International Workshop on Mathematical Practice
Dates : 10-11 Octobre 2019 à Aix-en-Provence
Faculté de Lettres, 3 avenue Robert Schuman, Aix-en-Provence, Bâtiment Pouillon
Salle des actes le 10 octobre
Salle du conseil le 11 octobre
There is a well-established tendency in mathematical philosophy to emphasize the importance of mathematical practice in answering epistemological questions concerning visualization, the use of diagrams, reasoning, explanation, purity of evidence, concepts, definitions, etc. This approach also claims that the analysis of specific mathematical practices, such as category theory, can yield interesting ontological results. The workshop does not limit itself to privilege an epistemological approach that could lead to new ontological perspectives, but rather assumes from the outset that mathematical concepts can not be fully studied without an approach that considers epistemology and ontology as intrinsically related.
Going beyond the approaches to mathematical practice that are based on Lakatos’ interpretation of mathematics as a quasi-empirical science, the workshop relies on the idea that mathematical concepts are socially constituted. What theory of social facts and social objects could explain the characteristics of mathematical concepts ? Or rather, are there mathematical concepts that can be better explained by one or the other rival theory ? Are there new ontological or epistemological perspectives that can be developed in this social philosophy of mathematics ?
The project that is at the basis of this workshop is not a renewal of David Bloor’s research in the sociology of mathematics, aimed at showing against Mannheim that a sociological study of mathematics is possible, or determining which branches of mathematics or which methods of mathematics might undergo sociological investigation. It is rather a study of the possibility of the application of philosophical theories on facts and social objects to mathematics. This approach requires an investigation of relevant mathematical examples that might be analyzed in the perspective of philosophical theories of "social ontology", as well as a comparative evaluation of advantages and disadvantages of different theories to address contemporary epistemological and mathematical questions. For example, Salomon Feferman characterized mathematical objectivity as a special case of intersubjective social objectivity ; José Ferreiros defined mathematical practice as an activity supported by individual and social agents with characters of stability, reliability, intersubjectivity ; Julian C. Cole sees mathematical objects as institutional rather than mental objects, referring to Searle’s theory of collective intentionality.
The purpose of the project is not to determine which social philosophical ontology is best applied to the construction of a mathematical social ontology, but rather to understand which epistemological and ontological issues are not addressed in traditional approaches to the philosophy of mathematics can emerge from this new methodological approach.
This interdisciplinary workshop is co-funded by the CNRS PICS Project “INTEREPISTEME. The effect of interdisciplinary collaboration on early 20th century epistemologies”, which aims at a comparative investigation of three distinct collaborative and interdisciplinary approaches that took place at the beginning of the century (the Revue de Métaphysique et de Morale, the Peano School and the Vienna Circle), in the belief that the philosophy of mathematics of that time already highlighted certain intersections between mathematical practice and the social constitution of scientific objects (e.g. the analysis of mathematical language, definitions and proofs in Peano’s Formulary as well as in Vailati’s investigations on the origin and death of socially constituted scientific objects and metaphors, or the ontological and epistemological questions raised by Otto Neurath, as he developed a visual language for the public communication of historical and statistical information).
Invited Speakers :
• José Ferreiros (Université de Seville, Spain)
• Sebastien Gandon (PHIER, Université de Clermont-Ferrand)
• Valeria Giardino (Archives Poincaré, Université de Lorraine)
• Yacin Hamami (Centre for Logic and Philosophy of Science, Vrije Universiteit
Brussel)
• Pierre Livet (Centre Gilles Gaston Granger, Aix-Marseille Université)
• Frédéric Patras (Laboratoire Dieudonné, Université Nice Sophia Antipolis)
• Christophe Salvat (Centre Gilles Gaston Granger, Aix-Marseille Université)
Provisionary Program :
Thursday October 10, 2019
Salle des Actes, Bâtiment Pouillon (bâtimet central) de la Faculté de droit et de science politique au 3 avenue Robert Schuman.
Friday October 11, 2019
Salle du Conseil, Bâtiment Pouillon (bâtiment central) de la Faculté de droit et de science politique au 3 avenue Robert Schuman.
Organisation : Paola Cantù (paola.cantu@univ-amu.fr)
Partners : CNRS PICS INTEREPISTEME and Centre Gilles Gaston Granger (CGGG
UMR 7304), Université Aix-Marseille.
Language : English.
Registration : compulsory but free.
Contact : Paola.Cantu@univ-amu.fr