A Relation of Zeno of Elea's Argument in 29 B 3 DK to the Contemporary Semantics and Plato's peritrope

The problem of this study consist in the fact that the argument from fragment 29 B 3 DK does not mention the continuity of the being analyzed by Zeno, whereas the standard interpretation of Zeno's arguments deals exclusively with the continual being. This incongruity impelled the author to enter into a discussion about interpretations of 29 B 3 DK and to suggest a new interpretation of it, which is different from the standard one. The material for this study is fragment 29 B 3 DK and its modern interpretations. To justify the validity of the new interpretation of 29 B 3 DK, the author uses a non-standard historico-philosophical methodology, which he developed in his previous works. This methodology allows using modern technical tools and discussions to identify a specific type of meaning of philosophical texts. This type of meaning is different from what the authors of these texts meant "in fact". To reveal this meaning means to indicate discussions, including contemporary ones, in which the argument from the text in question can be embedded. The study consists of five stages. At the first stage, the author indicates that, from the point of view of contemporary scholars, 29 B 3 DK generates a banal and benign regress of points, which dichotomously divide a segment. Since the regress is benign, Zeno's presumable thesis (that the plural being is impossible) remains unproved. At the second stage, the author offers an interpretation of 29 B 3 DK which is more charitable to Zeno than the interpretation of modern scholars. In accordance with this interpretation, what is generated here is a vicious regress of constituents of any complex object. Each subsequent constituent unites all the previous constituents into a complex object. So the proof of Zeno's thesis is quite valid. At the third stage, the author points to Bo Meinertsen's paper, which offers a way to block regresses of the same type as the type of regress from 29 B 3 DK in the author's interpretation, and shows that Meinertsen's approach is very debatable. At the fourth stage, the author indicates some problems of the modern semantics for propositional attitudes (Kent Bach) and of the semantics for the language of thought (Margaret Atherton and Robert Schwartz). These problems can be set forth using modified premises from the author's interpretation of 29 B 3 DK. At the fifth stage, the author shows that a variant argument from 29 B 3 DK makes it possible to present Plato's attack on Protagoras' homo mensura thesis in Theaetetus 170c-171c in a more favorable light than modern interpreters (Timothy D.J. Chappell; Miles Burnyeat; Ugo Zilioli) are willing to concede. The conclusion is drawn that 29 B 3 DK has a greater philosophical significance than researchers have recognized until now.

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