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Bu makale, Laks & Most’un 2016 tarihli Erken Dönem Yunan Filozofları derlemesi ışığında Elealı Zenon’un kişiliğine, felsefesine ve özellikle de ünlü “paradokslarına” yönelik yaygın yorumu anlattıktan sonra, bu yorumdaki sorunlara işaret etmek ve bir çözüm önerisi sunmak amacını taşımaktadır. Yaygın yorum Elealı Zenon’u paradokslarına, paradokslarını da argümantatif içeriklerine indirgemekte, ancak bu paradoksların birliğini, bütünsel işlevini ve sayısını açıklamakta zorlanmaktadır. Makale ilk bölümde yaygın yoruma göre Zenon’un ve paradokslarının ana özelliklerini sıraladıktan sonra, ikinci bölümde felsefe, felsefe tarihçiliği ve felsefe eğitimi alanlarında bu yorumdan kaynaklanan sorunlara işaretmekte ve üçüncü bölümde Laks & Most’un edisyonunda özellikle Platon ve Aristoteles geleneğindeki aktarımlara başvurarak bu sorunları çözecek alternatif bir yorum önermeye çalışmaktadır. Bu aktarımlarda Zenon’un pratik yaşamı ve özellikle diyalektikçiliği vurgulanmıştır. Zenon’un paradoksları diyalektik argümanlar olarak yorumlandığında, yalnızca bir öğretinin çürütülmesi veya desteklenmesi için araçsal argümanlar olarak görülmek yerine, okurun veya öğrencinin zorunlu olarak akıl yetisinin farklı şekillerde çalıştırılması amacını taşıyan pratikler olabilecekleri fark edilebilmektedir. Bu alternatif yorum, hem felsefe tarihçiliği açısından Zenon’u eristik, sofistik, retorik veya kuşkucu düşünürlerden daha açık şekilde ayrıştırabilmekte, hem felsefe eğitimi açısından paradoksların amaçsız bilmecelerden öte, öğrencinin kendi akıl yetisi ile karşı karşıya gelmesini talep eden argümanlar olduğunu ve felsefenin gerçeğin çıkarsız şekilde araştırılmasından ayrılamayacağını düşündürmektedir. The aim of this paper is to sketch the standard interpretation of the Eleatic philosopher Zeno’s personality, his philosophy, and especially his famous “paradoxes”, in light of Laks & Most’ 2016 edition of Early Greek Philosophers, in order to point out the shortcomings of this interpretation, and to suggest a solution. This standard interpretation of Zeno reduces his philosophy to his paradoxes, and his paradoxes to their argumentative content, while failing to sufficiently account for their unity, their overall purpose, and their number. These problems give rise to further difficulties relating to both the historiography of Ancient Philosophy and its pedagogy. After outlining this standard interpretation of Zeno’s philosophy and its consequent problems, the third part of the paper appeals to accounts issuing especially from the PlatonicAristotelian tradition in Laks & Most’s edition in order to construct an alternative interpretation accommodating the aforementioned problems. Thanks to the emphasis in these accounts on Zeno’s practical life and his identity as a dialectician, a reading of Zeno’s paradoxes as dialectical arguments enables us to consider them not merely as arguments instrumental in upholding or refuting a doctrine, but as practices intended to summon the rational capacity of the reader or student. This alternative interpretation not only differentiates Zeno more clearly from eristic, sophistic, rhetoric or skeptic thinkers, it also suggests, in terms of the teaching of philosophy, that these paradoxes are not gratuitous riddles, but arguments demanding the student’s rational participation, and that philosophy cannot be construed without reference to the uninterested pursuit of truth. more...

Zeno of Elea about 489 BC , is the favorite disciple of Parmenides about 514 BC . Zeno devotes himself in refuting the views of the opponents of Parmenides. Arguments against the possibility of motion, is first found in The Dialectic of Zeno. To examine the reality of motion, it is necessary to make a new look towards Zeno's reaction on motion. The ancient Greek philosophers are confused to think about space, time and motion. Zeno is the first who deeply thinks about these. His arguments, generally known as his paradoxes, seem to show that motion is simply an illusion which is not possible in any circumstances. Arguments of Zeno are based upon the argument which may be called the antinomy, i.e., a proof that since two contradictory propositions equally follows from a given assumption that must be false of infinite divisibility. But in our times, we know that the fallacies of his proofs, the confusion of the infinite divisibility of space and time with infinite dividedness, he does not notice himself. He argues from the geometrical line to the actual line. Indeed, a geometrical point has no magnitude and a geometrical line is infinitely divisible. But in everyday life the movement between any distance, is not infinitely divisible, nor any observed time which we live through as short or long, is infinitely divisible into moments. Zeno confused an analytic proposition with a synthetic proposition. An analytic proposition does not require any observation to confirm or disconfirm its truth while a synthetic proposition can be true if it corresponds to an actual state of affairs. A distance or time is infinitely divisible, is only an analytic proposition but actual distance traversed in same observed time is not infinitely divisible. Without motion our usual life would be stopped. Sun, moon, stars, planets and other stars cannot move without motion. If motion is not accepted then astronomy would be in vein. Even we cannot speak and write without the movement of our vocabulary organs and that of fingers respectively. So, the existence of motion has to accept in usual life, in scientific research and in all other aspects of life. Dr. Sudipta Chattopadhyay "An Analysis of Zeno's View Regarding Motion" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-3 | Issue-2 , February 2019, URL: https://www.ijtsrd.com/papers/ijtsrd20256.pdf more...

