Cher(e)s collègues,
Nous avons le plaisir de vous inviter au workshop sur la Pratique Mathématique qui se deroulera le jeudi 10 et le vendredi 11 Octobre à Aix-en-Provence, Faculté de droit et de science politique. Cordialement, Les organisateurs ____________________________________ International Workshop on Mathematical Practice Centre Gilles Gaston Granger, Aix-Marseille Université et CNRS Thursday October 10, 2019 Salle des Actes, Bâtiment Pouillon (bâtiment central) de la Faculté de droit et de science politique au 3 avenue Robert Schuman. 14h00-14h30 Paola Cantù (CNRS/Aix-Marseille Univ.) Social ontology and mathematical practice 14h30-15h30 Pierre Livet (Aix-Marseille Univ.) Ontology of epistemic activity and sociality of mathematical practice: processes and virtualities 15h45-16h45 Yacin Hamami (Vrije Universiteit Brussel) Proving Together: Shared Agency and Mathematical Proofs from a Planning Perspective 17h00-18h00 Valeria Giardino (CNRS/ENS) How to define (a) mathematical practice: a look at possible solutions (and dissolutions). 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. 9h00-10h00 José Ferreiros (Université de Seville) Objects by objectivity -- a Copernican shift 10h15-11h15 Sébastien Gandon (Université de Clermont-Ferrand) Externalismes et pratique mathématique 11h30-12h30 Frédéric Patras (CNRS/Univ. Nice). Bourbaki, « mathématicien collectif » Organisation : Paola Cantù ([email protected] <mailto:[email protected]> <mailto:[email protected] <mailto:[email protected]>>) Partners: CNRS, PICS INTEREPISTEME, Centre Gilles Gaston Granger (CGGG UMR 7304), Université Aix-Marseille. Language: English and French. Contact : Paola dot Cantu at univ-amu dot fr ________________ Abstracts José Ferreiros Objects by objectivity -- a Copernican shift Putnam has written: “The question of realism, as Kreisel long ago put it, is the question of the objectivity of mathematics and not the question of the [reality] of mathematical objects.” (Putnam 1975, p. 70) I shall elaborate on this point, considering the question of objectivity in truth value, as distinct from thick ontological objectivity, i.e. reality. This of course is a classic proposal, but it is normally underrepresented in the literature, perhaps because of the lack of a coherent general framework supporting such a proposal (see e.g. Colyvan’s Introduction, 2012, which merely mentions it). My approach can be regarded as a combination of views from Parsons 2004 and Feferman 2014, coming to a synthesis with the views in Ferreirós 2016; it’s opposed to e.g. the ideas of Shapiro in his version of structuralism. On this approach, it’s not that our mathematical activities are constrained by an objective reality of mathematical objects, but by the objective trut h or falsity of mathematical claims, which traces in turn to something other than an abstract ontology (on the cognitive, phenomenological, and semiotic origins of mathematical claims, see Ferreirós 2016). The existence of mathematical objects is dependent on such objectivity, and at times depends on hypothetical assumptions; thus it cannot be understood by mere analogy with the reality of concrete objects. More illuminating is the analogy with social objects, yet I will argue that there are significant disanalogies also here. Sebastien Gandon Externalismes et pratique mathématique. La notion de "pratique" fait l'objet d'élaborations théoriques dans les diverses formes d'externalisme sémantique développées dans la philosophie du langage des années 80-90. La conférence vise à introduire à ces discussions, et à étudier comment la pratique mathématique peut, dans ce cadre général, se singulariser. J'insisterai en particulier sur le rapport particulier qu'ont les pratiques mathématiques à la temporalité. Valeria Giardino How to define (a) mathematical practice: a look at possible solutions (and dissolutions). In the past 10 years, several works have focused on the practice of mathematics, to the extent of determining, at least according to some interpretations, a belated “practical turn” in the philosophy of mathematics. However, despite the flourishing of this new philosophical approach, it is not clear how its target - the practice of mathematics - is to be defined, nor whether a definition is needed at all. In this talk, I will briefly retrace the options that are available in the literature to describe the practice (or practices) of mathematics, and then explore the advantages and limits of endorsing as a general framework for mathematics Robert Brandom’s view of conceptual content as inferentially as well as socially articulated in the game of giving and asking for reasons. Yacin Hamami Proving Together: Shared Agency and Mathematical Proofs from a Planning Perspective “Proving theorems is one of the main activities that mathematicians engage in. Rebecca Morris and I have argued (Hamami and Morris, submitted) that proving is a goal-directed and temporally extended activity, and that for this reason it requires a form of planning agency in the sense of Bratman (1987). This led us to develop an account of plans and planning in the context of proving activities, but this account only deals with the single-agent