%0 Journal Article
%T Resolving Zeno’s Paradoxes Based on the Theory of the “Linear Analytic Summation” and Evaluation of Evolution of Responsesa
%J History of Philasophy
%I Iranian Society of History of Philosophy
%Z 2008-9589
%A Reza Shakeri
%A Ali Abedi Shahroodi
%D 1401
%\ 1401/05/03
%V 4
%N 12
%P 17-38
%! Resolving Zeno’s Paradoxes Based on the Theory of the “Linear Analytic Summation” and Evaluation of Evolution of Responsesa
%K Motion
%K Zeno’s paradoxes
%K theory of linear analytic summation
%K Aristotle
%K Kant
%K modern mathematics
%X Zeno challenged the problem of motion following his master Parmenides and presented his criticisms of the theory of motion based on four arguments that in fact introduced the paradoxes of this theory. These paradoxes, which contradict an evident problem (motion), provoked some reactions. This paper initially refers to two of Zeno’s paradoxes and then presents the responses provided by some thinkers of different periods. In his response to Zeno’s paradoxes, Aristotle separated the actual and potential runs of motion and, following a mathematical approach, resorted to the concept of infinitely small sizes. Kant has also referred to this problem in his antinomies. Secondly, the authors explain the theory of linear analytic summation, which consists of two elements: 1) The distance between two points of transfer can be divided infinitely; however, the absolute value of the subsequent distance is always smaller than the absolute value of the previous distance; 2) since the infinitude of the division is of an analytic rather than a synthetic nature, the summation limit of these distances will be equal to the initial distance. Based on this theory, as motion is not free of direction and continuous limits, an integral limit of distance is traversed at each moment, and the analytic, successive, and infinite limits of distance are determined. The final section of this paper is intended to evaluate the responses given to the paradoxes.
%U http://rimag.ir/fa/Article/36807