Cet article s’interroge sur ce qu’est l’ἀριθμητική τέχνη visée par Sextus dans le Contre les arithméticiens. Après avoir rappelé brièvement le contenu de M IV, on examine la nature de cette discipline. Une fois clarifiée la question de savoir en quoi consistait l’ἀριθμητική τέχνη dans l’Antiquité – et donc ce que visait Sextus dans M IV –, on examine son rapport avec les autres disciplines critiquées par Sextus dans le Contre les Professeurs. Cette enquête mène à mettre en lumière une (...) importante présupposition implicite dans l’attitude de Sextus à l’égard des sciences. (shrink)

In this article, I tackle a heretofore unnoticed difficulty with the application of Pyrrhonian scepticism to science. Sceptics can suspend belief regarding a dogmatic proposition only by setting up opposing arguments for and against that proposition. Since Sextus provides arguments exclusively against particular geometrical definitions in Adversus Mathematicos III, commentators have argued that Sextus’ method is not scepticism, but negative dogmatism. However, commentators have overlooked the fact that arguments in favour of particular geometrical definitions were absent in ancient geometry, and (...) hence unavailable to Sextus. While this might explain why they are also absent from Sextus’ text, I survey and evaluate various strategies to supply arguments in support of particular geometrical definitions. (shrink)

This article proposes a reconstruction of the Sextan critique against the Pythagorean conception of number as principle of all existing things. Taking into consideration all the parallel passages concerning the presentation and the polemic about the Pythagorean doctrine, the present article proposes a division of the sceptical critique into two sections, the first one presenting the Pythagorean reasons to consider the numbers as principle existing apart from numbered things, and the second one presenting the arguments that Sextus himself built against (...) them. This paper will show that this structure is consistent with the sceptical method, which consists in pointing out the ἰσοσθένεια among different positions which leads to suspension of judgment. Regarding the Pythagorean doctrine that emerges from these passages, the present article discusses the way in which Sextus testified a juxtaposition between Pythagorean and Platonic doctrines, probably due to a Middle-Platonic or Neopythagorean elaboration, against which Sextus used Platonic concepts, adopting in original way arguments taken from the Parmenides and the Phaedo. Despite the ἐποχή about the nature of the number, this article will argue that Sextus did not avoid to use the number in practical daily life, in a way that is consistent with the sceptical practical criterion. (shrink)

ArgumentThis article presents ancient documents on the subject of homeomeric lines. On the basis of such documents, the article reconstructs a definition of the notion as well as a proof of the result, which is left unproved in extant sources, that there are only three homeomeric lines: the straight line, the circumference, and the cylindrical helix. A point of particular historiographic interest is that homeomeric lines were the only class of lines defined directly as the extension of a mathematical property, (...) a move that is unparalleled in Greek mathematics. The far-reaching connections between mathematical homeomery and key issues in the ancient cosmological debate are extensively discussed here. An analysis of its relevance as a foundational theme will be presented in a companion paper in a future issue of Science in Context. (shrink)

À partir de l’analyse d’un passage du Contre les géomètres de Sextus Empiricus, cet article tente d’évaluer la signification réelle ainsi que les con­séquences épistémiques de la destruction épicurienne des objets de la géométrie. L’existence du clinamen ainsi que le schème explicatif des explications multiples sont interprétés comme des résultats positifs du refus par Épicure de toute géo­métrisation de la nature.