Zeno of Elea, despite being among the most important of the Pre-Socratic philosophers, is frequently overlooked by philosophers and scientists alike in modern times. Zeno of Elea’s arguments on have not only been an impetus for the most important scientific and mathematical theories in human history, his arguments still serve as a basis for modern problems and theoretical speculations. This is a study of his arguments on motion, the purpose they have served in the history of (...) science, and modern applications of Zeno of Elea’s arguments on motion. (shrink)

Originally published in 1936, this book presents the ancient Greek text of the paraphrases and quotations of Zeno's philosophical arguments, together with a facing-page English translation and editorial commentary. Detailed notes are incorporated throughout and a bibliography is also included. This book will be of value to anyone with an interest in Zeno and ancient philosophy.

For Kant's interpretation of Zeno in KrV A502-507/B530-535, scholars have usually referred to Plato's Phaedrus ; in reality the sources Kant uses are, on one hand, Brucker , and, on the other, Plato's Parmenides and Proclus' commentary on it, as quoted by Gassendi in a popular textbook he wrote on the history of logic. Per l'interpretazione kantiana di Zenone in KrV A502-507/B530-535 gli studiosi rinviano solitamente al Fedro platonico ; in realtà, le fonti cui Kant attinse sono, da un (...) lato il Brucker , dall'altro il Parmenide platonico e il commento di Proclo al passo, riportato dal Gassendi in una sua fortunata storia della logica. (shrink)

제논의 운동 역설 중에서 반분 역설과 아킬레우스 역설에 대한 아리스토텔레스의 해결책은 『자연학』 6권과 8권 두 곳에 담겨있다. 그리고 두 답변을 그는 각각 ‘질문자에 충분한 답변’과 ‘진리에 충분한 답변’이라고 부른다. 대부분 철학사가들은 이 중에서 8권의 ‘진리에 충분한 답변’을 그의 최종적인 해결책으로 받아들인다. 이에 대해 논자는 몇 가지 근거를 들어 6권의 ‘질문자에 충분한 답변’이 8권의 답변과 독립적으로 구성될 수 있음을 주장하고, 이들이 간과하고 있는 6권 답변의 의의를 해명하고자 한다. 양자의 답변이 구분될 수 있음은, 다시 말해서 6권의 답변을 8권 입장의 미완성된 단계쯤으로 격하시켜서는 (...) 안 되는 까닭은 첫째 그가 ‘제논의 역설’을 오늘날의 온전한 형태로 소개하는 곳은 『자연학』 8권이 아닌 6권이며, 8권은 『자연학』의 구조상 독립적인 성격을 갖기 때문이다. 게다가 그의 ‘연속이론’이 제시되는 곳은 8권이 아니라 6권인데, 6권은 제논의 운동역설을 소개하고 해결하는 것에 거의 전체가 할애된 곳이기 때문이다. 이런 형식상의 이유 이외에 둘째로 내용에 있어서도 우선 8권의 답변은 가능적 무한과 현실적 무한의 구분을 전제하지만, 6권은 가능성/현실성 구분이 전제되지 않은 채로 답변이 주어지기 때문이다. 넓게 말해서 6권 전체가 주제적으로 다루는 그의 ‘연속’ 이론은 ‘가능성/현실성’ 구분과 “무관하게” 구성될 수 있고, 같은 맥락에서 6권의 답변은 이 구분을 전제한 8권의 답변이 담아내지 못하는 연속 이론을 포함한 그의 자연철학의 몇 가지 진면모를 확인할 수 있게 해 준다. 셋째로 제대로 된 답변이기 위해서는 제논의 입장에서 답변으로 인정할만한 이유가 있어야 하는데, 8권의 답변은 제논의 입장에서 하나의 해결책으로 받아들일 수가 없다. 그러니까 이상의 세 측면에서 상식적으로 생각해 보자면, 그가 제논의 운동 역설을 어떻게 다루고 해결했는지는 6권에서 찾아야지, 8권만 가지고 결론을 내리는 것은 부당한 것으로 보인다. (shrink)

제논의 여러 역설들 중에서 후대에 가장 많이 논의된 역설은 운동 역설이다. 제논의 운동 역설의 종류는 넷으로 알려져 있다. 논자는 이 중에서 ‘반분 역설’과 ‘아킬레우스 역설’에 논의를 집중하고자 한다. 제논의 운동 역설은 아리스토텔레스의 보고에 전적으로 의존한다. 그는 6권과 8권에서 ‘반분 역설’을 보고하고 평가한다. 그는 6권의 답변과 8권의 답변을 각각 ‘질문자에 충분한 답변’과 ‘진리에 충분한 답변’이라고 부른다. 그리고 각 답변의 이론적 배경에는 ‘무한하게 분할되는’ 기하학적인 성격의 연속 개념과 ‘분할될 수 없는 형상적 연속’ 개념이 놓여 있다. 두 연속 개념에 기반한 두 답변에서 그가 (...) 사용하는 개념적인 도구와 학적 관심은 별도의 것으로 논의될 수 있고, 독립적으로 해석될 수 있다. 본 연구는 두 연속 개념 중에서 형상적 혹은 실체적 세계 이해의 존재론적 근거인 ‘분할될 수 없는 형상적 연속’ 개념의 해명에 논의를 집중할 것이다. 그리고 이를 위해 필요한 만큼 제논 역설의 전체 구조는 물론이고, ‘무한하게 분할되는 연속’ 개념과의 비교 분석이 제시될 것이다. 그의 세계 해석의 밑바탕에 깔려 있는 형상적 연속 공간의 구조를 분석하고, 이것이 제논 역설을 해결하는데 어떤 의의와 한계를 갖는지, 나아가 자연 세계 전체를 해석하는데 어떤 의의와 한계를 갖는지 논의할 것이다. (shrink)