The well-known Zeno's paradox about Achilles and the Tortoise is considered in the article in comparison to the analysis of a complex of medieval miniatures on which battle of the Knight with a Snail is represented. These images executed in a genre of Gothic grotesque were widespread in the margins of the Western European manuscripts of various contents especially at the end of the 13th – the first quarter of the 14th centuries. In our opinion, hopelessness of both agons (the Knight and the Snail, Achilles and the Tortoise) is a good illustration of some strategies of the relation of the philosopher to the truth more...

El objetivo de este trabajo es discutir la interpretación tradicional según la cual los razonamientos de Zenón de Elea en contra de la multiplicidad constituyen una defensa de la tesis monista. Intentaré demostrar que las objeciones zenonianas a la multiplicidad suponen una crítica previa a la existencia de "lo uno". Por este motivo, Zenón no es monista ni pluralista, sino, más bien, un crítico de las perspectivas metafísicas que consideran al ser en términos numéricos, i. e. como uno o como múltiple. Para ello me concentraré en el análisis de la interpretación que Aristóteles desarrolla sobre la filosofía de Zenón, considerando algunos pasajes de Física, Refutaciones sofísticas y, fundamentalmente, Metafísica, III. 4. 1001b7-13 (DK 29 A 21). También incluiré algunos testimonios del comentario a la Física de Simplicio, en los que se discuten las interpretaciones de Eudemo de Rodas y Alejandro de Afrodisia, que ratifican el punto de vista aristotélico sobre la filosofía de Zenón (In Ph. 99.7-18, DK 29 A 21; 138. 3-6, DK 29 A 22). The aim of this paper is to discuss the traditional interpretation according to which the arguments of Zeno of Elea against multiplicity constitute a defense of monism. I will try to prove that Zeno’s objections on plurality suppose a previous critique to the existence of the one. Therefore Zeno is neither a monist nor a pluralist but a philosopher who criticizes metaphysical theories that consider being in numerical terms, i. e. as many or as one. I will focus on the analysis of the interpretation of Zeno's philosophy developed by Aristotle. I will consider some passages from Physics, Sophistical Refutations and mainly Metaphysics III. 4. 1001b7-13 (DK 29 A 21). I will also include some testimonies from Simplicius’ commentary on Aristotle’s Physics, where he discusses the interpretations of Eudemus of Rhodes and Alexander of Aphrodisias that support the Aristotelian point of view on Zeno’s philosophy (In Ph. 99.7-18, DK 29 A 21; 138. 3-6, DK 29 A 22). Fil: Gardella, Mariana. Universidad de Buenos Aires; Argentina. Universidad Nacional de San Martín; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina more...

