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57-485: Huizi may refer to: Hui Shi (380 BC – 305 BC), Chinese philosopher Huizi (currency) , banknote of the Chinese Southern Song dynasty Topics referred to by the same term [REDACTED] This disambiguation page lists articles associated with the title Huizi . If an internal link led you here, you may wish to change the link to point directly to

114-512: A different perspective, highlighting Zeno's significant early insight into the complexities of infinity and continuous motion. Zeno's paradoxes remain a pivotal reference point in the philosophical and mathematical exploration of reality, motion, and the infinite, influencing both ancient thought and modern scientific understanding. The origins of the paradoxes are somewhat unclear, but they are generally thought to have been developed to support Parmenides ' doctrine of monism , that all of reality

171-632: A digital controller. Roughly contemporaneously during the Warring States period (475–221 BCE), ancient Chinese philosophers from the School of Names , a school of thought similarly concerned with logic and dialectics, developed paradoxes similar to those of Zeno. The works of the School of Names have largely been lost, with the exception of portions of the Gongsun Longzi . The second of

228-434: A few are definitively known today, including the renowned "Achilles Paradox", which illustrates the problematic concept of infinite divisibility in space and time . In this paradox, Zeno argues that a swift runner like Achilles cannot overtake a slower moving tortoise with a head start, because the distance between them can be infinitely subdivided, implying Achilles would require an infinite number of steps to catch

285-459: A fish ‑ so that still proves you don't know what fish enjoy!" Chuang Tzu said, "Let's go back to your original question, please. You asked me how I know what fish enjoy ‑ so you already knew I knew it when you asked the question. I know it by standing here beside the Hao." According to these ancient Daoist stories, Zhuangzi and Hui Shi remained friendly rivals until death. Chuang Tzu was accompanying

342-416: A funeral when he passed by the grave of Hui Tzu. Turning to his attendants, he said, "There was once a plasterer who, if he got a speck of mud on the tip of his nose no thicker than a fly's wing, would get his friend Carpenter Shih to slice it off for him. Carpenter Shih, whirling his hatchet with a noise like the wind, would accept the assignment and proceed to slice, removing every bit of mud without injury to

399-414: A man here who doesn’t know what a dan is. If he says, ‘What are the features of a dan like?’ and we answer, saying, ‘The features of a dan are like a dan,’ then would that communicate it?” The King said, “It would not.” “Then if we instead answered, ‘The features of a dan are like a bow, but with a bamboo string,’ then would he know?” The King said, “It can be known.” Hui Shi said, “Explanations are inherently

456-467: A matter of using what a person knows to communicate what he doesn’t know, thereby causing him to know it. Now if you say, ‘No analogies,’ that’s inadmissible.” The King said, “Good!” A. C. Graham argues that this philosophical position suggests some affinity between Hui Shi and the Mohists , in their shared opinion that "the function of names is to communicate that an object is like the objects one knows by

513-400: A mother." "If from a stick a foot long you every day take the half of it, in a myriad ages it will not be exhausted." It was in this way that the debaters responded to Hui Shi, all their lifetime, without coming to an end. The last statement in particular, "if from a stick a foot long you every day take the half of it, in a myriad ages it will not be exhausted" is notable for its resemblance to

570-599: A philosophical partnership, of two like-minded but disagreeing intellectual companions engaged in the joys of productive philosophical argument." Zeno%27s paradoxes#Dichotomy paradox Zeno's paradoxes are a series of philosophical arguments presented by the ancient Greek philosopher Zeno of Elea (c. 490–430 BC), primarily known through the works of Plato , Aristotle , and later commentators like Simplicius of Cilicia . Zeno devised these paradoxes to support his teacher Parmenides 's philosophy of monism , which posits that despite our sensory experiences, reality

627-471: A quantity of the air as it would move if this part were by itself: for no part even exists otherwise than potentially. Description from Nick Huggett: This is a Parmenidean argument that one cannot trust one's sense of hearing. Aristotle's response seems to be that even inaudible sounds can add to an audible sound. From Aristotle: ... concerning the two rows of bodies, each row being composed of an equal number of bodies of equal size, passing each other on