Zeno of Elea's paradoxes of motion are one of the most successful provocations in the history of philosophy. There are exactly four paradoxes, namely, the dichotomy, the arrow, Achilles, and the moving rows. This chapter presents the paradoxes in such a way that their strength, fascination, and profoundness are apparent. After providing some basic information about Zeno, the chapter sketches the research program that is the context of Zeno's paradoxes. It goes back to Parmenides and may (...) be called Parmenideanism. The dichotomy and the Achilles paradox are rather two variants of one thought than two different arguments. The moving rows are complicated and not much can be learned from them. Their presentation in the chapter is restricted to some rough outline after the discussion of reactions to the dichotomy and the Achilles. (shrink)

The five participants in this dialogue critically discuss Zeno of Elea's paradox of Achilles and the tortoise. They consider a number of solutions to and restatements of the paradox, together with their philosophical implications. Among the issues investigated include the appearance-reality distinction, Aristotle's distinction between actual and potential infinity, the concept of a continuum, Cantor's continuum hypothesis and theory of transfinite ordinals, and, as a solution to Zeno's puzzle, the distinction between infinite and indeterminate or inexhaustible divisibility.

Hermeneutical scholars doubt whether many past authors really existed. They are only a sort of construction built with the passing of time. Indeed, Zeno of Elea, for instance, was real, and historians attempted to establish what he wrote and intended to say. Our most important source for Zeno is Aristotle. Zeno’s paradoxes deeply influenced the latter’s Physics. Is Aristotle’s physics relevant to us? Yes, because philosophical problems are too complex not to be considered in their historical (...) development as well. In reading Zeno and Aristotle, we can see physical problems from a completely different perspective and learn a lot. In other terms, the historical Zeno is disorienting for us. On the other hand, Zeno’s historical legacy is extremely interesting for us. Indeed, we will see how Zeno’s and Aristotle’s reflections on continuum, extension, and movement could contribute to a better understanding of these notions in the contemporary debate. (shrink)

The aim of this paper is to revisit the problem about the influence of preceding philosophical theories on the Megaric group. Against the traditional view which defend either the influence of Parmenides or that of Socrates, I will try to show the impact of the philosophical position of Zeno of Elea. I will aim to defend that the Megarics use Zenonian antilogy as a part of eristic refutation. In the first section of this paper, I will present and (...) discuss the aforementioned interpretations that privilege either the Parmenidean or the Socratic influence on the Megarics. Then I will analyze the grounds and scope of Zenonian antilogy taking into account all the testimonies which present it as a tool to dicuss theories, rather than to defend them. Finally, I will show how the Megarics use Zenonian antilogy to construct paradoxes based on the numerous ambiguities concerning the signifier and meaning of words, predication, and reasoning, in order to reveal the limits of lógos and refute those who use it as a tool to grasp reality. (shrink)

Of Zeno’s book of forty paradoxes, it was the first that attracted Socrates’ attention. This is the paradox of the like and the unlike. On contemporary assessments, this paradox is largely considered to be Zeno’s weakest surviving paradox. All of these assessments, however, rely heavily on reconstructions of the paradox. It is only relative to these reconstructions that there is nothing paradoxical involved, or that there is some rather obvious mistake being made. This paper puts forward and defends (...) a novel interpretation of this paradox, according to which the concept of a unit plays a central role. There is every reason to think the paradox turns on the concept of a unit: after the presentation of the paradox the text of the Parmenides immediately turns to a discussion of units, and the concept of a unit is also central to the Greek conception of a plurality. If this interpretation is correct then the paradox that Zeno presented was the same as one discussed and solved in Frege’s Grundlagen. (shrink)

This paper considers some aspects of the early conception and use of the infinite in ancient Greece, in the spirit of recent results in the history of ancient mathematics. It follows aspects of the practice of reasoning ad infinitum from the extant corpus of and about Zeno of Elea up to early Hellenistic examples in Aristotle and Euclid. Starting with the idea of ‘reasoning from indefinite iteration’, based on the metalogical recognition of the unachievability of an inference process, (...) it identifies several different classes of more or less sophisticated arguments that make use of this idea, and examines the logical devices and notions required for their acceptance in the philosophical practice. Those include ‘Infinite regress’ properly speaking, where Non-Contradiction is used in the formation of indirect infinitary arguments. (shrink)

