In our research about Fuzzy Time and modeling time, "Unexpected Hanging Paradox" plays a major role. Here, we compare this paradox to the Zeno Paradox and the relations of them with our standard models of continuum and Fuzzy numbers. To do this, we review the project "Fuzzy Time and Possible Impacts of It on Science" and introduce a new way in order to approach the solutions for these paradoxes. Additionally, we have a more general discussion about (...) paradoxes, as Philosophical back ground of the subject and in this way, we introduce the concepts of General View, the first picture, BBF-General View. (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)

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)

Zeno’s paradoxes of motion, allegedly denying motion, have been conceived to reinforce the Parmenidean vision of an immutable world. The aim of this article is to demonstrate that these famous logical paradoxes should be seen instead as paradoxes of immobility. From this new point of view, motion is therefore no longer logically problematic, while immobility is. This is convenient since it is easy to conceive that immobility can actually conceal motion, and thus the proposition “immobility is mere illusion of (...) the senses” is much more credible than the reverse thesis supported by Parmenides. Moreover, this proposition is also supported by modern depiction of material bodies: the existence of a ceaseless random motion of atoms—the ‘thermal agitation’—in the scope of contemporary atomic theory, can offer a rational explanation of this ‘illusion of immobility’. Our new approach to Zeno’s paradoxes therefore leads to presenting the novel concept of ‘impermobility’, which we think is a more adequate description of physical reality. (shrink)

A solution of the zeno paradoxes in terms of a discrete space is usually rejected on the basis of an argument formulated by hermann weyl, The so-Called tile argument. This note shows that, Given a set of reasonable assumptions for a discrete geometry, The weyl argument does not apply. The crucial step is to stress the importance of the nonzero width of a line. The pythagorean theorem is shown to hold for arbitrary right triangles.

In this paper, we connected Zeno’s paradoxes and motions with the viscous friction force \. For the progressive version of the dichotomy paradox, if the body speed is constant, the sequences of positions and instants are infinite, but the series of distances and time variations converge to finite values. However, when the body moves with force \, the series of time variations becomes infinite. In this case, the body crosses infinite points, approximating to a final position forever, as (...) the progressive version of the dichotomy paradox describes. The same procedures with constant speed and motion with force \ result in different spatial sequences and the same series for the regressive version of the dichotomy paradox. Nonetheless, the regressive version of the dichotomy paradox does not describe a body that approximates a final position forever. Finally, for the Achilles paradox, we find the positional and temporal sequences of the man and the tortoise at constant speeds. Analogously to the progressive version of the dichotomy paradox, the positional and temporal sequences are infinite, but the spatial and temporal series converge to finite values. If Achilles and the tortoise are identical points that move with force \, and the turtle’s position in function of time presents a temporal advantage, the man and the animal will cross successive infinite places forever, and the quick hero will never overtake the slow reptile, as the paradox described. We conclude that the progressive version of the dichotomy and Achilles paradoxes can describe motions when the force is \. (shrink)

Zeno’s Paradoxes In the fifth century B.C.E., Zeno offered arguments that led to conclusions contradicting what we all know from our physical experience—that runners run, that arrows fly, and that there are many different things in the world. The arguments were paradoxes for the ancient Greek philosophers. Because many of the arguments turn crucially on … Continue reading Zeno’s Paradoxes →.

This article criticises one of Stuart Rachels' and Larry Temkin's arguments against the transitivity of 'better than'. This argument invokes our intuitions about our preferences of different bundles of pleasurable or painful experiences of varying intensity and duration, which, it is argued, will typically be intransitive. This article defends the transitivity of 'better than' by showing that Rachels and Temkin are mistaken to suppose that preferences satisfying their assumptions must be intransitive. It makes cler where the argument goes wrong by (...) showing that it is a version of Zeno's paradox of Achilles and the Tortoise. (shrink)

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

A solution of the zeno paradoxes in terms of a discrete space is usually rejected on the basis of an argument formulated by hermann weyl, The so-Called tile argument. This note shows that, Given a set of reasonable assumptions for a discrete geometry, The weyl argument does not apply. The crucial step is to stress the importance of the nonzero width of a line. The pythagorean theorem is shown to hold for arbitrary right triangles.

