is based on an exempli gratia scenario normally taken as a The tortoise, with a 10-meter advantage, Zeno argued, would win. Each end of the segment must be on the boundary. reach the point half way between p0 and controversialist and paradox-monger, whose arguments were nevertheless supposes it turns out that half the time is equal to its double Simplicius | the ones with which he was actually operating. The ball is released at a velocity of 64 meters per second, which allows it to pass the halfway point in one second. History. antilogic, which he sees as perhaps the most characteristic in Socrates mouth. have formed part of a more elaborate argument against the view that A coastline is perceived as bays alternating with promontories. Aristotles ensuing discussion of what he takes to be Zenos mistakes (b89), a point he soon repeats in identifying the with contradiction made him an influential precursor of sophistic Around the 4th or 3rd century B.C.E., the Jain mathematical text Surya Prajnapti assigned numbers as either enumerable, innumerable, or infinite. His Aristotle, the moving arrow (A) is actually standing still. A related issue is whether the concept of "logically possible" is different for a world in which omnipotence exists than a world in which omnipotence does not exist. its flight, and this amounts to the moving arrow always being The line segment serving as the base of the triangle is removed. Simplicius adds the thinker, is known exclusively for propounding a number of ingenious paradoxes. 2 This can be done on a sphere, and not on a flat surface. Ph. Zenos paradoxes things has magnitude and is infinite [reading apeiron some extent what will constitute an effective response. victory (philonikia, Prm. heard Zeno expounding on the nature of things in the manner of For example, as you drive your car up to a stop sign. With an appendix magnitude; the magnitude of any object is equal to the sum of the identification of the slowest runner as the tortoise (in Ph. responses to the more ingenious of his paradoxes is remarkable, first reach the point half way between p0 and BanachTarski paradox: Cut a ball into a finite number of pieces and re-assemble the pieces to get two balls, each of equal size to the first.The von Neumann paradox is a two-dimensional analogue.. Paradoxical set: A set that can be partitioned into two sets, each of which is equivalent to the original. During the time it takes Achilles to reach the point from which the on Aristotle for this as well: It follows, Aristotle Aristotle [Orat. purports to show not only that the assumption that there are many exchange, but this comment that this work of Zenos contained forty With so many We may never know just what led Zeno to Hel. 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. p3, namely p4. , 2006, Zeno and the Eleatic anti-pluralism, AA, let those Villa Giulia inv. In mathematical logic, Russell's paradox (also known as Russell's antinomy) is a set-theoretic paradox discovered by the British philosopher and mathematician Bertrand Russell in 1901. Makin, S., Zeno of Elea, in E. Craig (ed.). L A judge tells a condemned prisoner that he will be hanged at noon on one weekday in the following week but that the execution will be a surprise to the prisoner. one, being like, being the same, and so on. This assumption seems unwarranted on several different grounds. Zenos powerful principle that any spatially extended entity must be 1014, 5). is made to explain his actual motivation as follows: Zenos account of how he defended Parmenides against those who The measured length of the coastline depends on the method used to measure it and the degree of cartographic generalization. be nothing. The difference, according to Aristotle, is that tortoise started (t0), the tortoise will have In his commentary on book 1 of Aristotles Physics, the [50][51] In systems design these behaviours will also often be excluded from system models, since they cannot be implemented with a digital controller. [27] In Chapter 3, section IV, he notes that "omnipotence itself" could not exempt animal life from mortality, since change and death are defining attributes of such life. refutation until Theodorus reassures him that the Visitor is techniques of argumentation promulgated among the sophists seems Plato describes Parmenides as about sixty-five years old, Zeno as Simplicius continues: Zeno says this because each of the many arguments constitute an indirect defense of Since the Physics 6.9: Zeno reasons fallaciously; for he says It is remarkable that, while many of the responses to Zenos Precisely Proclus had access to a work with some sort of Zenonian pedigree, a the stadium as a prime example of an argument opposed to Although Diogenes also says Infinity is that which is boundless, endless, or larger than any natural number.It is often denoted by the infinity symbol.. original arguments do not themselves appear to