Almost everything that we know about Zeno of Elea is to be found in the opening pages of Plato's Parmenides. There we learn that Zeno was nearly 40 years old when Socrates was a young man, say 20. Since Socrates was born in 469 BC we can estimate a birth date for Zeno around 490 BC. Beyond this, really all we know is that he was close to Parmenides (Plato reports the gossip that they were lovers (...) when Zeno was young), and that he wrote a book of paradoxes defending Parmenides' philosophy. Sadly this book has not survived, and what we know of his arguments is second-hand, principally through Aristotle and his commentators (here I have drawn particularly on Simplicius, who, though writing a thousand years after Zeno, apparently possessed at least some of his book). There were apparently 40 ‘paradoxes of plurality’, attempting to show that ontological pluralism — a belief in the existence of many things rather than only one — leads to absurd conclusions; of these paradoxes only two definitely survive, though a third argument can probably be attributed to Zeno. Aristotle speaks of a further four arguments against motion (and by extension change generally), all of which he gives and attempts to refute. In addition Aristotle attributes two other paradoxes to Zeno. Sadly again, almost none of these paradoxes are quoted in Zeno's original words by their various commentators, but in paraphrase. (shrink)

After reporting in detail Aristotle’s texts and comments on the well-known motion paradoxes Arrow, Dichotomy, Achilles and Stadium, tracking back to the 5th century BCE and credited by Aristotle to Zeno of Elea, we next explain and dis-cuss traditional continuous solutions of the paradoxes, based on Cauchy’s limit concept. Afterward, the heated philosophical debate on supertasks and infinity machines is reported before the paradoxes are examined within the context of modern quantum theory. Already in 1905, Einstein concluded that (...) matter could not be a continuous thing. Classical continuous spacetime is replaced by ‘granular’ spacetime, and the concept of distance in granular spacetime is discussed. This is followed by a detailed presentation of modern discrete solutions in granular spacetime, several of which are published here for the first time. Finally, a procedure is presented to determine when traditional continuous methods suffice instead of discrete methods, and the handling of discrete versus continuous in physics is briefly reported. (shrink)

Review of Rossetti, L. _Parmenide e Zenone sophoi ad Elea_.

ABNER SHIMONY of the Paradox A PHILOSOPHICAL PUPPET PLAY Dramatis personae: Zeno , Pupil, Lion Scene: The school of Zeno at Elea. Pup. Master! ...

It will be shown in this article that an ontological approach for some problems related to the interpretation of Quantum Mechanics (QM) could emerge from a re-evaluation of the main paradox of early Greek thought: the paradox of Being and non-Being, and the solutions presented to it by Plato and Aristotle. More well known are the derivative paradoxes of Zeno: the paradox of motion and the paradox of the One and the Many. They stem from what was perceived by (...) classical philosophy to be the fundamental enigma for thinking about the world: the seemingly contradictory results that followed from the co-incidence of being and non-being in the world of change and motion as we experience it, and the experience of absolute existence here and now. The most clear expression of both stances can be found, again following classical thought, in the thinking of Heraclitus of Ephesus and Parmenides of Elea. The problem put forward by these paradoxes reduces for both Plato and Aristotle to the possibility of the existence of stable objects as a necessary condition for knowledge. Hence the primarily ontological nature of the solutions they proposed: Plato’s Theory of Forms and Aristotle’s metaphysics and logic. Plato’s and Aristotle’s systems are argued here to do on the ontological level essentially the same: to introduce stability in the world by introducing the notion of a separable, stable object, for which a ‘principle of contradiction’ is valid: an object cannot be and not-be at the same place at the same time. So it becomes possible to forbid contradiction on an epistemological level, and thus to guarantee the certainty of knowledge that seemed to be threatened before. After leaving Aristotelian metaphysics, early modern science had to cope with these problems: it did so by introducing “space” as the seat of stability, and “time” as the theater of motion. But the ontological structure present in this solution remained the same. Therefore the fundamental notion ‘separable system’, related to the notions observation and measurement, themselves related to the modern concepts of space and time, appears to be intrinsically problematic, because it is inextricably connected to classical logic on the ontological level. We see therefore the problems dealt with by quantum logic not as merely formal, and the problem of ‘non-locality’ as related to it, indicating the need to re-think the notions system, entity, as well as the implications of the operation ‘measurement’, which is seen here as an application of classical logic (including its ontological consequences) on the material world. (shrink)

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 critica 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. 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. 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. 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. (shrink)

The conceptualisation of movement has always been problematical for Western thought, ever since Parmenides declared our incapacity to conceptualise the plurality of change because our self-identical thought can only know an identical being. Exploiting this peculiar feature and constraint on our thought, Zeno of Elea devised his famous paradoxes of movement in which he shows that the passage from a position to movement cannot be conceptualised. In this paper, I argue that this same constraint is at the root (...) of our incapacity to conceptualise the unseen movement at the micro-level and that the aporetic idea of super-position far from opening the gate on a deeper reality is a symptomatic word for this lack of understanding. (shrink)

