ON THE INCOMMENSURABILITY, THE CONTINUUM AND THE INSEPARABLE LINES IN ARISTOTLE
DOI:
https://doi.org/10.26512/pl.v1i2.11536Keywords:
Incommensurability. Continuous. Indivisible linhes. Aristotle.Abstract
This work aims at to expose the arithmetic proof of incommensurability between the values to the legs and hypotenuse of a right triangle and the resulting impact of knowledge of irrational numbers among the Greeks. Then, we show the implications of these innovations to the analysis Aristotle’s Physics concerning the possibility of infinite divisibility of matter and the existence of linear continuous physical quantities. Thirdly, we use the rare Aristotelian treatise On the Indivisible Lines to complement this denial of the existence of discrete indivisible atomic entities.
Downloads
References
ANNAS, Julia. Aristotle, Number and Time. In: The Philosophical Quarterly, Vol. 25, No. 99 (Apr.), 1975, pp. 97-113.
ARISTÓTELES. Física. Tradução e notas de Ute Schmidt Osnanczik. México: Universidad Nacional Autonoma del México, 2001.
________. Metafísica. Tradução de Vizenzo Cocco. São Paulo: Abril Cultural, 1984.
BERTI, Enrico. As Razões de Aristóteles. São Paulo: Edições Loyola, 2002.
BORNHEIM, Gerd. Os Filósofos Pré-socráticos. São Paulo: Editora CULTRIX, 1998.
BOSTOCK, David. Space, Time, Matter, and Form: Essays on Aristotle’s Physics. Oxford: Oxford University Press, 2006.
CHANTRAINE, PIERRE. Dictionnaire Étymologique de la Langue Grecque: Histoire des Mots. Paris: Éditons Klincksieck, 1968.
DEHN, Max. Mathematics, 600 B.C-400 B.C. In: The American Mathematical Monthly, Vol. 50, N. 6 (Jun.-Jul), 1945, pp. 357-360.
FEYERABEND, Paul. Alguns Comentários à Teoria da Matemática e do Contínuo de Aristóteles, In: Adeus à Razão. Lisboa: Edições 70, 1991, pp. 259-288.
GANDZ, Solomon. On the Origin of the Term “Root”. In: The American Mathematical Monthly, Vol. 33, N. 5 (May), 1926, pp. 261-265.
KNNOR, Wilbur. “Rational Diameters” and the Discovery of Incommensurability. In: The American Mathematical Monthly, Vol. 105, N. 5 (May), 1998, pp. 421-429.
LEAR, Jonathan. Aristotle’s Philosophy of Mathematics. In: The Philosophical Review, Vol. 91, No. 2 (Apr.), 1982, pp. 161-192.
PETERS, Francis. Termos Filosóficos Gregos: Um Léxico Histórico. Lisboa: Fundação Calouste Gulbenkian, 1996.
Downloads
Published
Issue
Section
License
Copyright (c) 2016 Pólemos
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Todos os trabalhos que forem aceitos para publicação, após o devido processo avaliativo, serão publicados sob uma licença Creative Commons, na modalidade Attribution-NonCommercial-NoDerivatives 4.0 International Public License (CC BY-NC-ND 4.0). Esta licença permite que qualquer pessoa copie e distribua a obra total e derivadas criadas a partir dela, desde que seja dado crédito (atribuição) ao autor / Ã autora / aos autores / às autoras.
