Zeno of Elea
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Zeno of Elea(zē`nō, ē`lēə), c.490–c.430 B.C., Greek philosopher of the Eleatic schoolEleatic school
, Greek pre-Socratic philosophical school at Elea, a Greek colony in Lucania, Italy. The group was founded in the early 5th cent. B.C. by Parmenides, its greatest thinker. He denied the reality of change on the ground that things either exist or do not.
..... Click the link for more information. . He undertook to support in his only known work, fragments of which are extant, the doctrine of ParmenidesParmenides
, b. c.515 B.C., Greek philosopher of Elea, leading figure of the Eleatic school. Parmenides' great contribution to philosophy was the method of reasoned proof for assertions.
..... Click the link for more information. by demonstrating that motion and multiplicity are logically impossible. The substance of his argument against multiplicity was that a whole must be composed of ultimate indivisible units, or it must be divisible ad infinitum. If the whole is divisible ad infinitum, there is a contradiction involved in the assumption that an infinite number of parts can be added up to a finite total. The essence of his argument against motion was that a moving body can never come to the end of a line, as it must first cover half the line, then half the remainder, and so on ad infinitum. The thrust of these arguments was to demonstrate, through logical reasoning, the error of common-sense notions of time and space. According to Aristotle, Zeno was the first to employ the dialectical method. Contemporary philosophers and mathematicians have taken renewed interest in Zeno's problems.
See A. Grunbaum, Modern Science and Zeno's Paradoxes (1967).
Zeno of Elea
Born circa 490 B.C.; died circa 430 B.C. in Elea, southern Italy. Ancient Greek philosopher.
Zeno developed Parmenides’ teachings on the One, denying the knowability of sensuous existence and the plurality of things and their motion and seeking to prove the unthinkableness of being in general. Aristotle considered Zeno the founder of dialectics since the latter at the same time concerned himself with the detection of contradictions and, to all appearances, apparently believed that truth is made apparent by argument or the interpretation of conflicting opinions (there are indications that Zeno presented his teachings in dialogue form). He is known for his famous aporias (paradoxes).
Zeno’s arguments led to the crisis of ancient Greek mathematics which was overcome only by the atomistic theory of Democritus. The basic idea of Zeno’s aporias is, as with Parmenides, that discontinuity, plurality, and motion characterize a picture of the world as it is perceived by the senses but that this picture is unauthentic. The true picture of the world is achieved through thought. The attempt to conceptualize plurality leads mathematics into contradiction. Consequently, plurality is unthinkable. The same is to be said of the thinkability of motion. Zeno’s dialectic is founded on the postulate of the inadmissibility of contradictions in reliable thought; the appearance of contradictions arising from the assumption of the thinkableness of plurality, discontinuity, and motion is viewed as proof of the falsity of that assumption and at the same time as a demonstration of the true nature of the contrary thesis of the unity, continuity, and immobility of existence that is thinkable (and not perceptible by the senses).
Hegel criticized Zeno’s arguments from the position of idealistic dialectics (see Lektsii po istorii filosofii, vol. 9, Leningrad, 1932, pp. 231–45). From the standpoint of materialist dialectics, a critique is given by V. I. Lenin (see Poln. sobr. soch., 5th ed., vol. 29, pp. 230–33). The aporias of Zeno constituted an important stage in the development of ancient dialectics and exerted a considerable influence on the development of philosophy in the modern age as well, particularly on the philosophical foundations of mathematics.
FRAGMENTSIn H. Diels, Die Fragmente der Vorsokratiker, 9th ed., vol. 1. Berlin, 1959.
In A. Makovel’skii, Dosokratiki, part 2. Kazan, 1915.
REFERENCESSvatkovskii, V. P. “Paradoks Zenona o letiashchei strele.” Zhurnal Ministerstva narodnogo prosveshcheniia, 1888, no. 4, section 5, pp. 203–39.
Khersonskii, N. Kh. “U istokov teorii poznaniia (Po povodu argumentov Zenona protiv dvizheniia).” Ibid., 1911, no. 8.
Bogomolov, S. A. Aktual’naia beskonechnost’ (Zenon Eleiskii, Is. N’iuton, G. Kantor). Leningrad-Moscow, 1934.
Gokieli, L. P.Oprirode logicheskogo. Tbilisi, 1958. Pages 32–58.
Asmus, V. F. Istoriia antichnoi filosofii. Moscow, 1965. Pages 40–45.
Zeno of Elea: A Text, With Translation and Notes by H. D. P. Lee. Cambridge, 1936.
Fränkel, H. Wege und Formen frtihgriechischen Denkens. Munich, 1955.
Grünbaum, A. Modern Science and Zeno’s Paradoxes. London .
A. F. LOSEV