The plane of the present is a concept that is useful for discussing the various paradigms of time. Here by ‘plane of the present’ we mean the temporal interface that represents the present instant and that forms the boundary between the past and the future. We use the geometrical term ‘plane’ to indicate an extended surface in the space-time continuum, as opposed to a ‘point’ on some time axis. This point/plane dichotomy is intended to raise issues of extension and simultaneity (...) and to examine the degree to which these are meaningful concepts from various physical viewpoints. We will show by example in the present work that the plane of the present is a pivotal concept that offers considerable power in differentiating between various views of the nature of time. The concept of time within the main stream of physics thinking has followed a rather convoluted path over the past three millennia. Anticipating the modern motion picture, Zeno of Elea (c.490-c.430 B.C) questioned whether time should appropriately be viewed as a continuously flowing river, or should more properly be considered as a rapid sequence of stop-motion ‘freeze-frames’, in effect rendering geometrical each instant as a separate infinitesimal point on the line of time. Adopting this view, he asked how physical motion could occur. He argued paradoxically that motion is not possible, since it appears to happen only between the frozen frames of time instants.1 From the viewpoint of Zeno, the plane of the present would be simply the last and most recent in this sequence of freeze-frames. It would be that frozen instant, spanning the universe, which changes progressively as the instant we call ‘now’ becomes the frozen past and future possibility freezes into the ‘now’ of present reality. We note that the plane of the present as a concept does not resolve the arrow paradox that Zeno raised. It only provides a way of thinking about it. (shrink)

The four antinomies of Zeno of Elea continue to be provoking issues that remain relevant for the foundation of science. Aristotle used this antinomy to arrive at a deeper understanding of movement : it is a fluent continuum that he considers to be a whole. The parts, if any, are only potentially present. Similarly, quantum mechanics states that movement is quantized ; things move or change in nonreducible steps, the so-called quanta. This view is in contrast to classical (...) mechanics, where infinitesimally small steps are permitted. The objective of the present study is to show the merits of the Aristotelian approach. Examples from modern science serve to illustrate the philosophical statements. (shrink)

Aristotle was the first thinker to devise a logical system. He drew upon the emphasis on universal definition found in Socrates, the use of reductio ad absurdum in Zeno of Elea, claims about propositional structure and negation in Parmenides and Plato, and the body of argumentative techniques found in legal reasoning and geometrical proof. Yet the theory presented in Aristotle’s five treatises known as the Organon—the Categories, the De interpretatione, the Prior Analytics, the Posterior Analytics, and the Sophistical (...) Refutations—goes far beyond any of these. (shrink)

I examine the reasons Aristotle presents in Physics VIII 8 for denying a crucial assumption of Zeno’s dichotomy paradox: that every motion is composed of sub-motions. Aristotle claims that a unified motion is divisible into motions only in potentiality (δυνάμει). If it were actually divided at some point, the mobile would need to have arrived at and then have departed from this point, and that would require some interval of rest. Commentators have generally found Aristotle’s reasoning unconvincing. Against David (...) Bostock and Richard Sorabji, inter alia, I argue that Aristotle offers a plausible and internally consistent response to Zeno. I defend Aristotle’s reasoning by using his discussion of what to say about the mobile at boundary instants, transitions between change and rest. There Aristotle articulates what I call the Changes are Open, Rests are Closed Rule: what is true of something at a boundary instant is what is true of it over the time of its rest. By contrast, predications true of something over its period of change are not true of the thing at either of the boundary instants of that change. I argue that this rule issues from Aristotle’s general understanding of change, as laid out in Phys. III. It also fits well with Phys. VI, where Aristotle maintains that there is a first boundary instant included in the time of rest, but not a “first in which the mobile began to change.” I then show how this rule underlies Aristotle’s argument that a continuous motion cannot be composed of actual sub-motions. Aristotle distinguishes potential middles, points passed through en route to a terminus, from actual middles. The Changes are Open, Rests are Closed Rule only applies to actual middles, because only they are boundaries of change that the mobile must arrive at and then depart from. On my reading, Aristotle argues that the instant of arrival, the first instant at which the mobile has come to be at the actual middle, cannot belong to the time of the subsequent motion. If it did, the mobile would already be moving towards the next terminus and thus, per Phys. VI 6, would have already left. But it cannot have moved away from the midpoint at the very same moment it has arrived there. This means that the instant of arrival must be separated from the time of departure by an interval of rest. I show how Aristotle’s reasoning applies generally to rule out any continuous reflexive motion or continuous complex rectilinear motion. On my interpretation, however, the argument does not apply to every change of direction. When, as in the case of projectile motion, multiple movers and their relative powers explain why the mobile changes directions, distinct sub-motions are not involved. Aristotle holds that such motions cannot be continuous, not because they involve intervals of rest, but because they involve multiple causes of motion. My interpretation of the Changes are Open, Rests are Closed Rule allows us to make better sense of Aristotle’s argument than any previous interpretation. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Hume's Reading of Bayle: An Inquiry into the Source and Role of the Memoranda J. P. PITTION MY PURPOSE IN THIS PAPER is to discuss an aspect of Hume's reading of Pierre Bayle, the French "Philosopher of Rotterdam. ''1 I am not concerned here with the identification of Hume's direct borrowings from Bayle in the Treatise, nor with the much wider problem of a probable influence of Bayle on (...) Hume. It is indeed possible to identify in the Treatise a number of specific points taken from Bayle. Kemp Smith listed four at least: the account of skepticism, the discussion of Spinoza, the discussion of animal intelligence, and the criticism of the argument from design. 2 All of these come from Bayle's Dictionnaire. External evidence confirms that in 1732 Hume had a work of Bayle, presumably a copy of the Dictionnaire. Other borrowings from Bayle have been identified in the Treatise and in Hume's other works. This is no surprise, for in the eighteenth century Bayle's Dictionnaire was used as it was intended in the first instance, that is, as a reference work. In detailing the borrowings from Bayle, Kemp Smith also touched upon the broader question of influence when he stated that Hume's Pyrrhonism, particularly in relation to his treatment of religion, may also come from Bayle. Many recent scholars have followed suit. A problem of influence however is always a difficult one, and particularly so in this case. There was, as R. H. Popkin has pointed out, a broad awareness of continental skepticism among British philosophers of the eighteenth century. 3 However, apropos Berkeley, A. A. Luce has remarked that the trouble with eighteenth-century continental skepticism was that it had various objectives and took various forms. 4 This is true of Bayle himself. Within skepticism Bayle's position was known for its extremism, and it was this extremism that brought him notoriety. During the eighteenth century Bayle was the philosopher who promoted a systematic use of the Pyrrhonic mode of argument. He was acknowledged above all for having set up a double paradox: that any attempt at a rational theodicy must lead to Manicheism and that to argue for a rationalist Christian ethics is to argue the case of an atheistic one as well. In other words, in the early eighteenth century Bayle played the part of a contemporary Pyrrho and Zeno of Elea: he was known for this double stance, and it is for ' This is a slightly revised version of a paper read at the McGill Bicentennial Hume Conference, held at McGiUUniversity, Montreal, in September, 1976. I wishto offer my thanks to Professors H. M. Bracken and D. F. Norton for their assistanceon this version, and I am particularly grateful to Professor James Moore of Concordia University for his comments on the interpretation put forward here in relation to section III of the Memoranda (seen. 8). 2N. KempSmith, The Philosophy of David Hume (NewYork, 1964),pt. III, chap. XIV, app. C. 3 "David Hume and the Pyrrhonian Controversy," Review of Metaphysics VI (September, 1952):65-81. 4 The Dialectic of Immaterialisrn (London, 1963),p. 67. [373] 374 HISTORY OF PHILOSOPHY this stance that he was mentioned. It is doubtful whether many of those who do refer to Bayle during this period understood him beyond these terms, whether they sought to understand, or whether they even bothered to read Bayle's lengthy arguments. It is clear that few really grasped his complex, often ambiguous objectives. Mention of a Baylian position by an eighteenth-century writer is therefore no guarantee that the writer has actually read Bayle's works: Bayle is a sort of figurehead for Pyrrhonism, Manicheism, or often even atheism, but one can doubt that there is behind the mention of these basic positions any serious reflection on his thought. There are exceptions of course. Luce and H. M. Bracken have shown that Bayle played a seminal role in the formation of Berkeley's thought? But as a rule, knowledge of Bayle among writers of the Enlightenment was vague; references to him, nonspecific. In most cases it is scarcely possible to speak of an influence. My aim in this... (shrink)