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)

The author argues that, Although zeno's paradoxes on motion cannot be resolved in their own terms, They are nonetheless illegitimate. Examining the paradox of achilles and the tortoise, He finds that the mechanism of zeno's argument consists in an equivocal concept of motion characterized at once by a constant rate and by proportionate segments of movement. He then contends it is illegitimate to treat the concept of motion and its subconcepts like the postulates of a deductive system. (...) However, That the common theory of meaning presupposed by zeno's paradoxes is erroneous would have to be demonstrated metaphysically. (staff). (shrink)

We treat here three apparently uncorrelated topics from the point of view of dense measurement: The EPR paradox, the teleportation process, and Wheeler's delayed-choice experiment (DCE). We begin with the DCE and show, using its unique nature and the histories formalism, that use may ascertain and fix the notion of dense measurement (the Zeno effect). We show here by including the experimenter (observer) as an inherent part of the physical system and using the Aharonov–Vardi notion of dense measurement (...) along a path, that knowledge of certain properties of the incoming system (after a measurement) is equivalent to dense measurement. We reach the same conclusion by discussing the teleportation process, and the EPR paradox from, the same point of view. (shrink)

I SHOW THAT THE COSMOLOGICAL ARGUMENT OF AQUINAS FOR THE EXISTENCE OF GOD COMMITS A RATHER TRIVIAL LINGUISTIC FALLACY, BY SHOWING THAT (1) SOME OF ZENO'S PARADOXES COMMIT A TRIVIAL LINGUISTIC FALLACY, AND THAT (2) THE COSMOLOGICAL ARGUMENT IS SUFFICIENTLY SIMILAR TO THESE PARADOXES THAT IT COMMITS THE SAME FALLACY. COPLESTON'S VIEW THAT "MENTION OF THE MATHEMATICAL INFINITE SERIES IS IRRELEVANT" TO "ANY" OF AQUINAS'S ARGUMENTS FOR GOD'S EXISTENCE IS THUS SHOWN FALSE.

Zeno’s arguments are generally regarded as ingenious but downright unsound paradoxes, worth of attention mainly to disclose why they go wrong or, alternatively, to recognise them as clever, even if crude, anticipations of modern views on the space, the infinite or the quantum view of matter. In either case, the arguments lose any connection with the scientific and philosophical problems of Zeno’s own time and environment. In the present paper, I argue that it is possible to make sense (...) of Zeno’s arguments if we recognise that Zeno was indeed a close follower of Parmenides, who wanted to show that, if the plurality of beings existed, then various absurd consequences would follow. He intended to highlight the compact and inarticulate nature of the being, and the human character of the system of world partitions producing the entities and the objects on which our knowledge is based. (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. (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)

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)

Aristotle’s solution to Zeno’s arrow paradox differs markedly from the so called at-at solution championed by Russell, which has become the orthodox view in contemporary philosophy. The latter supposes that motion consists in simply being at different places at different times. It can boast parsimony because it eliminates velocity from the ontology. Aristotle, by contrast, solves the paradox by denying that the flight of the arrow is composed of instants; rather, on my reading, he holds that the (...) flight is a unity which is ontologically prior to the temporal parts that may be abstracted from it. I label this position temporal holism; and an entity that is ontological prior to its temporal parts lasting. Lasting, I argue, is the key to Aristotle’s solution to the arrow paradox, but it has received insufficient attention in the relevant literature. I therefore set out here to investigate lasting and highlight its major role in Aristotle’s metaphysics more broadly, and in his solution to other problems of change. I show, too, how lasting within a contemporary context underwrites a parsimonious and intuitive solution to the arrow paradox that retains instantaneous velocity, and hence solves a problem for those who think velocity is required within the ontology to underwrite certain causal roles. (shrink)

