ANCIENT GREEK MATHEMATICO-PHYSICAL PARADOX

  • Glenn W. Erickson Universidade Federal de Santa Maria, UFSM.
  • John A. Fossa Universidade Federal do Rio Grande do Norte, UFRN

Resumo

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.

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Referências

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.

CHIHARA, Charles. "On the Possibility of Completing an Infinite Process". Philosophical Review (1965): 74-87.

GROARKE, Leo. "Zeno's Dichotoni.Y: Undermining the Modem Response". Auslegung 9 (1982): õl-75.

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.

LEAR, Jonathan. "A Note on Zeno's Arrow". Phronesis 26 (1981): 91-104.

PLATO. Parmenides. ln: The Collected Dialogues of Plato, including the Letters. Ed. Edith Hamilton and Huntington Cairns. New York: Pantheon, 1961.

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.

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.

BOOTH, N. B. "Zeno's Paradoxes". Journal of Hellenic Studies 77 (1957): 187-201.

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.

DEJNOZKA, Jan. "Zeno's Paradoxes and the Cosmological Argument". Philosophy o! Religion 25 (1989): 65-81.

GALE, Richard M., ed. The Philosophy ofTime. New York: Anchor, 1968, 387-494.

GRUNBAUM, A "Messrs. Black and Taylor on Temporal Paradoxes'. Analysis 12.6 (1952): 144-148.

--. "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.

KNORR, Wilbur R. "Zeno's Paradoxes Still in Motion". Ancient Philosophy 3 (1983): 55-66.

KING, H. R. "Aristotle and the Paradoxes of Zeno". Journal of Philosophy 21 (1949): 657-õlO.

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.

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.

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.

ROSS, W. D. Aristotle's Physics. Oxford, 1936, 81-82.

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.

SORABJI, Richard. "Aristotle on the Instant of Change". Aristotelian Society Supplement 50 (1976): 69- 89.

SZÉKELY, Laszlô. "Motion and the Dialectical View of the World". Studies in Soviet Thought 39 (1990): 241-255.

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.

TE HENNEPE, Eugene. 'Language Reform and Philosophical Materialism: Another Round With Zeno'. Analysis 23 [Suppl.] (1963): 43-49.

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.

WHITE, Michael J. "The Spatial Arrow Paradox". Pacific Philosophical Ouarterly 68 (1987): 71-77.

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.

ZART, Paulus Johannes. About Time: A Philosophical Inquiry into the Origin and Nature of Time. Oxford: North-Holland, 1976. Ch. XI.

Publicado
1996-12-31
Como Citar
Erickson, G. W., & Fossa, J. A. (1996). ANCIENT GREEK MATHEMATICO-PHYSICAL PARADOX. Veritas (Porto Alegre), 41(164), 681-690. https://doi.org/10.15448/1984-6746.1996.164.35918
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