnizian mathesis universalis;
* the difficulties and advantages of introducing different symbolisms and new proof procedures in mathematics;
* the analysis of interdisciplinary approaches in relation to the research on the foundations of mathematics and logic, on the basis of several examples that I found in the work of Hermann Graßmann, in the works of the members of the Peano school (Giuseppe Peano, Giovanni Vailati, Alessandro Padoa, Rodolfo Bettazzi), but also in some French authors like Louis Rougier.
Research domains
Philosophy
History, Philosophy and Sociology of Sciences
Skills
19th and 20th century logic and mathematics
The Peano School, Veronese, Grassmann, Bolzano, Gödel
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L'objectivité en mathématiques / Objectivity in mathematics38, 2022
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The Peano School: Logic, Epistemology and DidacticsPhilosophia Scientiae, 25-1, 2021, ⟨10.4000/philosophiascientiae.2786⟩
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The Peano School: Logic, Epistemology and DidacticsPhilosophia Scientiae, 2021, ⟨10.4000/philosophiascientiae.2786⟩
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The Epistemological Thought of Otto HölderPhilosophia Scientiae, 17 (1), 2013, 978-2-84174-620-0
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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
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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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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, inPress
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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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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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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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Peano and GödelGabriella Crocco and Eva-Maria Engelen. Kurt Gödel: Philosopher-Scientist, Presses Universitaires de Provence, pp.107—126, 2016, 9782853999762
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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
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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⟩
Book sections
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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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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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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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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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E. Paganini, La vaghezza.2009, p
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Venezia : le due città.2008, pp. 10-30
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The librarian as an antidote: recognizing the misinformation online to improve the educational reference for patients"12th International Congress on Medical Librarianship and the 2017 EAHIL Workshop, Jun 2017, Dublin, Ireland
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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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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
Conference papers
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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
Conference papers
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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 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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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
Conference papers
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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
Conference papers
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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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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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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
Conference papers
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Épistémologies interdisciplinaires au début du XXe siècleAssises du CEPERC, Feb 2017, Aix-en-Provence, France
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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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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
Conference papers
halshs-01828856v1
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International Logic Workshop 'Logic in Question' - Université Paris-SorbonneA pragmatic conception of logic., May 2012, Paris, France
Conference papers
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Senza misura niente grandezzaWorkshop Is It Wrong to Measure?, Jun 2012, Urbino, Italy
Conference papers
halshs-01828859v1
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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
Conference papers
halshs-00726544v1
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12th MidWest PhilMath Workshop - Notre Dame UniversityAn argumentative analysis of the method of ideal elements in mathematics, Nov 2011, France
Conference papers
halshs-00726547v1
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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
Conference papers
halshs-00726549v1
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Algoritmi e argomenti Algorithms and argumentsWorkshop Linguaggio, mente e logica, Sep 2010, Milano, Italy
Conference papers
hal-00588392v1
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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
Conference papers
hal-00588383v1
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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
Conference papers
hal-00588384v1
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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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hal-00588247v1
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Alla ricerca delle fallacie nei discorsi pubbliciGuanxinet, Valdagno (PD), Apr 2010, Italy
Conference papers
hal-00588393v1
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Le fallacie dell'argomentazioneNoesis, Apr 2010, Treviglio, Italy
Conference papers
hal-00588395v1
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Changes in Bolzano's definition of mathematics9th National Conference of the Italian Society for Analytic Philosophy, University of Padua, Sep 2010, Padoa, Italy