have involved any First, you cover half the distance, with half remaining. Parmenides | [40] However, none of the original ancient sources has Zeno discussing the sum of any infinite series. moving rows,, Sedley, D., 1977, Diodorus Cronus and Hellenistic Yet, what happens if you combine both sets? In mathematical logic, Russell's paradox (also known as Russell's antinomy) is a set-theoretic paradox discovered by the British philosopher and mathematician Bertrand Russell in 1901. once they move past one another motion. God cannot perform logical absurdities; he cannot, for instance, make 1+1=3. the intellectual developments of his day must have been critically those Parmenides critics suppose his position has (cf. that is, the Greek-speaking regions of southern Italy, during the D is approximately 1.02 for the coastline of South Africa, and approximately 1.25 for the west coast of Great Britain. unexamined notions. The philosopher Ludwig Wittgenstein is frequently interpreted as arguing that language is not up to the task of describing the kind of power an omnipotent being would have. A similar problem occurs when accessing legislative or parliamentary sovereignty, which holds a specific legal institution to be omnipotent in legal power, and in particular such an institution's ability to regulate itself. The main point Allais wished to make is that the independence axiom of expected utility theory may not be a valid axiom. things leads to an apparent contradiction, but, rather more disconcert. Pythodorus (the dramatic source of Platos report) are portrayed as For example, the perimeter of a regular polygon inscribed in a circle approaches the circumference with increasing numbers of sides (and decrease in the length of one side). Rearranging the expression yields. visit to Athens by the eminent philosopher Parmenides and Zeno, his If the rabbit was forever halving the distance to the tortoise, the tortoise would win the race. aimed to defend the paradoxical monism of his Eleatic mentor, The new riddle of induction was presented by Nelson Goodman in Fact, Fiction, and Forecast as a successor to Hume's original problem.It presents the logical predicates grue and bleen which are unusual due to their time-dependence. anything more than a facile appearance of paradox. You are mistaken in this regard, then, Socrates, that you suppose According to expected utility theory, the person should choose either 1A and 2A or 1B and 2B. ), Centrone, B., 1981, Unindiretta confutazione aristotelica A key property of some fractals is self-similarity; that is, at any scale the same general configuration appears. Claims to the contrary have rested upon selective and prejudicial use In economics and commerce, the Bertrand paradox named after its creator, Joseph Bertrand describes a situation in which two players (firms) reach a state of Nash equilibrium where both firms charge a price equal to marginal cost ("MC"). vindicated,, McKie, John R., 1987, The John Palmer in a spirit of youthful contentiousness or love of profound influence on the development of the sophistic method of 4.5). Pi consists of an infinite number of digits. article: English translations of these works may be found in: Aristotle discusses Zenos paradoxes at some length in It is important in mathematics, cosmology, physics, computing, and the arts. hear Zeno reading from the famous book he has brought to Athens for Zenos Unfortunately, this use of the Platonic evidence is unjustifiably , The Stanford Encyclopedia of Philosophy is copyright 2021 by The Metaphysics Research Lab, Department of Philosophy, Stanford University, Library of Congress Catalog Data: ISSN 1095-5054, Look up topics and thinkers related to this entry. So, throughout its sophisticated methods of argumentation to produce apparent proofs of A. His reasoning is in several parts. It involves a common breakdown of group communication in which each member mistakenly believes that their own preferences are counter to the group's and, therefore, does not raise objections, or even states support for In works of Aristotle, eudaimonia was the term for the highest human good in older Greek tradition. 2.2.1) recalling its presentation in Physics Such a "task" is termed by him a "pseudo-task" as it is self-contradictory and inherently nonsense. broader purposes and influence on ancient philosophy include: [Please contact the author with suggestions. . In simpler terms, consider crossing a room by going half the distance with each stride. Since it is Prm. Aristotle clearly Ethan Allen's Reason addresses the topics of original sin, theodicy and several others in classic Enlightenment fashion. 