In the Western philosophical tradition, the earliest recognized paradoxes are attributed to Zeno of Elea (ca. 490–430 B.C.E.) and to Eubulides of Miletus (fl. 4th century B.C.E.). In the Chinese tradition, the earliest and most well-known paradoxes are ascribed to figures associated with the “School of Names” (ming jia 名家), a diverse group of Warring States (479–221 B.C.E.) thinkers who shared an interest in language, logic, and metaphysics. Their investigations led some of these thinkers to propound puzzling, paradoxical (...) statements such as “Today go to Yue but arrive yesterday,” “White horses are not horses,” and “Mountains and gorges are level.” Such paradoxes seem to have been intended to highlight fundamental features of reality or subtleties in semantic relations between words and things. Why were thinkers who advanced paradoxes categorized as a school of “names”? In ancient China, philosophical inquiry concerning language and logic focused on the use of “names” (ming 名, also terms, labels, or reputation) and their semantic relations to “stuff” (shi 實, also objects, features, events, or situations). Hence for classificatory purposes, second-century B.C.E. Han-dynasty archivists grouped together assorted pre-Han figures whose most prominent ideas seemed to concern the relation between names and stuff—or at least strange, unorthodox uses of names—and dubbed them a school or lineage (jia 家) devoted to the study of names. Unfortunately, both the label and the grouping are misleading. Historically, the school was a retrospective, taxonomical fiction. The figures classified under the “School of Names” never formed a distinct circle, movement, tradition, or line of influence devoted to any particular doctrine, theme, method, or way of life. Their intellectual interests overlapped at most only partly, while also overlapping extensively with those of texts associated with other schools or traditions, such as the Mohist “Dialectics” 墨辯, the Zhuangzi 莊子, the Xunzi 荀子, and the Annals of Lü Buwei 呂氏春秋. What perhaps does set the School of Names apart is that some (though not all) of the figures associated with it apparently delighted in propounding paradoxical or preposterous sayings, while the other texts just mentioned generally (though not exclusively) seek to explain and debunk such utterances. (shrink)