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684-500: A quarter of the way there. Before traveling a quarter, she must travel one-eighth; before an eighth, one-sixteenth; and so on. The resulting sequence can be represented as: This description requires one to complete an infinite number of tasks, which Zeno maintains is an impossibility. This sequence also presents a second problem in that it contains no first distance to run, for any possible ( finite ) first distance could be divided in half, and hence would not be first after all. Hence,

741-424: A race, the quickest runner can never over­take the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead. In the paradox of Achilles and the tortoise , Achilles is in a footrace with a tortoise. Achilles allows the tortoise a head start of 100 meters, for example. Suppose that each racer starts running at some constant speed, one faster than

798-579: A race-course as they proceed with equal velocity in opposite directions, the one row originally occupying the space between the goal and the middle point of the course and the other that between the middle point and the starting-post. This...involves the conclusion that half a given time is equal to double that time. An expanded account of Zeno's arguments, as presented by Aristotle, is given in Simplicius's commentary On Aristotle's Physics . According to Angie Hobbs of Sheffield university, this paradox

855-431: A response to some of them. Popular literature often misrepresents Zeno's arguments. For example, Zeno is often said to have argued that the sum of an infinite number of terms must itself be infinite–with the result that not only the time, but also the distance to be travelled, become infinite. However, none of the original ancient sources has Zeno discussing the sum of any infinite series. Simplicius has Zeno saying "it

912-524: A solution to this paradox by arguing that in moving across a measured length, the distance is not covered in successive fractions of the length, but in one stage. Due to the lack of surviving works, most of the other paradoxes listed are difficult to interpret. A dialogue in the Shuo Yuan portrays Hui Shi as having a tendency to overuse analogies ( 譬 pi , which can also be translated as "illustrative examples") with Hui Shi justifying this habit with

969-481: A solution to this paradox by arguing that in moving across a measured length, the distance is not covered in successive fractions of the length, but in one stage. Due to the lack of surviving works from the School of Names, most of the other paradoxes listed are difficult to interpret. "What the Tortoise Said to Achilles", written in 1895 by Lewis Carroll , describes a paradoxical infinite regress argument in

1026-408: A thousand grains make a sound. Hence a thousand nothings become something, an absurd conclusion. Aristotle's response: Zeno's reasoning is false when he argues that there is no part of the millet that does not make a sound: for there is no reason why any such part should not in any length of time fail to move the air that the whole bushel moves in falling. In fact it does not of itself move even such

1083-464: A unit of space that can be mentally divided into ever smaller units while remaining spatially the same) from things (or distances) that are infinite in extension ("with respect to their extremities"). Aristotle's objection to the arrow paradox was that "Time is not composed of indivisible nows any more than any other magnitude is composed of indivisibles." Thomas Aquinas , commenting on Aristotle's objection, wrote "Instants are not parts of time, for time

1140-416: Is impossible to traverse an infinite number of things in a finite time". This presents Zeno's problem not with finding the sum , but rather with finishing a task with an infinite number of steps: how can one ever get from A to B, if an infinite number of (non-instantaneous) events can be identified that need to precede the arrival at B, and one cannot reach even the beginning of a "last event"? Three of

1197-535: Is intended to be considered together with the paradox of Achilles and the Tortoise, problematizing the concept of discrete space & time where the other problematizes the concept of infinitely divisible space & time. According to Simplicius , Diogenes the Cynic said nothing upon hearing Zeno's arguments, but stood up and walked, in order to demonstrate the falsity of Zeno's conclusions. To fully solve any of

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1254-459: Is just change in position over time. Another proposed solution is to question one of the assumptions Zeno used in his paradoxes (particularly the Dichotomy), which is that between any two different points in space (or time), there is always another point. Without this assumption there are only a finite number of distances between two points, hence there is no infinite sequence of movements, and

1311-495: Is not made up of instants any more than a magnitude is made of points, as we have already proved. Hence it does not follow that a thing is not in motion in a given time, just because it is not in motion in any instant of that time." Some mathematicians and historians, such as Carl Boyer , hold that Zeno's paradoxes are simply mathematical problems, for which modern calculus provides a mathematical solution. Infinite processes remained theoretically troublesome in mathematics until

1368-412: Is one, and that all change is impossible , that is, that nothing ever changes in location or in any other respect. Diogenes Laërtius , citing Favorinus , says that Zeno's teacher Parmenides was the first to introduce the paradox of Achilles and the tortoise. But in a later passage, Laërtius attributes the origin of the paradox to Zeno, explaining that Favorinus disagrees. Modern academics attribute