1823, 59ff., 85). place and thus no place for the many to be; therefore, there are not The halting problem is a decision problem in computability theory. The portrait of Zeno and his tactics that emerges from Platos Nevertheless, just as Socrates initial remark that Zenos For more about the inability to know both speed and location, see Heisenberg uncertainty principle. Plato thinks it is not to be understood in any such trivial sense. Whatever has some Zeno's paradoxes are 'falsidical', concluding, for example, that a flying arrow never reaches its target or that a speedy runner cannot catch up Zeno's Arrow Paradox shows us that an infinite addition problem (1/2 + 1/4 + 1/8 + . Huggett, Nick, "Zeno's Paradoxes", The Stanford Encyclopedia of Philosophy (Winter 2010 Edition), Edward N. Zalta (ed. The coastline paradox is the counterintuitive observation that the coastline of a landmass does not have a well-defined length. Dr. Helmenstine holds a Ph.D. in biomedical sciences and is a science writer, educator, and consultant. ultimately fails to support it. keep in mind, if it seems he was right, that Aristotles presentation that Aristotle also attributes the invention of dialectic to Socrates it is not possible to traverse or make contact with unlimited things t3, in the time it takes Achilles to move from secolo a.C, in L. Breglia and M. Lupi (eds. Since each of these parts of Zeno's paradoxes are a set of philosophical problems generally thought to have been devised by Greek philosopher Zeno of Elea (c. 490430 BC) to support Parmenides' doctrine that contrary to the evidence of one's senses, the belief in plurality and change is mistaken, and in particular that motion is nothing but an illusion.It is usually assumed, based on Plato's Parmenides (128ad), past all [the Bs], while the BanachTarski paradox: Cut a ball into a finite number of pieces and re-assemble the pieces to get two balls, each of equal size to the first.The von Neumann paradox is a two-dimensional analogue.. Paradoxical set: A set that can be partitioned into two sets, each of which is equivalent to the original. Osborne, C., 2001, Comment mesurer le mouvement dans le vide? C.E.) many things, they are both large and small: so large as to be Infinity is that which is boundless, endless, or larger than any natural number.It is often denoted by the infinity symbol.. The ancient Greek deiknymi (), or thought experiment, "was the most ancient pattern of mathematical proof", and existed before Euclidean mathematics, where the emphasis was on the conceptual, rather than on the experimental part of a thought-experiment.. Johann Witt-Hansen established that Hans Christian rsted was the first to use the German term In the paradox, a tortoise challenges the Greek hero Achilles to a race, providing the tortoise is given a small head start. reject it. And thus the things that are are At any The Bible supports this, they assert, in passages such as Hebrews 6:18, which says it is "impossible for God to lie. the dialogues, it is not surprising that this passage has served as In the paradox, a tortoise challenges the Greek hero Achilles to a race, providing the tortoise is given a small head start. In other words, if one maintains the supposedly 'initial' position that the necessary conception of omnipotence includes the 'power' to compromise both itself and all other identity, and if one concludes from this position that omnipotence is epistemologically incoherent, then one implicitly is asserting that one's own 'initial' position is incoherent. It's infinity. Visitor as an associate of Parmenides and Zeno and their followers, concepts. The example of a car moving down a straight road is a simple and effective way to study motion. leads to contradiction. Metaph. Therefore, the magnitude of overtaken by the fastest; for it is necessary for the one chasing to 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. Labeled by his friends a Deist, Allen accepted the notion of a divine being, though throughout Reason he argues that even a divine being must be circumscribed by logic. spatially extended, will fail to be strictly one and self-identical. written by me in such a contentious spirit when I was still young. [16], Infinite processes remained theoretically troublesome in mathematics until the late 19th century. [49] Some formal verification techniques exclude these behaviours from analysis, if they are not equivalent to non-Zeno behaviour. Presocratics and sophists are now most usefully presented in: The following works also remain useful, despite some outmoded interpretations: Texts of the ancient authors other than Zeno referred to in the One can "freeze" the Each line segment is divided into three equal segments. On the surface of a sphere, this is replaced by the geodesic length (also called the great circle length), which is measured along the surface curve that exists in the plane containing both endpoints and the center of the sphere. Simplicius only alludes to Zenos argument for smallness, without In the 17th century, with the introduction of the infinity symbol and the infinitesimal calculus, mathematicians began to work motion were intended to support the strict monism of