case. Yet, proving does have in practice a strong social dimension, for it is often the case that several mathematicians engage in proving a theorem together, proving being then a case of shared activity involving a form of shared agency (Roth, 2017). In this talk, I will discuss how our single-agent account of proving activities could be developed and extended into a multi-agent account of shared proving activities, that is, into an account of proving activities in which groups of mathematicians are engaged together. More specificall y, I will discuss how Bratman’s recent account of shared activities and shared agency (Bratman, 2014) could be used to this purpose. Michael E. Bratman. Intention, Plans, and Practical Reason. Harvard University Press, Cambridge, MA, 1987. Michael E. Bratman. Shared Agency: A Planning Theory of Acting Together. Oxford University Press, New York, 2014. Yacin Hamami and Rebecca Morris. Plans and planning in mathematical proofs. Submitted. Abraham Sesshu Roth. Shared agency. In E.N. Zalta, editor, The Stanford Encyclopedia of Philosophy (2017 Edition). 2017.” Pierre Livet Ontology of epistemic activity and sociality of mathematical practice : processes and virtualities What could be the appropriate ontology for this specific practice : epistemic activity, and in particular, mathematical practice ? Surely not an ontology of substances and properties - which is supposed to be the ontology of the entities, but they can be transformed by processes, and practice is on the side of processes. A more adequate ontology is an ontology of processes. Processes cannot constitute an ontology without taking into account their connections. Notice that connections between processes are themselves processes (connecting processes). Nevertheless, connection between two processes cannot determine the totality of the two processes (if connections are not continuous - which is the normal state of affairs, because continuity of connection might imply identity between the two processes). As a consequence, connection between two processes can reveal or even trigger unsuspected aspects of both processes -what I call "virtualities". In analogy with the social domain, in order for processes to achieve "socialization" of the two processes (I borrowed this term from R. Girard) it has to be ensured that their virtualities are compatible (at least for a part), that some virtualities detected by one of the processes can still be activated after the connection with the other. In the social domain, artefacts are entities that facilitate this reactivation. They play the role of landmarks, relays, supports for activities that need the cooperation of several persons at different moments. Symbols are artefacts. Mathematical symbols like figures are also artefacts. One of their first use in history was to make difficult to cheat about exchanged quantities and facilitate accurate evaluations of great stocks - and coherence between successive evaluations. In order to achieve this result, they require to be linked with rules of operation. An important property of this kind of rules is that they ensure reactivation and rehearsal even in the domain of virtualities. Mathematical entities emerge from this situation, as they combine the stability of their rules and the unfolding of virtualities - expanding the sequence of integers, exploring fractions, discovering numbers impossible to reduce to fractions, etc. In this respect, mathematical entities extend to their limits the capabilities of processes to "socialize". In other words, they extend their virtualities while ensuring their possibility of reactivation. But while social processes admit some deviating virtualities in order to keep on socializing, mathematical socialization define and respect the differences between different mathematical entities and explore the differences between the conditions of reactivation of different kinds of virtualities. Frédéric Patras Bourbaki, « mathématicien collectif » Le cas de Nicolas Bourbaki, si on l'aborde du point de vue de son fonctionnement collectif plutôt que de sa production scientifique proprement dite, pose tout un ensemble de problèmes sur la nature du travail mathématique, ses ressorts collectifs, ses visées. Le propos de l'exposé sera triple : essayer d'établir l'ensemble des règles, explicites ou tacites, d'organisation du groupe ; analyser le groupe en tant qu'institution (auto-proclamée ?) mais aussi anti-institution (selon le modèle original, qui en ensuite évolué -ce qui sera aussi un objet d'étude) ; comprendre l'articulation de ces éléments sociologiques/organisationnels/institutionnels au travail et à la production mathématique du groupe et à ses ambitions théoriques. _______________________ Paola Cantu' Chercheur CNRS (CRCN) Centre Gilles Gaston Granger. Epistémologie Comparative. UMR 7304 - Aix-Marseille Université Faculté de Lettres - Maison de la Recherche 29, Av. Robert Schuman - 13621 Aix-en-Provence Cedex 1 - France +33(0)782543935 [email protected] http://centregranger.cnrs.fr/spip.php?article141 <http://centregranger.cnrs.fr/spip.php?article141> -- Pour toute question, la FAQ de la liste se trouve ici: https://www.vidal-rosset.net/educasup/
