ANCIENT GREEK MATHEMATICO-PHYSICAL PARADOX
DOI:
https://doi.org/10.15448/1984-6746.1996.164.35918Keywords:
Paradoxo, Matemática, ZenonAbstract
Neste artigo revisa-se a literatura sobre paradoxos matemático-físicos gregos antigos. Trata-se de paradoxo de números irracionais, o dilema de Democritus, a antinomia de mudança, bem como os seguintes paradoxos de Zenon: a dicotomia, o Aquiles, os blocos móveis, o argumento contra a pluralidade, o dilema e a semente de painço.
Downloads
References
ARISTOTLE. Physics. In: The Basic Works of Aristotle. Ed. Richard McKeon. New York: Random, 1941.
BLACK, Max. "Achilles and the Tortoise". Analysis 11.5 (1951): 91-101. DOI: https://doi.org/10.1093/analys/11.5.91
CHIHARA, Charles. "On the Possibility of Completing an Infinite Process". Philosophical Review (1965): 74-87. DOI: https://doi.org/10.2307/2183531
GROARKE, Leo. "Zeno's Dichotoni.Y: Undermining the Modem Response". Auslegung 9 (1982): õl-75. DOI: https://doi.org/10.17161/AJP.1808.9022
HEATH, Thomas L. A History of àreek Mathematics. Oxford: Clarendon, 1921.
HINTON, J. M. and MARTIN, c. B. "Achilles and the Tortoise'. Analysis 14.3 (1953): 56:68. DOI: https://doi.org/10.1093/analys/14.3.56
LEAR, Jonathan. "A Note on Zeno's Arrow". Phronesis 26 (1981): 91-104. DOI: https://doi.org/10.1163/156852881X00196
PLATO. Parmenides. ln: The Collected Dialogues of Plato, including the Letters. Ed. Edith Hamilton and Huntington Cairns. New York: Pantheon, 1961. DOI: https://doi.org/10.1515/9781400835867
SMITH, Joseph Wayne. Reason, Science and Paradox: Against Received Opinion in Science and Philosophy. London: Croom Helm, 1986, Ch. 5.
TANNERY, Paul. "Le concept Scientifique de Continu: Zénon d'Elée et George Cantor". Revue Philosophique de la France et de l'Étranger 20 (1885): 385-410.
VLASTOS, Gregory. "Zeno of Elea''. EncycliJpedia of Philosophy. Ed. Paul Edwards. New York: Macmillan, 1967, V. 8, 369-379.
--. "Zeno's Race Course'. Studies in Presocmtic Philosofy. Ed. R. E. Allen and D. !. Furley. London: Routledge, 1974a, v. 2, 201-220.
--. "A Note on Zeno's Arrow". Studies in Presocmtic Philosophy. v. 2. Ed. Allen, R. E., and D. J. Furley. London: Routledge, 1974b, 184-200. Von FRITZ, Kurt. "The Discovery of lncommensurability by Hippasus of Metapontum". Annals of Mathematics 46 (1945): 242-264. DOI: https://doi.org/10.2307/1969021
WHITEHEAD, A N. Process and Reality. Cambridge: Cambridge UP. 1929, 101-1 08.
Works consulted
BENDEGEM, Jean Paul van. "Zeno's Paradoxes and the Tile Argument'. Philosophy of Science 54 (1987): 295-302. DOI: https://doi.org/10.1086/289379
BOOTH, N. B. "Zeno's Paradoxes". Journal of Hellenic Studies 77 (1957): 187-201. DOI: https://doi.org/10.2307/629357
BOUWSMA, O. K. Toward a New Sensibility. Lincoln: U. of Nebraska P, 1982, 213-240.
BROCHARD, Victor. Études de Philosophie Ancienne et de Philosophie Moderne. Paris, 1912, 7-9.
CAJORI, F. "The History of Zeno's Arguments on Motion". American Mathematical Monthly 22 (1915): 1-6, 39-47, 77-82, 109-115, 143-149, 179-186, 253-258, 292-297. DOI: https://doi.org/10.1080/00029890.1915.11998110
DEJNOZKA, Jan. "Zeno's Paradoxes and the Cosmological Argument". Philosophy o! Religion 25 (1989): 65-81. DOI: https://doi.org/10.1007/BF00136967
GALE, Richard M., ed. The Philosophy ofTime. New York: Anchor, 1968, 387-494. DOI: https://doi.org/10.1007/978-1-349-15243-8_5
GRUNBAUM, A "Messrs. Black and Taylor on Temporal Paradoxes'. Analysis 12.6 (1952): 144-148. DOI: https://doi.org/10.1093/analys/12.6.144
--. "Modem Science and the Refutation of the Paradoxes of Zeno". Scientific Monthly 81 .5 (1955): 234-239.
--. Modern Science and Zeno's Paradoxes. Middletown, CN: Wesleyan. UP, 1967.