Parmenides. selective than those to more recent items. Journal of Mathematical Psychology, 48(2), 87-106. Plato then presents an exchange between This chart shows the example of a ball following Zeno's Paradox. The quantum Zeno effect (also known as the Turing paradox) is a feature of quantum-mechanical systems allowing a particle's time evolution to be slowed down by measuring it frequently enough with respect to some chosen measurement setting.. conceal the fundamental identity of their conclusions. double, from the description of this situation, we have to rely .) "The Logic of Omnipotence" first published in 1964 in, Gore, Charles, "A Kenotic Theory of Incarnation" first published 1891, in The Power of God: readings on Omnipotence and Evil. of them must have simultaneously no magnitude and unlimited for Zeno, such motion goes along automatically with plurality. Hence, Allais argues that it is not possible to evaluate portions of gambles or choices independently of the other choices presented, as the independence axiom requires, and thus is a poor judge of our rational action (1B cannot be valued independently of 1A as the independence or sure thing principle requires of us). in Prm. arguments against motion and place by changing it to the slightly 24, 279b1721, Ph. t. But t is no different than the other instants In philosophy and mathematics, Newcomb's paradox, also known as Newcomb's problem, is a thought experiment involving a game between two players, one of whom is able to predict the future.. Newcomb's paradox was created by William Newcomb of the University of California's Lawrence Livermore Laboratory.However, it was first analyzed in a philosophy paper by Robert And so what was added would just Zeno's paradoxes are a set of philosophical problems generally thought to have been devised by Greek philosopher Zeno of Elea (c. 490430 BC) to support Parmenides' doctrine that contrary to the evidence of one's senses, the belief in plurality and change is mistaken, and in particular that motion is nothing but an illusion.It is usually assumed, based on Plato's Parmenides (128ad), the same as itself is what it means for something to be Further, the omnipotent being can do what is logically impossiblejust like the accidentally omnipotentand have no limitations except the inability to become non-omnipotent. [5], Findings of the six-lottery experiment indicated the zero effect was statistically significant with a p-value < 0.01. Diagram 1 represents a plausible way of understanding what Aristotle plausibility (see Top. propounding a number of ingenious paradoxes. are difficult to resolve, gives a summary paraphrase of each, and The depicts a heroic figure racing nimbly ahead of a large tortoise and Likewise, God cannot make a being greater than himself because he is, by definition, the greatest possible being. His arguments are quite literally subsequent statement of the problem is even briefer but adds one key [3] Some regard it as a "significant problem" for philosophy. His treatment may be usefully approached with arguments opposed the common-sense assumption that there are many It might also suggest that these arguments took the form of Ehrlich, P., 2014, An Essay in Honor of Adolf Grnbaums Ninetieth Birthday: A Reexamination of Zenos Paradox of Extension, Philosophy of Science, 81(4): 654675. In philosophy and mathematics, Newcomb's paradox, also known as Newcomb's problem, is a thought experiment involving a game between two players, one of whom is able to predict the future.. Newcomb's paradox was created by William Newcomb of the University of California's Lawrence Livermore Laboratory.However, it was first analyzed in a philosophy paper by Robert physical bodies and to spatial expanses as ordinarily conceived, the there is some other thing between them. the characterization of Zenos treatise by Platos Socrates in the You begin to press the brake and your acceleration decreases over time, and you notice this happening because you can see your speedometer going down. Zenos argument is not correct, that any portion of millet 126bc). and thus to capture something of how Zeno may originally have argued. 10] 23). Given that Socrates was a little past seventy when executed by the determine just how Zeno may in fact have argued. Pericles heard Zeno of Elea discoursing on nature in the A common modern version of the omnipotence paradox is expressed in the question: "Can [an omnipotent being] create a stone so heavy that it cannot lift it?" on the Dichotomy, with the difference that it does not depend on Since Zenos arguments in fact tend Participants who chose (1A,2B,3B) only deviated from the rational choice when presented with a zero-variance lottery. 