Pythagoras -- Confucius -- Heracleitus -- Parmenides -- Zeno of Elea -- Socrates -- Democritus -- Plato -- Aristotle -- Mencius -- Zhuangzi -- Pyrrhon of Elis -- Epicurus -- Zeno of Citium -- Philo Judaeus -- Marcus Aurelius -- Nagarjuna -- Plotinus -- Sextus Empiricus -- Saint Augustine -- Hypatia -- Anicius Manlius Severinus Boethius -- Śaṅkara -- Yaqūb ibn Ishāq aṣ-Ṣabāḥ al-Kindī -- Al-Fārābī -- Avicenna -- Rāmānuja -- Ibn Gabirol -- Saint Anselm of Canterbury (...) -- al-Ghazālī -- Peter Abelard -- Averroës -- Zhu Xi -- Moses Maimonides -- Ibn al-'Arabī -- Shinran -- Saint Thomas Aquinas -- John Duns Scotus -- William of Ockham -- Niccolò Machiavelli -- Wang Yangming -- Francis Bacon, Viscount Saint Alban (or Albans), Baron of Verulam -- Thomas Hobbes -- René Descartes -- John Locke -- Benedict de Spinoza -- Gottfried Wilhelm Leibniz -- Giambattista Vico -- George Berkeley -- Charles-Louis de Secondat, baron de La Brède et de Montesquieu -- David Hume -- Jean-Jacques Rousseau -- Immanuel Kant -- Moses Mendelssohn -- Marie-Jean-Antoine-Nicolas de Caritat, marquis de Condorcet -- Jeremy Bentham -- Georg Wilhelm Friedrich Hegel -- Arthur Schopenhauer -- Auguste Comte -- John Stuart Mill -- Søren Kierkegaard -- Karl Marx -- Herbert Spencer -- Wilhelm Dilthey -- William James -- Friedrich Nietzsche -- Friedrich Ludwig Gottlob Frege -- Edmund Husserl -- Henri Bergson -- John Dewey -- Alfred North Whitehead -- Benedetto Croce -- Nishida Kitarō -- Bertrand Russell -- G.E. Moore -- Martin Buber -- Ludwig Wittgenstein -- Martin Heidegger -- Rudolf Carnap -- Sir Karl Popper -- Theodor Wiesengrund Adorno -- Jean-Paul Sartre -- Hannah Arendt -- Simone de Beauvoir -- Willard Van Orman Quine -- Sir A.J. Ayer -- Wilfrid Sellars -- John Rawls -- Thomas S. Kuhn -- Michel Foucault -- Noam Chomsky -- Jürgeb Gabernas -- Sir Bernard Williams -- Jacques Derrida -- Richard Rorty -- Robert Nozick -- Saul Kripke -- David Kellogg Lewis -- Peter (Albert David) Singer. (shrink)

For a long time, Parmenides has been considered the first real metaphysician in history, a theorist of a disembodied being, unreachable by the scientific knowledge of the world. In his Eleatic Lectures, Giovanni Cerri goes back to his renown interpretation of Parmenides as a scientist fully aware of the epistemological foundations of knowledge, and capable of foreshadowing the ultimate outcome of the evolution of science, that is, the discovery of being as a single homogeneous body. Cerri also shows that the (...) works of two other thinkers who were trained in the heart of the school of Elea itself support his interpretation: on the one hand Zeno, with his arguments against plurality; on the other hand Leucippus, the inventor of atomism. Ten scholars have been called to discuss this broad interpretation of a crucial page in the history of thought. Cerri replies to each of them in the final pages of the volume, engaging in a dense dialogue. (shrink)

The four antinomies of Zeno of Elea, especially Achilles and the tortoise continue to be provoking issues which are even now not always satisfactory solved. Aristotle himself used this antinomy to develop his understanding of movement: it is a fluent continuum that has to be treated as a whole. The parts, if any, are only potentially present in the whole. And that is exactly what quantum mechanics is claiming: movement is quantized in contrast to classical mechanics. The objective (...) of this study is to show the merits of the Aristotelian approach. It is a good candidate for serving as the philosophical background for understanding fundamental aspects of quantum mechanics. Especially mentioned are the influence of the final state in quantum mechanics that in philosophy could be correlated with the final cause. Like in the work of Aristotle also in this study examples from science are presented to illustrate the philosophical approach. But, in contrast to ancient Greek, the examples now relate to issues which are only fully accessible to the scientifically trained reader. As the main conclusion the dialogue between scientists and philosophers is strongly recommended which will result in progress in both disciplines. (shrink)

This is an English translation of one of the more challenging and enigmatic of Plato's dialogues between Socrates and Parmenides and Zeno of Elea, that begins with Zeno defending his treatise of Parmenidean monism against those partisans of plurality. Focus Philosophical Library translations are close to and are non-interpretative of the original text, with the notes and a glossary intending to provide the reader with some sense of the terms and the concepts as they were understood by (...) Plato's immediate audience. (shrink)

This book studies various perspectives in the history of European philosophy on the relationship between time and movement. Ever since the pre-Socratic thinker Zeno of Elea linked time and space to understand bodily movement, his so-called paradoxes of motion have remained unsolved. One of his most important critics, the French philosopher Henri Bergson, criticized the usual connection between time and space and established a new way of understanding time as duration (durée). Whereas Zeno presented an objectivist understanding (...) of time, Bergson emphasized its subjectivist meaning. Both contradictory positions seem incompatible, referring to pure intellect (Zeno) on the one hand or pure sensation (Bergson) on the other. Looking at Hegel's Phenomenology, this book shows that the outer and inner consciousness of time became crucial to his principle of movement and change. In his view, time is an integral part of dialectical processes that are historically substantiated. Hegel sought to subordinate pure concepts and ideas so that they would become indispensable moments of the self knowing spirit. Cassirer appreciated the idealism of coming into being but rejected Hegel's concept of the absolute. Instead, he established his philosophy of symbolic forms, in which the development of different perceptions and conceptions of time - from situational affective experience to the mathematical system of relations - determines the direction of the symbolic formation process. In the end, the sensitive concept of time is replaced by the relational concept of natural numbers, in which all here-and-now experiences are embedded. Finally, Bourdieu attempts to reintegrate symbolic forms into social processes. The book reflects on the concepts mentioned here by discussing their pros and cons in order to shed more light on the relationship between time and movement in European thought. (shrink)