1425-472: Is singular and unchanging. The paradoxes famously challenge the notions of plurality (the existence of many things), motion, space, and time by suggesting they lead to logical contradictions . Zeno's work, primarily known from second-hand accounts since his original texts are lost, comprises forty "paradoxes of plurality," which argue against the coherence of believing in multiple existences, and several arguments against motion and change. Of these, only

1482-407: Is therefore motionless at that instant of time and at the next instant of time but if both instants of time are taken as the same instant or continuous instant of time then it is in motion. In the arrow paradox, Zeno states that for motion to occur, an object must change the position which it occupies. He gives an example of an arrow in flight. He states that at any one (durationless) instant of time,

1539-466: The Tian Xia does not, however, explain how Hui Shi argued these theses. Though the theses seem haphazard, and the list lacking in logical structure, Chris Fraser argues that they can be divided into four natural groups: Another passage from the Tian Xia attributes 21 more paradoxes to Hui Shi and other members of the School of Names, which they are said to have used in their debates. Compared to

1596-477: The Dichotomy paradox described by Zeno of Elea . Zeno's paradox takes the example of a runner on a finite race track, arguing that, because runner must reach the halfway point before they can reach the finish line, and the length of the track can be divided into halves infinitely many times, it should be impossible for them to reach the finish line in a finite amount of time. The Mohist canon appears to propose

1653-592: The Tang dynasty . For this reason, knowledge of his philosophy relies on the several Chinese classic texts that refer to him, including the Zhan Guo Ce , Lüshi Chunqiu , Han Feizi , Xunzi , and most frequently, the Zhuangzi . Nine Zhuangzi chapters mention Hui Shi, calling him "Huizi" 26 times and "Hui Shi" 9 times. "Under Heaven" (chapter 33), which summarizes Warring States philosophies, contains all of

1710-467: The Ten Theses listed above, they appear even more absurd and unsolvable:       惠施以此為大觀於天下而曉辯者，天下之辯者相與樂之。卵有毛，雞三足，郢有天下，犬可以為羊，馬有卵，丁子有尾，火不熱，山出口，輪不蹍地，目不見，指不至，至不絕，龜長於蛇，矩不方，規不可以為圓，鑿不圍枘，飛鳥之景未嘗動也，鏃矢之疾而有不行不止之時，狗非犬，黃馬、驪牛三，白狗黑，孤駒未嘗有母，一尺之捶，日取其半，萬世不竭。辯者以此與惠施相應，終身無窮。       Hui Shi by such sayings as these made himself very conspicuous throughout the kingdom, and

1767-405: The Ten Theses of Hui Shi suggests knowledge of infinitesimals: That which has no thickness cannot be piled up; yet it is a thousand li in dimension. Among the many puzzles of his recorded in the Zhuangzi is one very similar to Zeno's Dichotomy: "If from a stick a foot long you every day take the half of it, in a myriad ages it will not be exhausted." The Mohist canon appears to propose

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1824-492: The Tile Argument can be resolved, and that discretization can therefore remove the paradox. In 1977, physicists E. C. George Sudarshan and B. Misra discovered that the dynamical evolution ( motion ) of a quantum system can be hindered (or even inhibited) through observation of the system . This effect is usually called the " Quantum Zeno effect " as it is strongly reminiscent of Zeno's arrow paradox. This effect

1881-407: The arrow is neither moving to where it is, nor to where it is not. It cannot move to where it is not, because no time elapses for it to move there; it cannot move to where it is, because it is already there. In other words, at every instant of time there is no motion occurring. If everything is motionless at every instant, and time is entirely composed of instants, then motion is impossible. Whereas

1938-459: The claim that communication is impossible without analogies: A client said to the King of Liang, “In talking about things, Hui Shi is fond of using analogies. If you don’t let him use analogies, he won’t be able to speak.” The King said, “Agreed.” The next day he saw Hui Shi and said, “I wish that when you speak about things, you speak directly, without using analogies.” Hui Shi said, “Suppose there’s

1995-443: The conclusion that instants in time and instantaneous magnitudes do not physically exist. Lynds argues that an object in relative motion cannot have an instantaneous or determined relative position (for if it did, it could not be in motion), and so cannot have its motion fractionally dissected as if it does, as is assumed by the paradoxes. Nick Huggett argues that Zeno is assuming the conclusion when he says that objects that occupy

