A survey of Euclid's Elements, this text provides an understanding of the classical Greek conception of mathematics and its similarities to modern views as well as its differences. It focuses on philosophical, foundational, and logical questions — rather than strictly historical and mathematical issues — and features several helpful appendixes.

Deux opuscules nous sont parvenus de Thābit ibn Qurra sur la théorie des parallèles. Ces deux traités sont bien connus et ont fait déjà l'objet de plusieurs commentaires et traductions. Nous pensons reprendre ici aussi bien l'édition que la traduction et le commentaire pour mieux situer la contribution de Thābit ibn Qurra après la publication récente de ses œuvres en astronomie et en mathématiques.

‘Saving the appearances’,, is a slogan that, in its time, stood or was made to stand for many different methodological positions in many different branches of ancient natural science. It is not my aim, in this paper, to attempt to tackle the subject as a whole. I shall concentrate on just one inquiry, astronomy. Nor, with astronomy, can I do justice to all the complexities of what was certainly one of the central methodological issues, if not the central issue, in (...) the history of ancient theoretical astronomy. I have a quite limited aim, to examine the foundations, and test the applicability, of a widespread and influential line of interpretation of ancient Greek astronomy according to which it was essentially, or at least predominantly, what we may call ‘instrumentalist’ in character—that is, broadly speaking, that Greek astronomical theories were devices or fictions put forward purely for the sake of calculations with no claims to correspond with physical reality. (shrink)

Truth, etc. is a wide-ranging study of ancient logic based upon the John Locke lectures given by the eminent philosopher Jonathan Barnes in Oxford. Its six chapters discuss, first, certain ancient ideas about truth; secondly, the Aristotelian conception of predication; thirdly, various ideas about connectors which were developed by the ancient logicians and grammarians; fourthly, the notion of logical form, insofar as it may be discovered in the ancient texts; fifthly, the question of the 'justification of deduction'; and sixthly, the (...) attitude which has been called logical utilitarianism and which restricts the scope of logic to those forms of inference which are or might be useful for scientific proofs. In principle, the book presupposes no knowledge of logic and no skill in ancient languages: all ancient texts are cited in English translation; and logical symbols and logical jargon are avoided so far as possible. There is no scholarly apparatus of footnotes, and no bibliography. It can be read in an armchair. Anyone interested in ancient philosophy, or in logic and its history, will find it interesting. (shrink)

"Orginally published by: Leiden, NV: Koninklijke Brill, 1993.".

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)

Cet article étudie les principales classifications grecques anciennes des sciences mathématiques. Je souligne le rôle joué par Platon dans cette topique.

Fondée sous les auspices du père de notre modernité philosophique Descartes, puis consolidée par des penseurs aussi importants que Leibniz, Bolzano ou Husserl, la mathesis universalis paraît représenter à elle seule l'ambitieux programme du « rationalisme classique ». Des philosophes tels que Husserl, Russell, Heidegger ou Cassirer ont pu s'accorder en ce point. Le développement de la « science moderne » aurait porté ce grand « rêve dogmatique » pour mener vers son terme le destin de la métaphysique occidentale. Pourtant (...) les recherches historiques récentes ont montré que l'idée de « mathématique universelle » existait bien avant Descartes, que ce dernier ne revendiquait d'ailleurs aucune rupture sur ce point et que sa réflexion se situait même assez clairement dans l'héritage des Anciens. Comment dès lors justifier que les Anciens, avec lesquels le programme des Classiques était censé rompre, aient pu déjà se préoccuper de « mathématique universelle »? Plus simplement encore, de quoi se préoccupaient donc ces philosophes sous ce concept? Le regain d'intérêt pour la mathesis universalis à la fin du XIXe siècle n'avait-il pas conduit paradoxalement à la perte de son sens comme problème? Cette étude a pour but de suivre ces questions jusqu'à leur origine et de montrer leur importance dans le dialogue entre mathématique et philosophie. Pages de début Remerciements Introduction La constitution de la « mathématique universelle » comme problème philosophique I. Aristote II. « Mathématique universelle » et théories mathématiques : Aristote, Euclide, Epinomis III. Le moment néo-platonicien Vers la science de l'ordre et de la mesure IV. La renaissance de la mathématique universelle V. La mathesis universalis cartésienne Conclusion Annexe I. La quaestio de scientia mathematica communi Annexe II. Essai bibliographique sur la mathesis universalis chez Descartes etLeibniz Bibliographie Index nominum Pages de fin. (shrink)

‘Saving the appearances’, , is a slogan that, in its time, stood or was made to stand for many different methodological positions in many different branches of ancient natural science. It is not my aim, in this paper, to attempt to tackle the subject as a whole. I shall concentrate on just one inquiry, astronomy. Nor, with astronomy, can I do justice to all the complexities of what was certainly one of the central methodological issues, if not the central issue, (...) in the history of ancient theoretical astronomy. I have a quite limited aim, to examine the foundations, and test the applicability, of a widespread and influential line of interpretation of ancient Greek astronomy according to which it was essentially, or at least predominantly, what we may call ‘instrumentalist’ in character—that is, broadly speaking, that Greek astronomical theories were devices or fictions put forward purely for the sake of calculations with no claims to correspond with physical reality. (shrink)

Truth, etc. is a wide-ranging study of ancient logic based upon the John Locke lectures given by the eminent philosopher Jonathan Barnes in Oxford. The book presupposes no knowledge of logic and no skill in ancient languages: all ancient texts are cited in English translation; and logical symbols and logical jargon are avoided so far as possible. Anyone interested in ancient philosophy, or in logic and its history, will find much to learn and enjoy here.