This works aims to propose an edition, a translation into French and a commentary of the pseudo-aristotelian treatise Περὶ ἀτόμων γραμμῶν. The edition is based on D. Harlfinger's 1971 manuscripts review known to bear the treatise. Most of the time, in the edition the readings of the manuscripts were favoured to the editors' and commentators' emendations. The translation is as close as possible to the Greek text despite its very elliptical wording and its occasional defective syntax. Initialy, the commentary tries to set the background to this text (dating hypothesis in spite of attributing it to a precise and definite author) and to define the links which exist between the text and, on the one hand, the other Aristotelian treatises and, on the other hand, the philosophical works that are refuted. The commentary then helps to justify the editorial choices and translations in comparison to existing variants and corrections suggested by previous editors and commentators.The aim of the Περὶ ἀτόμων γραμμῶν is to prove the impossibility of indivisible lines. It belongs to a more general confutation of atomism in the Aristotelian school. Aristotle previously refuted the existence of atoms in the physical field, setting up a theory of continuity. The author of this treatise takes up the issue confronting it to geometrical objects. He proves impossible the indivisibility of a line or the fact that a line may be composed of indivisible elements. After having defined the point, he proves that a line can neither be composed of points. To conclude, the author draws the distinction between a limit and a joint.; Ce travail consiste en une édition, une traduction française et un commentaire du traité pseudo-aristotélicien Περὶ ἀτόμων γραμμῶν. L'édition est faite à partir de la recension effectuée par D. Harlfinger en 1971 de tous les manuscrits connus contenant ce traité. Dans l'édition, le plus souvent, la lecture des manuscrits a été préférée aux éventuelles corrections des éditeurs et commentateurs. La traduction se veut la plus proche possible du texte grec nonobstant son caractère très elliptique et, parfois, syntaxiquement fautif. Le commentaire s'attache en premier lieu à contextualiser ce texte (hypothèses de datation à défaut de pouvoir l'attribuer indiscutablement à tel ou tel auteur) et à déterminer les liens qu'il y a entre lui et, d'une part, les autres textes du corpus aristotélicien et, d'autre part, les traités philosophiques qu'il réfute. En outre, le commentaire permet de justifier les choix éditoriaux et de traduction en comparant la leçon retenue aux variantes existantes et aux corrections apportées par les éditeurs et commentateurs successifs du traité. L'objectif du Περὶ ἀτόμων γραμμῶν est de démontrer l'impossible existence de lignes indivisibles. Il prend place dans une réfutation générale de l'atomisme dans l'école aristotélicienne. Aristote avait réfuté l'existence des atomes dans le domaine physique, y opposant une théorie continuiste, l'auteur de ce traité reprend ce problème en l'appliquant aux objets géométriques. Il démontre l'impossibilité qu'une ligne soit indivisible ou composée d'indivisibles, puis, après avoir défini le point, l’impossibilité qu'une ligne en soit composée. Enfin, l'auteur établit une distinction entre limite et articulation. more...

The reductio ad absurdum has been elected by Zeno as the only method permitting to descry the true reality, invisible both to the senses and to the common way of thinking. Showing some continuity with the previous philosophers, not only in the search for a procedure in order to speculation to advance, but also on the same route departing from what is nearer, more acquainted and particular (visible) toward what is less acquainted, more distant and universal (invisible), to say it with aristothelic words, Zeno made use of aporetic arguments as the only possible way to catch a glimpse of the ‘domain of Being’. This, in fact, is invisible not only to our senses, but also to our ordinary reasoning. Therefore, just the ‘way of not-being’, the only one that could be walked after Parmenides, as Wolff says, allows us to have an insight of what is ‘really invisible’. So invisible that it is unreachable also to thought., A reductio ad absurdum foi elevada por Zenão de Eléia a único método que permitiria vislumbrar a verdadeira realidade, invisível tanto aos sentidos quanto à maneira de pensar comum. Mostrando uma certa continuidade com os filósofos anteriores, não só na busca de um procedimento para que a especulação pudesse avançar, como também na mesma rota de afastamento daquilo que é mais próximo, conhecido e particular (visível) em direção àquilo que é menos conhecido, distante e universal (invisível), para dizê-lo em termos aristotélicos, Zenão utilizou-se de argumentos aporéticos como único caminho possível para poder entrever o ‘reino do Ser’. Esse, com efeito, é invisível não somente aos nossos sentidos, como também ao nosso raciocínio ordinário. Eis que somente a ‘via do não-ser’, a única que poderia ser trilhada após Parménides, como diz Wolff, nos permite ter uma ideia, por quanto vaga, daquilo que é ‘verdadeiramente invisível’. Tão invisível ao ponto de ser inalcançável até mesmo pelo pensamento. more...