My aim in this paper is to suggest a new outlook concerning the nature of Zeno’s paradoxes. The attention is directed towards the three famous paradoxes known as “Dichotomy,” “Achilles and the Tortoise,” and “The Arrow.” An analysis of the paradigmatic proposals for a solution shows that an adequate solution has not yet been reached. An answer is provided instead to the question “How Zeno’s paradoxes emerge in their quality of aporiae?,” that is to say in their quality (...) of impasses, of problem situations without an exit, what is the original meaning of the Greek word “aporia.” It is my claim that this is the correct rational approach for solving these conceptual puzzles. In other words, I am not proposing formal solutions by criticizing and/or altering their premises assuming the continuous or discrete nature of space and time, but I try to draw the philosophical attention to the way we possess the phenomenon of motion as a result of the perception of space-time in human experience. (shrink)

MATHEMATICAL RESOLUTIONS OF ZENO’s PARADOXES of motion have been offered on a regular basis since the paradoxes were first formulated. In this paper I will argue that such mathematical “solutions” miss, and always will miss, the point of Zeno’s arguments. I do not think that any mathematical solution can provide the much sought after answers to any of the paradoxes of Zeno. In fact all mathematical attempts to resolve these paradoxes share a common feature, a feature that (...) makes them consistently miss the fundamental point which is Zeno’s concern for the one-many relation, or it would be better to say, lack of relation. This takes us back to the ancient dispute between the Eleatic school and the Pluralists. The first, following Parmenide’s teaching, claimed that only the One or identical can be thought and is therefore real, the second held that the Many of becoming is rational and real.1 I will show that these mathematical “solutions” do not actually touch Zeno’s argument and make no metaphysical contribution to the problem of understanding what is motion against immobility, or multiplicity against identity, which was Zeno’s challenge. I would like to point out at this stage that my contention. (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)

We outline Brentano’s theory of boundaries, for instance between two neighboring subregions within a larger region of space. Does every such pair of regions contain points in common where they meet? Or is the boundary at which they meet somehow pointless? On Brentano’s view, two such subregions do not overlap; rather, along the line where they meet there are two sets of points which are not identical but rather spatially coincident. We outline Brentano’s theory of coincidence, and show how he (...) uses it to resolve a number of Zeno-like paradoxes. (shrink)

In this paper, I develop an original view of the structure of space—called infinitesimal atomism—as a reply to Zeno’s paradox of measure. According to this view, space is composed of ultimate parts with infinitesimal size, where infinitesimals are understood within the framework of Robinson’s nonstandard analysis. Notably, this view satisfies a version of additivity: for every region that has a size, its size is the sum of the sizes of its disjoint parts. In particular, the size of a (...) finite region is the sum of the sizes of its infinitesimal parts. Although this view is a coherent approach to Zeno’s paradox and is preferable to Skyrms’s infinitesimal approach, it faces both the main problem for the standard view and the main problem for finite atomism, leaving it with no clear advantage over these familiar alternatives. (shrink)

In this note i argue against harold n. lee's assertion ("mind," october, 1965) that resolution of zeno's paradoxes is closely connected with the modern mathematical distinction between density and continuity. zeno's paradoxes would arise as much if space or time is dense as they do if it is continuous. in fact the paradoxes only arise if one combines a mathematical analysis of space and time with a non-mathematical conception of motion.

Professor Grünbaum's much-discussed refutation of Zeno's metrical paradox turns out to be ad hoc upon close examination of the relevant portion of measure theory. Although the modern theory of measure is able to defuse Zeno's reasoning, it is not capable of refuting Zeno in the sense of showing his error. I explain why the paradox is not refutable and argue that it is consequently more than a mere sophism.