Aristotle argued that there are no true statements of the form. In his lectures on history of philosophy Hegel does not challenge this view and in his Science of Logic expresses admiration for Aristotle's rebuttal of Zeno of Elea's attempt to find such contradictions in his paradoxes of motion. Yet more than once in his logics Hegel insists that everything is contradictory. I approach this problem from two directions. First, Widerspruch often means, and is understood by Hegel to (...) mean, ‘opposition’ rather than ‘contradiction’ in the strict logical sense. Thus Catullus's simultaneous love and hatred of Clodia is a contradiction, but not an Aristotelian, or formal logical, contradiction. I defuse Hegel's occasional suggestions of Aristotelian contradictions in motion and time. Second, I exploit Hegel's tacit rejection of Aristotle's official bivalence account of truth and falsity, in favour of the view that truth is approached by successive improvements in our inevitably imperfect attempts to attain it. In this respect Hegel's procedure is similar to that of Aristotle himself, who characteristically constructs his own view of metaphysics, physics, ethics, etc., from the imperfect, but not flatly false, opinions of his predecessors. ‘The truth is the whole’, that is, the whole sequence of our attempts to reach it. (shrink)

In his collection of anecdotes, Lives, Opinions, and Remarkable Sayings of the Most Famous Ancient Philosophers, Diogenes Laertius devotes a chapter to the life of Zeno of Elea. Zeno's reputation is based on his celebrated paradoxes, amply discussed by Aristotle: a moving body will never reach its (pre-defined) telos, since it first has to cover half (or more than half) the remaining distance; the faster will never catch up with the slower, since it first has to get (...) to the point from which the slower has just left. Zeno's style is laconic, like that of an Aesop fable. Maxima e minimis: there is no superfluous word. Everything needed to arrive at the conclusion is explicitly stated. (shrink)

Gregory Vlastos was one of the twentieth century's most influential scholars of ancient philosophy. Over a span of more than fifty years, he published essays and book reviews that established his place as a leading authority on early Greek philosophy. The two volumes that comprise Studies in Greek Philosophy include nearly forty contributions by this acknowledged master of the philosophical essay. Many of these pieces are now considered to be classics in the field. Perhaps more than any other modern scholar, (...) Gregory Vlastos was responsible for raising standards of research, analysis, and exposition in classical philosophy to new levels of excellence. His essays have served as paradigms of scholarship for several generations. Available for the first time in a comprehensive collection, these contributions reveal the author's ability to combine the skills of a philosopher, philologist, and historian of ideas in addressing some of the most difficult problems of ancient philosophy. Volume I collects Vlastos's essays on Presocratic philosophy. Wide-ranging concept studies link Greek science, religion, and politics with philosophy. Individual studies illuminate the thought of major philosophers such as Heraclitus, Parmenides, Anaxagoras, and Democritus. A magisterial series of studies on Zeno of Elea reveals the author's power in source criticism and logical analysis. Volume II contains essays on the thought of Socrates, Plato, and later thinkers and essays dealing with ethical, social, and political issues as well as metaphysics, science, and the foundations of mathematics. (shrink)

A journey of a thousand miles begins, obviously, with a single step. But isn’t it equally obvious that a step of a single metre must begin with a single millimetre? And before you can begin the last micron of that millimetre, don’t you have to get through 999 other microns first? And so ad infinitum? That “ad infinitum” bit is what worried the philosopher Zeno of Elea. Can our every action really consist of sub actions each consisting of (...) sub sub actions ... so that before we can move at all, we have to perform a literally infinite number of distinct, consecutive actions? (shrink)

Gregory Vlastos was one of the twentieth century's most influential scholars of ancient philosophy. Over a span of more than fifty years, he published essays and book reviews that established his place as a leading authority on early Greek philosophy. The two volumes that comprise Studies in Greek Philosophy include nearly forty contributions by this acknowledged master of the philosophical essay. Many of these pieces are now considered to be classics in the field. Perhaps more than any other modern scholar, (...) Gregory Vlastos was responsible for raising standards of research, analysis, and exposition in classical philosophy to new levels of excellence. His essays have served as paradigms of scholarship for several generations. Available for the first time in a comprehensive collection, these contributions reveal the author's ability to combine the skills of a philosopher, philologist, and historian of ideas in addressing some of the most difficult problems of ancient philosophy. Volume I collects Vlastos's essays on Presocratic philosophy. Wide-ranging concept studies link Greek science, religion, and politics with philosophy. Individual studies illuminate the thought of major philosophers such as Heraclitus, Parmenides, Anaxagoras, and Democritus. A magisterial series of studies on Zeno of Elea reveals the author's power in source criticism and logical analysis. Volume II contains essays on the thought of Socrates, Plato, and later thinkers and essays dealing with ethical, social, and political issues as well as metaphysics, science, and the foundations of mathematics. (shrink)