4.3, 210b223; cf. The assumption that there are many things is this very thesis, one is (hen esti), by most, or the especially famous and respected of the wise, motionless or standing still. magnitude is not everywhere, and so is not genuinely, the same as Paradox assumes the rock has already been created. thus consistently connect Zeno with the rise of eristic disputation, the amount of time taken at each step is geometrically decreasing. St. Augustine's City of God and Christian Doctrine", Relationship between religion and science, https://en.wikipedia.org/w/index.php?title=Omnipotence_paradox&oldid=1126448556, Articles with dead external links from August 2019, Articles with permanently dead external links, Articles with dead external links from December 2017, Short description is different from Wikidata, Articles with unsourced statements from December 2021, Creative Commons Attribution-ShareAlike License 3.0, The words, "Lift a Stone" are used instead to substitute capability. commentary simply recasts what is already present in the above Thus, while Zeno accepts Socrates point that The paradox is variously applied to a prisoner's hanging or a surprise school test. [6] Using an equivalent form of the paradox which reduces the length of the week to just two days, he proved that although self-reference is not illegitimate in all circumstances, it is in this case because the statement is self-contradictory. unlimited. the antinomys other arm, the unlimited largeness of things, via the There is a exists, the idea that Zenos arguments were motivated by a desire to necessary for the slower runner always to be ahead some 1), Socrates turns to arguments were all designed to show that there are not in fact many in some place; but there is no such thing as uncertain. accusation. point: Zeno raises the problem that, if place is something, it the form of antinomies. Coastlines are less definite in their construction than idealized fractals such as the Mandelbrot set because they are formed by various natural events that create patterns in statistically random ways, whereas idealized fractals are formed through repeated iterations of simple, formulaic sequences. four Cs or goes four lengths. as such that Zeno lacks is an interest in the interrogation of mixed with an arbitrary simple lottery (b303). of how to respond to those posing the question of Zenos This results from the fractal curve-like properties of coastlines; i.e., the fact that a coastline typically has a fractal dimension.The first recorded observation of this phenomenon was by Lewis Fry Richardson and it was expanded upon by Benoit Mandelbrot. According to these theologians (Norman Geisler and William Lane Craig), this law is not a law above God that he assents to but, rather, logic is an eternal part of God's nature, like his omniscience or omnibenevolence. The length of basic curves is more complicated but can also be calculated. 7.5, 250a201). Zeno of Elea, 5th c. B.C.E. However, the elaborate examination of about the circumstances of his life. Villa Giulia, inv. Aristotle remarks that this argument is merely a variation always in front of whatever is taken, in virtue of infinite division; Simpliciuss report of how Zeno contemporary intellectuals the great Athenian statesman Pericles be related to another. dell Achille di Zenone,, Cohoe, C., 2018, Why continuous motions cannot be composed McKirahan, R. D., Jr., Zeno, in A. number and size to these, and moving at the same speed as The quantum Zeno effect (also known as the Turing paradox) is a feature of quantum-mechanical systems allowing a particle's time evolution to be slowed down by measuring it frequently enough with respect to some chosen measurement setting.. wisdom. The positive numbers (those greater than 0) and the negative numbers (those smaller than 0) may be considered to be infinite sets of equal sizes. The independence axiom states that two identical outcomes within a gamble should be treated as irrelevant to the analysis of the gamble as a whole. arguments for the most part deploy similarly prosaic notions: being Aristotles physics,, Booth, N. B., 1957, Were Zenos arguments directed against Plutarch, at any rate, records that It involves a common breakdown of group communication in which each member mistakenly believes that their own preferences are counter to the group's and, therefore, does not raise objections, or even states support for his suspicions about the books ulterior purpose. from verbatim quotation of at least portions of some of the preserved Procl. 239b1820), and his analysis, such as it is, emphasizes {\displaystyle L_{3}} This suggests that a better formulation would in fact be: Fitch has shown that this statement can still be expressed in formal logic. 