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Geometrical Analysis in Ancient Greek Mathematics

Thematic issue of Philosophia Scientiæ 25/3 (November 2021)

Guest editors : Gianluca LONGA & Sébastien GANDON

Submission Deadline: 1 July 2020

Acceptance Notification: 1 October 2020

Final version due: 1 April 2021

Submission Address: gianluca.longa@gmail.com

Description: The goal of this thematic issue is to outline the state of research on the significance and the extent of the analytical method as practiced in ancient Greek geometry. The importance of this type of reasoning for pre-modern mathematics has been recognized since the first historical research on ancient mathematics (Montucla 1758). Numerous attempts have also been made to explain the nature and meaning of this method, from Descartes, Newton and Leibniz to the contemporary epistemological and logical research (among others Polya 1945, Hintikka and Remes 1974, Lakatos 1978). However, despite this long critical tradition, today it is not yet possible to establish a commonly agreed interpretation of ancient geometric analysis: what is the aim of the analytical procedure in comparison with other methods such as the method of exhaustion or reductio, which are also used in ancient Greek geometry? Is the analytical method heuristic or apodictic? What is the relationship between the ancient form of analysis and its modern outcome (its use by Lagrange, for example, in the 18th century)?

This thematic issue is intended to take stock of the current state of the question, at a time when new studies and new proposals have emerged (Netz 2000, Menn 2002, Fournarakis and Christianidis 2006, Acerbi 2007 and 2011, Sidoli 2018) and when the need to bring together the different disciplines involved in these questions is increasingly felt.

We welcome papers on any of the following topics:

  • History of philosophy: ancient interpretations of Greek geometric analysis (Plato, Aristotle, the Aristotelian tradition, Proclus), the Arabic tradition, the Modern interpretations (Descartes, Newton, Leibniz),

  • Logic and philosophy of mathematics: exploration of the links between geometric analysis and heuristics, diagrammatic reasoning, formal logic (sequent calculus, intuitionistic type theory);

  • History of ancient mathematics: formulaic language and givens’ terminology in the extant examples of ancient geometrical analysis, continuity and rupture in the evolution of the method of analysis from Archimedes to Diophantus.

  • Manuscripts should be submitted in French, English, or German, and prepared for anonymous peer review.

  • Abstracts in French and English of 200-300 words in length should be included.

  • Articles should not exceed 50,000 characters (spaces, list of references and footnotes included).

  • Please send submissions to: gianluca.longa@gmail.com.

Guidelines for authors are to be found on the journal’s website: http://philosophiascientiae.revues.org/633.

Bibliographie

Acerbi, F. (2011). The language of the "Givens": Its forms and its use as a deductive tool in Greek mathematics. Archive for History of Exact Sciences, 65(2), 119-153.

Behboud, A. (1994). Greek Geometrical Analysis. Centaurus 37, 52–86.

Fournarakis, P., & Christianidis, J. (2006). Greek geometrical analysis: A new interpretation through the givens-terminology. Bollettino di storia delle scienze matematiche, 26(1), 33-56.

Hintikka, J. and U. Remes (1974). The Method of Analysis. Its geometrical origin and its general significance. Dordrecht/Boston: D. Reidel Publishing Company.

Knorr, W. (1986). The Ancient Tradition of Geometric Problems. New York: Dover Publication.

Lakatos, I. (1978). The Method of Analysis-Synthesis. In J. Worrall and G. Currie (Eds.), Mathematics, Science and Epistemology, pp. 70–107. Cambridge: Cambridge University Press.

Mahoney, M. (1968). Another Look at Greek Geometrical Analysis. Archive for History of Exact Sciences, 5(3/4), 318-348.

Menn, S. (2002). Plato and the Method of Analysis. Phronesis 47(3), 193-223.

Netz, R. (2000). Why did Greek mathematicians public their analysis? In Ancient and Medieval Traditions in the Exact Sciences: Essays in Memory of Wilbur Knorr, pp. 139–157.

Polya, G. (1945a). How to solve it: a new aspect of mathematical method. Princeton : Princeton Univercity Press.

Saito, K. and N. Sidoli (2010). The function of diorism in ancient Greek analysis. Historia Mathematica 37, 579–614.

Saito, K. and N. Sidoli (2012). Comparative analysis in Greek geometry. Historia Mathematica 39(1), 1–33.

Sidoli, N. C. (2018). The concept of given in Greek mathematics. Archive for History of Exact Sciences, 1-50.

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