2052-466: The dam of the Hao River when Chuang Tzu said, "See how the minnows come out and dart around where they please! That's what fish really enjoy!" Hui Tzu said, "You're not a fish - how do you know what fish enjoy?" Chuang Tzu said, "You're not I, so how do you know I don't know what fish enjoy?" Hui Tzu said, "I'm not you, so I certainly don't know what you know. On the other hand, you're certainly not

2109-488: The end. It may be that Zeno's arguments on motion, because of their simplicity and universality, will always serve as a kind of ' Rorschach image ' onto which people can project their most fundamental phenomenological concerns (if they have any)." An alternative conclusion, proposed by Henri Bergson in his 1896 book Matter and Memory , is that, while the path is divisible, the motion is not. In 2003, Peter Lynds argued that all of Zeno's motion paradoxes are resolved by

2166-426: The end." "The tortoise is longer than the snake." "The carpenter's square is not square." "A compass should not itself be round." "A chisel does not surround its handle." "The shadow of a flying bird does not [itself] move." "Swift as the arrowhead is, there is a time when it is neither flying nor at rest." "A dog is not a hound." "A bay horse and a black ox are three." "A white dog is black." "A motherless colt never had

2223-502: The first two paradoxes divide space, this paradox starts by dividing time—and not into segments, but into points. Aristotle gives three other paradoxes. From Aristotle: If everything that exists has a place, place too will have a place, and so on ad infinitum . Description of the paradox from the Routledge Dictionary of Philosophy : The argument is that a single grain of millet makes no sound upon falling, but

2280-440: The intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=Huizi&oldid=1246780949 " Category : Disambiguation pages Hidden categories: Short description is different from Wikidata All article disambiguation pages All disambiguation pages Hui Shi The Yiwenzhi attributes a philosophical work to Hui Shi, but it is no longer extant, probably being lost prior to

2337-428: The late 19th century. With the epsilon-delta definition of limit , Weierstrass and Cauchy developed a rigorous formulation of the logic and calculus involved. These works resolved the mathematics involving infinite processes. Some philosophers , however, say that Zeno's paradoxes and their variations (see Thomson's lamp ) remain relevant metaphysical problems. While mathematics can calculate where and when

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2394-572: The latter 9 references by name. Belonging to the School of Names , Hui Shi's philosophy is characterised by arguments centred around the relativity of the concepts of sameness ( 同 tong ) and difference ( 異 yi ). He frequently used analogies and paradoxes to convey his arguments. The final chapter of the Zhuangzi , Tian Xia ( 天下 'Under Heaven') claims that Hui Shi held ten main opinions, referred to as "The Ten Theses" or "The Ten Paradoxes", and lists them as follows: The list in

2451-521: The moving Achilles will overtake the Tortoise of Zeno's paradox, philosophers such as Kevin Brown and Francis Moorcroft hold that mathematics does not address the central point in Zeno's argument, and that solving the mathematical issues does not solve every issue the paradoxes raise. Brown concludes "Given the history of 'final resolutions', from Aristotle onwards, it's probably foolhardy to think we've reached

2508-530: The name" Most of the other Zhuangzi passages portray Hui Shi (Huizi) as a friendly rival of Zhuangzi ( Wade–Giles : Chuang Tzu ). Hui Shi acts as an intellectual foil who argues the alternative viewpoint, or criticizes the Daoist perspective, often with moments of humor. The best known of the Zhuang-Hui dialogues concerns the subjectivity of happiness. Chuang Tzu and Hui Tzu were strolling along

2565-491: The nose, while the plasterer just stood there completely unperturbed. Lord Yuan of Sung, hearing of this feat, summoned Carpenter Shih and said, 'Could you try performing it for me?' But Carpenter Shih replied, 'It's true that I was once able to slice like that but the material I worked on has been dead these many years.' Since you died, Master Hui, I have had no material to work on. There's no one I can talk to any more." Chad Hansen (2003:146) interprets this lament as "the loss of

2622-442: The other. After some finite time, Achilles will have run 100 meters, bringing him to the tortoise's starting point. During this time, the tortoise has run a much shorter distance, say 2 meters. It will then take Achilles some further time to run that distance, by which time the tortoise will have advanced farther; and then more time still to reach this third point, while the tortoise moves ahead. Thus, whenever Achilles arrives somewhere