HAGER, Paul. "Russell and Zeno's Arrow Paradox". Russell 7 (1987): 3-10. DOI: https://doi.org/10.15173/russell.v7i1.1691
KNORR, Wilbur R. "Zeno's Paradoxes Still in Motion". Ancient Philosophy 3 (1983): 55-66. DOI: https://doi.org/10.5840/ancientphil19833119
KING, H. R. "Aristotle and the Paradoxes of Zeno". Journal of Philosophy 21 (1949): 657-õlO. DOI: https://doi.org/10.2307/2019365
KRETZMAN, Norman. "Aristotle on the Instant of Change". Aristotelian Society Supplement 50 (1976): 91-114.
LEE, Harold N. "Are Zeno's Paradoxes Based on a Mistake?" Mind ns 74 (1965): 563-70. DOI: https://doi.org/10.1093/mind/LXXIV.296.563
LEE, H. P. D. Zeno of Elea: A text with Translation and Notes. Cambridge UP, 1936.
McKIE, John R. "The Persuasiveness of Zeno's Paradoxes". Philosophy and Phenomenological Research 47 (1987): 631 639. DOI: https://doi.org/10.2307/2107232
MILL, J. S. System ot Logic. 5th. ed. 389-390.
OWEN, G. E. L. "Zeno and the Mathematicians". Proceedings of the Aristotelian Society 58 (1957-58): 199-222. DOI: https://doi.org/10.1093/aristotelian/58.1.199
ROSS, W. D. Aristotle's Physics. Oxford, 1936, 81-82. DOI: https://doi.org/10.1093/actrade/9780198141099.book.1
ROSSETTI, Livio. "The Rhetoric of Zeno's Paradox". Philosophy and Rhetoric 21 (1988): 145-152.
RUSSELL. Bertrand. Our Knowledge of the Externai World. New York, Norton, 1929. Lectures V and VII.
SALMON, Wesley. Space, Time and Motion. Encino, CA: Dickenson. 1975. --. ed. Zeno's Paradoxes. lndianapolis: Bobbs, 1970.
SHERRY, David M. "Zeno's Metrical Paradox Revisited". Philosophy of Science 55 (1988): 58-73. DOI: https://doi.org/10.1086/289416
SORABJI, Richard. "Aristotle on the Instant of Change". Aristotelian Society Supplement 50 (1976): 69- 89. DOI: https://doi.org/10.1093/aristoteliansupp/50.1.69
SZÉKELY, Laszlô. "Motion and the Dialectical View of the World". Studies in Soviet Thought 39 (1990): 241-255. DOI: https://doi.org/10.1007/BF00838038
TANNERY. Paul. La Géometrie Grecque. Paris: Gauthier-Villars, 1877, 124-125.
--. Pour l'Histoire de la Science Hellene. Paris: Félix Alcan, 1887, 247-261.
TAYLOR, Richard. "Mr. Wisdom on Temporal Paradoxes". Analysis 14.4 (1952): 15-17. DOI: https://doi.org/10.1093/analys/13.1.15
TE HENNEPE, Eugene. 'Language Reform and Philosophical Materialism: Another Round With Zeno'. Analysis 23 [Suppl.] (1963): 43-49. DOI: https://doi.org/10.1093/analys/23.Suppl-1.43
THOMSON, James. "Infinity in Mathematics and Logic". Encyclopedia of Philosophy. Ed. Paul Edwards. London: Macmillan, 1967, v. 4, 183-190.
USHENKO, A ''Zeno's Paradoxes". Mind 55 (1946): 151-165. DOI: https://doi.org/10.1093/mind/LV.219.151
WHITE, Michael J. "The Spatial Arrow Paradox". Pacific Philosophical Ouarterly 68 (1987): 71-77. DOI: https://doi.org/10.1111/j.1468-0114.1987.tb00285.x
WHITROW, J. G. The Natural Philosophy ofTime. London, 1961. 135-137.
WISDOM, J. O. "Achilles on a Physical Racecourse". Analysis 12.6 (1951): 67-72. DOI: https://doi.org/10.1093/analys/12.3.67
ZART, Paulus Johannes. About Time: A Philosophical Inquiry into the Origin and Nature of Time. Oxford: North-Holland, 1976. Ch. XI.
Downloads
Published
How to Cite
Issue
Section
License
Copyright
The submission of originals to Revista Veritas implies the transfer by the authors of the right for publication. Authors retain copyright and grant the journal right of first publication. If the authors wish to include the same data into another publication, they must cite Revista Veritas as the site of original publication.
Creative Commons License
Except where otherwise specified, material published in this journal is licensed under a Creative Commons Attribution 4.0 International license, which allows unrestricted use, distribution and reproduction in any medium, provided the original publication is correctly cited. Copyright: © 2006-2020 EDIPUCRS</p