The meager second-hand reports on the life of Zeno of Elea and his book with the famous paradoxes is rather seen as testimonies of his reception or criticism, coming chiefly from Plato, Aristotle, Eudemus and Simplicius. The last author in his extensive commentary to Aristotle’s Physics has preserved several citations from Zeno’s work that still are subject of various interpretations and controversies. While Zeno’s paradoxes are one the most often cited of themes in all Pre-Socratics, there is still no recent and more exhaustive edition of ancient testimonies on this challenging thinker. Most doubts and controversies are due to the deficiency and divergence of the source data, the difficulties of reading various passages in the texts that tend to be frequently complicated by the scholars. In his Parmenides, Plato mentions Zeno’s arguments against plurality rather selectively and one-sidedly, citing only one of them and totally disregarding other paradoxes. On the other hand, Aristotle in his Physics, discusses somewhat differently and more extensively the context of Zeno’s aporias concerning the one – many, infinite divisibility, motion, place and sound. The same issue is taken up by Simplicius in his commentary. It remains highly debatable whether Zeno, in opposition to Parmenides, formulated also his arguments against the one as an indivisible point, which Aristotle and Eudemus seem to suggest. That is why Zeno was called double-tongued, since he was regarded as the discoverer of dialectic understood as a method of constructing argument on both sides, i.e., posing only aporetic issues without trying to resolve them. According to Aristotle, Zeno’s arguments were still an object of heated discussions. He viewed Zeno’s aporias as paralogisms, i.e., arguments that presuppose fallacious premises and conclusions, suggesting also its own solutions. Nevertheless, in modern times, though in quite different problematic context, Zeno’s paradoxes attracted most eminent philosophers and mathematicians, who constructed highly sophisticated theoretical models for the purpose of analyzing and solving the problems posed by Zeno. While theoretically Zeno of Elea still remains an important point of reference here, these solutions significantly exceed the historical reading of his arguments. After a very general exegetical introduction, we put forward a new arrangement and translation of the major testimonies on Zeno of Elea. The few passages that are generally regarded as fragmenta verbatim are also cited in the original. The source material is presented in a reconstructive order that is somewhat different from the previous editions of Zeno. Our aim is to capture the specific problematic context of the ancient authors who refer and question Zeno’s arguments, without isolating and break up theses texts. The particular passages have been provided with thematic headings. more...

La cesura referencial entre el mundo descrito por las matemáticas y el mundo de la experiencia corriente es conocida, al menos, desde las aporías de Zenón. La imagen del mundo de la cultura contemporánea está fuertemente determinada por el conocimiento científico. Las teorías científicas incluyen en su explanans un lenguaje matemático cada vez más sofisticado. ¿Puede este lenguaje, aplicado a la descripción y explicación de hechos del mundo, ser traducido al lenguaje natural sin pérdida relevante de significado?., The referential caesura between the world described by mathematics and the world of ordinary experience is known at least since Zeno’s aporias. The image of the world of contemporary culture is strongly influenced by scientific knowledge. Scientific theories include in its explanans a mathematical language increasingly sophisticated. Can this language applied to the description and explanation of facts in the world be translated into natural language without significant loss of meaning?. more...

Meršić izvorište Zenonova paradoksa ‘Ahilej’ vidi u dvosmislenostima pojma beskonačnosti.Te se dvosmislenosti prema njem (i tradiciji koju započinje Gregorius od St. Vincenta) razrješuju pojmom konvergentnoga geometrijskoga niza. Pritom Meršić daje opću ontološku teoriju s prednošću konačnoga pred beskonačnim, te razvija modalno tumačenje diferencijalnoga računa polazeći od Newtonova pojma fluksije., Meršić sees the origin of Zeno’s paradox ‘Achilles’ in the ambiguities of the concept of the infinity. According to him (and to the tradition started by Gregory St. Vincent), those ambiguities are resolved by the concept of convergent geometric series. In this connection, Meršić proposes a general ontological theory with the priority of the finite over the infinite, and, proceeding from Newton’s concept of fluxion, he develops a modal interpretation of differential calculus. more...

Meršić izvorište Zenonova paradoksa ‘Ahilej’ vidi u dvosmislenostima pojma beskonačnosti.Te se dvosmislenosti prema njem (i tradiciji koju započinje Gregorius od St. Vincenta) razrješuju pojmom konvergentnoga geometrijskoga niza. Pritom Meršić daje opću ontološku teoriju s prednošću konačnoga pred beskonačnim, te razvija modalno tumačenje diferencijalnoga računa polazeći od Newtonova pojma fluksije., Meršić sees the origin of Zeno’s paradox ‘Achilles’ in the ambiguities of the concept of the infinity. According to him (and to the tradition started by Gregory St. Vincent), those ambiguities are resolved by the concept of convergent geometric series. In this connection, Meršić proposes a general ontological theory with the priority of the finite over the infinite, and, proceeding from Newton’s concept of fluxion, he develops a modal interpretation of differential calculus. more...

Se le atribuyen a Zenón de Elea [490 a. C.l, cuatro argumentos sutiles y profundos, conocidos como las cuatro aporías de Zenón sobre el movimiento, que lo convierten en el iniciador de la filosofía del infinito. Estos cuatro argumentos han merecido la atención de filósofos y matemáticos durante más de dos mil años y siguen siendo fuente de preguntas y reflexiones sobre la naturaleza del tiempo y el espacio. more...

BIOGRAPHICAL ESSAY Zeno of Elea (born ca. 490 BC) was a Greek philosopher and logician. A member of the Eleatic school of philosophy, he was famous throughout antiquity for the [...]