2679-436: The paradox is resolved. According to Hermann Weyl , the assumption that space is made of finite and discrete units is subject to a further problem, given by the " tile argument " or "distance function problem". According to this, the length of the hypotenuse of a right angled triangle in discretized space is always equal to the length of one of the two sides, in contradiction to geometry. Jean Paul Van Bendegem has argued that

2736-506: The paradox to Zeno. Many of these paradoxes argue that contrary to the evidence of one's senses, motion is nothing but an illusion . In Plato's Parmenides (128a–d), Zeno is characterized as taking on the project of creating these paradoxes because other philosophers claimed paradoxes arise when considering Parmenides' view. Zeno's arguments may then be early examples of a method of proof called reductio ad absurdum , also known as proof by contradiction . Thus Plato has Zeno say

2793-497: The paradoxes, however, one needs to show what is wrong with the argument, not just the conclusions. Throughout history several solutions have been proposed, among the earliest recorded being those of Aristotle and Archimedes. Aristotle (384 BC–322 BC) remarked that as the distance decreases, the time needed to cover those distances also decreases, so that the time needed also becomes increasingly small. Aristotle also distinguished "things infinite in respect of divisibility" (such as

2850-609: The purpose of the paradoxes "is to show that their hypothesis that existences are many, if properly followed up, leads to still more absurd results than the hypothesis that they are one." Plato has Socrates claim that Zeno and Parmenides were essentially arguing exactly the same point. They are also credited as a source of the dialectic method used by Socrates. Some of Zeno's nine surviving paradoxes (preserved in Aristotle's Physics and Simplicius's commentary thereon) are essentially equivalent to one another. Aristotle offered

2907-487: The same space as they do at rest must be at rest. Based on the work of Georg Cantor , Bertrand Russell offered a solution to the paradoxes, what is known as the "at-at theory of motion". It agrees that there can be no motion "during" a durationless instant, and contends that all that is required for motion is that the arrow be at one point at one time, at another point another time, and at appropriate points between those two points for intervening times. In this view motion

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2964-406: The strongest and most famous—that of Achilles and the tortoise, the Dichotomy argument, and that of an arrow in flight—are presented in detail below. That which is in locomotion must arrive at the half-way stage before it arrives at the goal. Suppose Atalanta wishes to walk to the end of a path. Before she can get there, she must get halfway there. Before she can get halfway there, she must get

3021-461: The tortoise has been, he still has some distance to go before he can even reach the tortoise. As Aristotle noted, this argument is similar to the Dichotomy. It lacks, however, the apparent conclusion of motionlessness. If everything when it occupies an equal space is at rest at that instant of time, and if that which is in locomotion is always occupying such a space at any moment, the flying arrow

3078-413: The tortoise. These paradoxes have stirred extensive philosophical and mathematical discussion throughout history , particularly regarding the nature of infinity and the continuity of space and time. Initially, Aristotle 's interpretation, suggesting a potential rather than actual infinity, was widely accepted. However, modern solutions leveraging the mathematical framework of calculus have provided

3135-474: The trip cannot even begin. The paradoxical conclusion then would be that travel over any finite distance can be neither completed nor begun, and so all motion must be an illusion . This argument is called the " Dichotomy " because it involves repeatedly splitting a distance into two parts. An example with the original sense can be found in an asymptote . It is also known as the Race Course paradox. In

3192-507: Was considered an able debater. All other debaters vied with one another and delighted in similar exhibitions. [They would say,] "There are feathers in an egg." "A fowl has three feet." "The kingdom belongs to Ying." "A dog might have been [called] a sheep." "A horse has eggs." "A tadpole has a tail." "Fire is not hot." "A mountain gives forth a voice." "A wheel does not tread on the ground." "The eye does not see." "The finger indicates, but needs not touch [the object]." "Where you come to may not be

3249-476: Was first theorized in 1958. In the field of verification and design of timed and hybrid systems , the system behaviour is called Zeno if it includes an infinite number of discrete steps in a finite amount of time. Some formal verification techniques exclude these behaviours from analysis, if they are not equivalent to non-Zeno behaviour. In systems design these behaviours will also often be excluded from system models, since they cannot be implemented with

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