Zeno's Paradoxes. A Cardinal Problem 1. On Zenonian Plurality (original) (raw)
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Zeno's Paradoxes. A Cardinal Problem. I. On Zenonian Plurality
The Baltic International Yearbook of Cognition, Logic and Communication, 2006
It will be shown in this contribution that the Received View on Zeno’s paradoxical arguments is untenable. Upon a close analysis of the Greek sources, it is possible to do justice to Simplicius’s widely neglected testimony, where he states: "In his book, in which many arguments are put forward, he shows in each that a man who says that there is a plurality is stating something contradictory". Thus we will demonstrate that an underlying structure common to both the Paradoxes of Plurality (PP) and the Paradoxes of Motion (PM) shores up all Zeno's arguments. This structure bears on a correct — Zenonian — interpretation of the concept of “division through and through”, by taking the philosophical legacy on the "Being-Now" of his master Parmenides properly into account.
Zeno's Paradoxes: A Cardinal Problem
2001
Du présent, rien d'autre que du présent Sartre, La nausée INTRODUCTION.-It will be shown in this contribution that the Received View on Zeno's paradoxical arguments is untenable. Upon a close analysis of the Greek sources 1 , it is possible to do justice to Simplicius's widely neglected testimony, where he states: In his book, in which many arguments are put forward, he shows in each that a man who says that there is a plurality is stating something contradictory [DK 29B 2]. Thus we will demonstrate that an underlying structure common to both the Paradoxes of Plurality (PP) and the Paradoxes of Motion (PM) shores up all his arguments. 2 This structure bears on a correct-Zenonian-interpretation of the concept of "division through and through", which takes into account the often misunderstood Parmenidean legacy, summed up concisely in the deictical dictum τo ' o ν ' στ ι : "the Being-Now is". 3 The feature, generally overlooked but a key to a correct understanding of all the arguments based on Zeno's divisional procedure, is that they do not presuppose space, nor time. Division merely requires extension of an object present to the senses and takes place simultaneously. This holds true for both PP and PM! Another feature in need of rehabilitation is Zeno's plainly avered but by others blatantly denied phaenomenological-better: deictical-realism. Zeno nowhere denies the reality of plurality and change. Zeno's arguments are not a reductio, if only because the logical prejudice that 1 The reference textcritical edition for the fragments [B] and related testimonia [A] is: H. Diels and W. Kranz [DK in what follows. See the list of sigla at the end of this paper], Fragmente der Vorsokratiker, to the numbering of which I will comply in accordance with scholarly tradition. 2 In this we reckon in Owen a precursor, although our analysis of Zeno's arguments will be very different from his. See G.E.L. Owen, "Zeno and the mathematicians",
2007
In this paper I will describe seven paradoxes, due to Zeno of Elea. I will show that they contain subtle arguments, not easily brushed aside. Resolution of the paradoxes in several cases requires nineteenth-century mathematics, which neither Zeno nor his contemporaries could have contemplated. In two cases, I will contend that the paradoxes are not solved even today.
Systasis, 2024
This paper investigates the problems posed by Zeno's well-known paradoxes, or aporias regarding the notions of infinity, continuity and motion, which are still very much relevant today. First, it presents two of Zeno's paradoxes, Achilles and Arrow, and examines various proposed solutions, from Aristotle's arguments about these questions to the Standard Solution. It then provides an analysis of the Continuum Hypothesis, identified as a central challenge for the Standard Solution, and offers an exploration of the responses to the Standard Solution to highlight key objections to its underlying concepts. Finally, it offers insights into the methods that can be employed to continue to search for a solution to these paradoxes in the future.
Aristotle and Zeno's paradoxes
The paper is concerned with the Aristotle's solution to the three most famous Zeno's paradoxes-the Dichotomy, Achilles and the tortoise and the Arrow. His solution is compared with the contemporary, so called standard solution, which is widely accepted not only because of the way it resolves the paradoxes by itself but also because it agrees with the contemporary state of mathematics and physics. This connection with theories and ideas that were developed much later than Aristotle and now are widely accepted is an important part of the reason why the standard solution is regarded as a better solution nowadays. The aim of the paper is to show that also if we put aside these external considerations and try to look at Aristotle's solution on its own, we will see that it has counterintuitive consequences that make it unsatisfactory. With respect to Dichotomy and the Achilles and the tortoise paradoxes this counterintuitive consequence is the principle that the whole can exist independently of its parts. With respect to the Arrow paradox this counterintuitive consequence is that a physical object that is moving always occupies a portion of space larger than its size.
Solution to one of Zeno's Paradoxes: The Dichotomy
We here solve one of the paradoxes of Zeno, The Dichotomy. We prove that the foundation of this paradox is the same as that of The Sorites and The Liar. Basically, the extraordinary difference between exclusively human and computer language seems to never be acknowledged by the people proposing the mentioned paradoxes. Yet, if such a difference had ever been acknowledged by them, their paradoxes would be told to be simple allurements to illustrate scientific truths.
A “Minimal”- Set Theoretical Resolution Of Zeno's Paradox Of “Achilles and Tortoise”
In this article we analyze Zeno’s paradox of “Achilles and Tortoise” using exclusively the theory of infinite sets. In contrast with spatiotemporal based attempts for resolution of the paradox, our interpretation and resolution entails only set theory without making any assumptions on the spatiotemporal structure, since in our opinion Zeno’s paradoxes are purely logical paradoxes. This is in accordance to the Eleatic thought, which discarded the “reality” composed by the senses. In particular, we propose a resolution of the paradox from a minimal subset of the set theoretical axioms ZFC that is in concord with the mathematics developed in Pythagorean and Eleatic Schools, based on discrete structures.
Zeno's Boetheia toi Logoi: Thought Problems about Problems for Thought
This essay addresses two central issues that continue to trouble interpretation of Zeno’s paradoxes: 1) their solution, and 2) their place in the history of philosophy. I offer an account of Zeno’s work as pointing to an inevitable paradox generated by our ways of thinking and speaking about things, especially about things as existing in the continua of space and time. In so doing, I connect Zeno’s arguments to Parmenides’ critique of “naming” in Fragment 8, an approach that I believe adds considerably to our understanding of both Zeno’s puzzles and this enigmatic aspect of Parmenides’ thought.