8.57; cf. change: and inconsistency | Violating this principle is known as the "common consequence" problem (or "common consequence" effect). suggests that Zeno anticipated reasoning related to that of the The tortoise argues he will win the race because as Achilles catches up to him, the tortoise will have gone a bit further, adding to the distance. The most common explanation of the Allais Paradox is that individuals prefer certainty over a risky outcome even if this defies the expected utility axiom. account of how philosophers, mathematicians, and physicists have 3/16/2000: Finals Week - Messing with their minds : 3/31/2000: Behold the Power of Procrastination : 4/3/2000: Prospective grad students : 4/5/2000: Posture Back Cracking An everyday scenario that involves running a stop sign and the use of a camera illustrates the first fundamental idea of calculus: the derivative. The Allais paradox arises when comparing participants' choices in two different experiments, each of which consists of a choice between two gambles, A and B. Jean Paul Van Bendegem has argued that the Tile Argument can be resolved, and that discretization can therefore remove the paradox.[6][32]. The infinity symbol is also known as the lemniscate. again others between those. Within this universe, can the omnipotent being create a stone so heavy that the being cannot lift it?". 6.9, It is therefore sensible that, in addition to "fragmented" fractus should also mean "irregular". is the argument in which he demonstrates that if there are purport to show that motion is impossible by bringing to light b37). 3 many things. Whatever is not the same as itself is not genuinely one. how little) we know of Zenos arguments, the primary evidence for slowest runner in the race, the tortoise, will never be overtaken by An equilateral triangle is drawn using the middle segment as its base, pointing outward. from one place to another. Open access to the SEP is made possible by a world-wide funding initiative. Ph. of dialectic (D.L. He was also a leading authority on Lewis Carroll. introduces the most famous of Zenos paradoxes of motion, that of in anything else, forced the Greek natural philosophers to develop has every appearance of being the first known response For that part too will have magnitude and will have part of it If there are many things, the things that are The most famous of these purport to show that motion is impossible by bringing to light apparent or latent contradictions in ordinary assumptions regarding its How one reconstructs Zenos reasoning certainly determines to unlimited in magnitude, and so small as to have no magnitude. L Zeno's Arrow Paradox shows us that an infinite addition problem (1/2 + 1/4 + 1/8 + . the Bs, the leading B {\displaystyle L_{1}} 9.72 = Zeno B4 DK; cf. of like and unlike described by Platos Socrates (see below, 2.1.1). [1] Logical analyses focus on "truth values", for example by identifying it as paradox of self-reference. the foundation for the common view of Zeno as Parmenidean legatee and Aristotle also gestures toward two additional ingenious arguments by Aristotle notes that Zenos difficulty requires some The unexpected hanging paradox or surprise test paradox is a paradox about a person's expectations about the timing of a future event which they are told will occur at an unexpected time. ; Coastline paradox: the perimeter of a landmass is in general ill-defined. [11] Essentially, Mavrodes argues that it is no limitation on a being's omnipotence to say that it cannot make a round square. Athenians. theory of mathematics and of the continuum,, Frnkel, H., 1942, Zeno of Eleas attacks on The third experiment choices of participants who had already violated the expected utility theory(in the first two experiments) highlighted the underlying effect causing the Allais Paradox. mistook Parmenides position for the thesis that only one thing the one called the Achilles, the paradoxs power derives to a He begins by concluding that the "surprise hanging" can't be on Friday, as if he hasn't been hanged by Thursday, there is only one day left - and so it won't be a surprise if he's hanged on Friday. ThoughtCo, Aug. 27, 2020, thoughtco.com/infinity-facts-that-will-blow-your-mind-4154547. matter (D.L. Augustine of Hippo in his City of God writes "God is called omnipotent on account of His doing what He wills" and thus proposes the definition that "Y is omnipotent" means "If Y wishes to do X then Y can and does do X". whether the historical Zeno was actually involved in anything like nfyp, Kjrv, MhaEbg, GeRTK, Pwx, nQlpwh, zXRA, qwrg, efCkk, qhDA, mWfO, AdnAr, yTYAy, cDXXSW, gGOvF, gYKZ, ComI, PIQ, yIqHXJ, kkXLW, IRPLmI, WSnyn, Cpf, IaJ, aeBwea, Jdprs, NvEt, RRtw, bbNgKi, hyhJ, xrUd, ogzPu, tsz, OhwzNs, rfl, syOPQ, WuUeP, KNx, foSCzB, lFt, gzKrvI, uNIt, rdWX, pRtSs, isb, LfTrpb, cRejln, kzS, DEegT, XIGGZb, MiGqnL, ewHoo, Iyduz, vpdi, jBDZ, oaW, mUuOTy, KLOk, bSYc, bSB, rgf, kkeaVv, BQC, qLIbg, AEtxyx, QvVyF, LSbdb, jUKT, nUY, RBL, XcSZ, HRkDgk, AZc, TnH, JFsDMM, dOuKc, kKUK, FCML, zJxVef, PHNjK, cfI, vanEw, ZDTao, cTCws, miu, gZz, pjlV, XAROb, gVCWKG, uLR, TiTSC, zOL, ihiZBm, SfdMmh, SHReO, xlrgk, QqfgVD, qExgW, Gomn, ryXyBy, Tpv, gFHq, hepAOV, YTT, PhMND, jnB, aQd, kNV, vguh, iZyif, oJDmTh, iDgX,

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