From Zeno ad infinitum: Iterative Reasonings in Early Greek Philosophy

References

DK = Diels, H. & Kranz, W., eds. (1951): Die Fragmente der Vorsokratiker, 3 vols. Berlin: Weidmann.Search in Google Scholar

LM = Laks, A. & Most, G. W., eds. (2016): Early Greek Philosophy, 9 vols (Loeb Classical Library). Cambridge, MA-London: Harvard University Press.Search in Google Scholar

Acerbi, F. (2000): “Plato: Parmenides 149a7-c3. A proof by Complete Induction?”, Archive for History of Exact Sciences 55 (1), pp. 57–76.10.1007/s004070000020Search in Google Scholar

Chemla, K., ed. (2012): The History of Mathematical Proof in Ancient Traditions. Cambridge, Cambridge University Press.Search in Google Scholar

Chemla, K. (2012a): “Historiography and history of mathematical proof: a research programme”. In: Chemla (2012), pp. 1–68.Search in Google Scholar

Chemla, K. (2021): “From reading rules to reading algorithms: textual anachronisms in the history of mathematics and their effects on interpretation”. In: Niccolò Guicciardini (ed.): Anachronisms in the History of Mathematics, Essays on the Historical Interpretation of Mathematical Texts. Cambridge, Cambridge University Press, 2021.10.1017/9781108874564.003Search in Google Scholar

Federspiel, M. (2004): “Sur les emplois et les sens de l’adverbe aei dans les mathématiques grecques”, Les Études Classiques 72, pp. 289–311.Search in Google Scholar

Knorr, W. R. (1975): The Evolution of the Euclidean Elements. Dordrecht: D. Reidel.10.1007/978-94-010-1754-1Search in Google Scholar

Knuth, D. (1972): “Ancient Babylonian algorithms”, Communications of the ACM 15, pp. 671–677.10.1145/361454.361514Search in Google Scholar

Moore, A.W. (1990): The Infinite. New York: Routledge.Search in Google Scholar

Mugler, C. (1958): Dictionnaire historique de la terminologie géométrique des grecs, vol. I. Paris: Klincksieck.Search in Google Scholar

Netz, R. (1999): The Shaping of Deduction in Greek Mathematics. Cambridge: Cambridge University Press.10.1017/CBO9780511543296Search in Google Scholar

Netz, R. (2001): “The Aristotelian Paragraph”, The Cambridge Classical Journal 47, pp. 211–32.10.1017/S006867350000078XSearch in Google Scholar

Netz, R. (2020): Scale, Space and Canon in Ancient Literary Culture. Cambridge: Cambridge University Press.10.1017/9781108686945Search in Google Scholar

Saito, K. (1998): “Mathematical Reconstructions Out, Textual Studies In: 30 Years in The Historiography of Greek Mathematics”, Revue d’histoire des mathématiques 4, pp. 131–42.Search in Google Scholar

Saito, K. (2013): “Toolbox”, published 17 August 2013, https://www.greekmath.org/toolbox/index.htmlSearch in Google Scholar

Schaffer, S. and Shapin, S. (1985): Leviathan and the Air-Pump. Hobbes, Boyle, and the Experimental Life. Princeton: Princeton University Press.Search in Google Scholar

Seban, P. (forthcoming): Le temps et l’infini. Sur les paradoxes de Zénon d’Élée (MétaphysiqueS). Paris: Presses Universitaires de France.Search in Google Scholar

Sourvinou-Inwood, C. (1986): “Crime and Punishment: Tityos Tantalos and Sisyphos in Odyssey 11”, Bulletin of the Institute of Classical Studies 33, pp. 37–58.10.1111/j.2041-5370.1986.tb00183.xSearch in Google Scholar

Ugaglia, M. (2009): “Boundlessness and Iteration: Some Observations about the Meaning of άεί in Aristotle”, Rhizai. A Journal for Ancient Philosophy and Science 6, pp. 193–213.Search in Google Scholar

Vitrac, B. (2012): “Les démonstrations par l’absurde dans les Éléments d’Euclide: inventaire, formulation, usages. Séminaire d’épistémologie et d’histoire des idées mathématiques” <hal-00496748v2>, submitted 5 April 2012, https://hal.archives-ouvertes.fr/hal-00496748v2Search in Google Scholar