_From the Introduction:_ "Stoic philosophy, of which Epictetus (c. a.d. 50–130) is a representative, began as a recognizable movement around 300 b.c. Its founder was Zeno of Cytium (not to be confused with Zeno of Elea, who discovered the famous paradoxes). He was born in Cyprus about 336 b.c., but all of his philosophical activity took place in Athens. For more than 500 years Stoicism was one of the most influential and fruitful philosophical movements in the Graeco-Roman (...) world. The works of the earlier Stoics survive only in fragmentary quotations from other authors, but from the Renaissance until well into the nineteenth century, Stoic ethical thought was one of the most important ancient influences on European ethics, particularly because of the descriptions of it by Cicero, through surviving works by the Stoics Seneca, Marcus Aurelius, and also Epictetus--and also because of the effect that it had had in antiquity, and continued to have into the nineteenth century, on Christian ethical views. Nowadays an undergraduate or graduate student learning about ancient philosophy in a university course may well hear only about Plato and Aristotle, along perhaps with the presocratics; but in the history of Western thought and education this situation is somewhat atypical, and in most periods a comparable student would have learned as much or more about Stoicism, as well as two other major ancient philosophical movements, Epicureanism and Scepticism. In spite of this lack of explicit acquaintance with Stoic philosophers and their works, however, most students will recognize in Epictetus various ideas that are familiar through their effects on other thinkers, notably Spinoza, in our intellectual tradition.". (shrink)

The contemplation of the end of life — life's ending — provokes the emotions of fear, alarm and despondency. Fears about the end of life are almost universal. The Stoic Zeno of Elea first analyzed the problem accurately when he pointed out what he thought the fundamental problems of human existence consisted of. He identified the fundamental anxieties as being fear of the gods and a fear of death. Both fears, he thought, could be therapeutically eliminated: fear of (...) the gods was pointless since they did not care about us, and fear of death could be rationalized away by reasonable philosophical argumentation. Without wishing to resurrect Zeno's arguments, one can safely say that he was spectacularly wrong in his view of the power of rational argument. The fears about life's ending are multifaceted. They consist of fears about the process of aging, the prospect of one's own dying and one's own death, and the fact that our lives and activities — as they are lived within the confines of our corporeal bodies — will come to an inevitable end.There are also problems and anxieties concerned with the fact that the passage of time and the visible effects it leaves on our physical selves make us conscious that, at some time or other, we are, like other material objects, subject to decay and wearing down. The process is a great equalizer and no one who lives long enough is spared the spectacle of witnessing and experiencing the gradual process of the decline of their physical powers and of their cognitive functions. No matter what sort of life has been led, the ending of that particular life is certain.In this paper I want to discuss some views about the nature of these fears about the later stages of life, aging, old age and death and their roots in the philosophical and metaphysical views we have come to endorse. (shrink)

Οκον τν μέλλοντα τέχνην ητορικν μετιέναι πρτον μέν δε τατα δ διρσθαι, κα εληέναι τιν χαρακτρα κατέρου το εδουδ, ν ᾧ τε νγκη τ πλθος πλανσθαι Kα ν ᾧ μή . To the best of my knowledge the soundness of the first six words of this sentence has never been questioned, yet to accept them as they are in the manuscripts means to close one's eyes to the direction of the argument. At 260d5–9 rhetoric personified and allowed to plead its (...) case makes the ‘big’ statement that anyone learning how to speak would do well to know the truth about his subject but that even if he knows it he would not be able νεν μο, i.e. without the aid of rhetoric, πείθειν τέχν. From that point on the issues are whether rhetoric justly claims to be a τέχν, what territory it covers and how the procedure of someone practising it τέχν may differ from that of one for whom it is an τεχνος τριβή . Even if rhetoric engages in πάτη and proves e.g. one and the same thing to be both just and unjust , success will be with τέχν τοτο δρν ; witness Zeno of Elea, a master in such arguments λέγοντα τέχν when he makes the same things appear like and unlike or one and many . To judge shrewdly what kind of subjects deceive people more easily the rhetorician himself must have a firm grasp of the truth: λόγων ρα τέχνην, ταρε, τν λήθειαν μ εδώς, δόξας δ τεθηρευκώς, γελοίαν τινά, ς οικε, κα τεχνον παρέξεται. (shrink)

NOTA PRELIMINAR: o texto a seguir representa a versão ampliada (e corrigida conforme as indicações dos pareceristas) do artigo homônimo, publicado na revista Archai em 2014. Por algum problema técnico, acabou sendo publicada, na época, a primeira versão, sem as melhorias sugeridas pelos avaliadores. Eis, então, a versão ‘definitiva’ do artigo “Zenão e a impossibilidade da analogia”: -/- 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. (shrink)

Richard Popkin’s meticulous translation--the most complete since the eighteenth century--contains selections from thirty-nine articles, as well as from Bayle’s four Clarifications. The bulk of the major articles of philosophical and theological interest--those that influenced Leibniz, Berkeley, Hume, and Voltaire and formed the basis for so many eighteenth-century discussions--are present, including David, Manicheans, Paulicians, Pyrrho, Rorarius, Simonides, Spinoza, and Zeno of Elea.