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Colloque Analyse géométrique grecque, 4-6 mars 2020

Colloque Analyse géométrique grecque, 4-6 mars 2020

Greek Geometrical Analysis. Problems and Prospects

The aim of this conference is to outline the state of research on the significance and the extent of the analytical method as practiced in Greek geometry. The importance of this reasoning for pre-modern mathematics has been recognised since the first historical inquiry into ancient mathematics (Montucla 1758). Numerous attempts have also been made to explain the features and the function of this technique, from Descartes, Newton and Leibniz to the contemporary epistemological and logical investigations (among others Polya 1945, Hintikka and Remes 1974, and Lakatos 1978). Despite this long critical tradition, today it is not yet possible to establish a commonly agreed account of Greek geometrical analysis : what is its purpose in comparison with other methodologies practiced in Greek geometry ? Is the analytical procedure heuristic or apodictic ? What is the relationship between the ancient form of analysis and its modern outcome ? Throughout the conference, we will take into account these and other connected questions, at a time when new studies and innovative proposals have emerged, and the need of an interdisciplinary approach is increasingly felt.

Wednesday, March 4

14:30 Arrival and Registration

14:50 Viktor Blåsjö, Utrecht University, Two Formal Purposes of Analysis in Greek Geometry

15:40 Jean Christianidis, University of Athens, Does the Ancient Analysis-and-Synthesis Pair Constitute a Proper Interpretative Framework for Diophantus’ Solutions ?

16:30 Coffee Break

17:00 Marco Panza, IHPST & Chapman University, Analysis, Constructions, and Diagrams in Greek Geometry

19:45 Dinner

Thursday, March 5

09:20 Gianluca Longa, Université Clermont Auvergne, Greek Geometrical Analysis : Collating the Corpus

10:10 Alain Petit, Université Clermont Auvergne, Analysis between Dialectic and Geometry : Proclus’ Proper Platonism

11:00 Coffee Break

11:20 Ken Saito, Osaka Prefecture University, Analysis, si uti scias, potens EST : Reappraisal of Heuristic Power of Greek Geometrical

12:20 Lunch Break

14:20 Naoya Iwata, University of Oxford, Plato and Geometrical Analysis

15:10 Giulio Di Basilio, Trinity College Dublin, What Does It Mean to Deliberate Geometrically ? Aristotle’s EN III 3 and the Method of Analysis

16:00 Coffee Break

16:20 Anne Duffee, Sewanee University, Are Problems Analytic or Synthetic ? An Investigation into Apollonius’ Parabolae

19:45 Dinner

Friday, March 6

09:20 Piotr Blaszczyk, Pedagogical University of Cracow, Modes of Diagrammatic Reasoning

10:10 Nicolas Michel & Ivahn Smadja, Paris 7 & Université de Nantes, Euclid at a Crossroads. On Chasles’ Interpretation of Euclid’s Lost Porisms

11:00 Coffee Break

11:20 Idit Chikurel, Humboldt University of Berlin, Influences of Greek Geometrical Analysis on Salomon Maimon’s Methods of Invention

12:10 Close of meeting

Organising committee : Sébastien GANDON (Université Clermont Auvergne), Vincent GÉRARD (Université Clermont Auvergne), Gianluca LONGA (Université Clermont Auvergne), Marco PANZA (IHPST & Chapman University)

Contact : gianluca.longa@uca.fr

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