CfP: Geometrical Analysis in Ancient Greek Mathematics
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.
Guidelines for authors are to be found on the
journal’s website: http://philosophiascientiae.