Conference papers
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Theory of Magnitudes and Theory of MeasurementInternational Workshop Hoelder, Archives Poincaré, Université de Nancy2, Mar 2010, France
Conference papers
hal-00588385v1
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Le fallacie argomentative nel discorso filosofico e scientificoDipartimento di Filosofia, Università di Bologna, Apr 2010, Bologna, Italy
Conference papers
hal-00588394v1
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Algorithms and arguments7th Conference on Argumentation of the International Society for the Study of Argumentation, Jun 2010, Amsterdam, Netherlands
Conference papers
hal-00588382v1
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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
Conference papers
halshs-00603237v1
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On real and ideal elements in mathematicsParis-Nancy PhilMath Workshop, Oct 2009, Nancy, France
Conference papers
hal-00588386v1
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Facultaire Colloquium.Bolzano's correspondence with Exner. An analysis of letters 4-9., May 2009, Amsterdam, France
Conference papers
halshs-00603231v1
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Geometry as a theory of extensive magnitudesInternational Workshop Ontological Shifts in Geometry, Paris, Université Paris Diderot, Jun 2009, Paris, France
Conference papers
hal-00588389v1
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Vailati: Logica e PragmatismoCaffè Filosofico, Crema, Mar 2009, Crema, Italy
Conference papers
hal-00588399v1
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Grassmann's epistemology: multiplication and constructivism''From Past to Future: Grassmann's Work in Context. The Grassmann Bicentennial Conference, Sep 2009, Potsdam, Germany
Conference papers
hal-00587740v1
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Grassmann's epistemology : multiplication and constructivism.Grassmann's epistemology : multiplication and constructivism., Sep 2009, France. p
Conference papers
halshs-00623971v1
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La conception épistémologique de Hermann GrassmannSéminaire de Philosophie des Mathématiques, Sep 2009, Marseille, France
Conference papers
hal-00588396v1
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A Theory-relative notion of IdealityIP Fellow Seminar, Apr 2009, Nancy, France
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hal-00588403v1
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Ideal magnitudes and numbers: a matter of degree?IP Fellow Seminar, Jan 2009, Paris, France
Conference papers
hal-00588404v1
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Caffè Filosofico.Vailati : Logica e Pragmatismo., Mar 2009, Crema, Italy
Conference papers
halshs-00603239v1
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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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hal-00588387v1
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Quantité et mesure - International WorkshopOn the foundations of a theory of magnitudes in the XIXth century., Mar 2009, Paris, France
Conference papers
halshs-00604105v1
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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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hal-00588391v1
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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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hal-00588388v1
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International Workshop Ontological Shifts in Geometry.Geometry as a theory of extensive magnitudes., Jun 2009, Paris, France
Conference papers
halshs-00604101v1
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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
Conference papers
hal-00588397v1
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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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hal-00588398v1
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Séminaire des Archives Husserl 2008-2009.La théorie des représentations et des propositions en soi., Dec 2008, Paris, France
Conference papers
halshs-00602503v1
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Ontology, Mind and Language.Identity and Equality in Padoa's Works., Sep 2008, Bergamo, Italy
Conference papers
halshs-00603848v1
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Facultair Colloquium.Bolzano'Criticism of Kant'Notion of Mathematics as the Science of Quantities., May 2008, Vrije, Netherlands
Conference papers
halshs-00602502v1
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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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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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hal-00587744v1
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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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halshs-00618076v1
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La théorie des représentations et des propositions en soiSéminaire des Archives Husserl, Ecole Normale Supérieure, Dec 2008, Paris, France
Conference papers
hal-00588400v1
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Colloquium Logico-Philosophicum.Hermann Grassmanns extensive Grössen. La théorie des grandeurs extensives de Hermann Grassmann., Jan 2006, Nürnberg, Germany
Conference papers
halshs-00602489v1
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Histoire de Géométries (séminaire).Giuseppe Veronese et les fondements de la géométrie., Mar 2006, Paris, France
Conference papers
halshs-00602481v1
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Seminario di teoria critica di Gallarate.Teorie dell'argomentazione., Nov 2006, Gallarate, Italy
Conference papers
halshs-00602497v1
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Caffé Filosofico.Filosofia e le logiche del dialogo., Sep 2006, Crema, Italy
Conference papers
halshs-00602494v1
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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
Conference papers
halshs-00602493v1
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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
Conference papers
halshs-00602204v1
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Internationalen Christian-Wolf-Kongresses.Mathématiques als Grobenlehre., Apr 2004, Saale, Germany. p. 13-24
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halshs-00618072v1
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