The article assumes that the expression “comparative relativism”—the title of the Common Knowledge symposium in which the essay appears—is neither tautological nor oxymoronic. Rather, the author construes the term as an apt synthetic characterization of anthropology and illustrates that idea by means of four quotations, taken from authors as different as Richard Rorty and David Schneider, Marcel Mauss and Henri Michaux. The quotations can be said to “exemplify” anthropology in terms that are interestingly (and diversely) restrictive: some of them amount (...) to extrinsic negations of anthropology that would paralyze it; others suggest intrinsic negativities that would propel it. All of the passages chosen evoke the idea of belief, which is profoundly implicated, in all possible senses (and especially the worse ones), in the majority of arguments that connect the themes of anthropology, comparison, and relativism. (shrink)

Zeno's paradoxes of motion are considered as challenges to the practice of describing motion in terms of continuous functions. A brief description of some work of adolf gruenbaum toward the resolution of these paradoxes is given. A new form of zeno's dichotomy paradox is described, And it is claimed that the paradox, In this form, Is not amenable to the explanations of gruenbaum. This is demonstrated by giving the new form of the paradox a second, (...) More mathematical description. In a short summary it is claimed that the challenges of zeno's paradoxes are still unanswered. (shrink)

It has been argued that we find zeno's paradoxes of motion persuasive because physical time is dense and continuous, While time as we experience it is discrete. But we do not experience time as a succession of distinct, Countable, Consecutively ordered mental "nows." nor is it common to attempt the futile mental task of traversing in thought the infinite number of spatial subintervals in zeno's paradoxes, As has also been suggested. Rather, We find the paradoxes persuasive because there (...) are a number of different conceptual and linguistic problems inherent in them. For instance, Understanding how it is possible for achilles to come to the end of an endless sequence of spatial intervals requires disambiguating different senses of the word "end.". (shrink)

The homogeneity of time (i.e. the fact that there are no privileged moments) underlies a fundamental symmetry relating to the energy conservation law. On the other hand the obvious asymmetry between past and future, expressed by the metaphor of the arrow of time or flow of time accounts for the irreversibility of what happens. One takes this for granted but the conceptual tension it creates against the background of time''s presumed homogeneity calls for an explanation of temporal becoming. Here, it (...) is approached with the help of a claim to the effect that the instant (moment) itself has a structure isomorphic to that of time as a whole. Then the asymmetry of past and future in regard to temporal becoming is associated with the internal structure of the very moment, and not with external relations between different moments of time. In this paper ideas of ancient atomism and contemporary dialectics are brought together. It is for the sake of a contrast to what is known as logical atomism that I choose to call this view dialectical atomism. The latter admits dialectical contradictions and, so far as the logical status of contradictions is concerned, bears reference to paraconsistent logics. In the paper there is an outline of a method of converting any consistent axiomatic formal system into a paraconsistent theory. (shrink)

A version of nonstandard analysis, Internal Set Theory, has been used to provide a resolution of Zeno's paradoxes of motion. This resolution is inadequate because the application of Internal Set Theory to the paradoxes requires a model of the world that is not in accordance with either experience or intuition. A model of standard mathematics in which the ordinary real numbers are defined in terms of rational intervals does provide a formalism for understanding the paradoxes. This model suggests that (...) in discussing motion, only intervals, rather than instants, of time are meaningful. The approach presented here reconciles resolutions of the paradoxes based on considering a finite number of acts with those based on analysis of the full infinite set Zeno seems to require. The paper concludes with a brief discussion of the classical and quantum mechanics of performing an infinite number of acts in a finite time. (shrink)

While Aristotle provides the crucial testimonies for the paradoxes of motion, topos, and the falling millet seed, surprisingly he shows almost no interest in the paradoxes of plurality. For Plato, by contrast, the plurality paradoxes seem to be the central paradoxes of Zeno and Simplicius is our primary source for those. This paper investigates why the plurality paradoxes are not examined by Aristotle and argues that a close look at the context in which Aristotle discusses Zeno holds the (...) answer to this question. (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)