766:(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 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."
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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 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.
722:... concerning the two rows of bodies, each row being composed of an equal number of bodies of equal size, passing each other on 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.
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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.
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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 the end. It may be that Zeno's arguments on motion, because of their simplicity and universality, will always serve as a kind of '
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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
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problems. While mathematics can calculate where and when 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
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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, the arrow is neither moving to where it is, nor to where it is not. It cannot move to
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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 is therefore motionless at that instant of time and at the next instant of time but if both instants of time are taken
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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 the other. After some finite time, Achilles will have run 100 meters, bringing him to the tortoise's starting point.
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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
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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 a quantity of
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commentary thereon) are essentially equivalent to one another. Aristotle offered 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
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Zeno's reasoning, however, is fallacious, when he says that if everything when it occupies an equal space is at rest, and if that which is in locomotion is always occupying such a space at any moment, the flying arrow is therefore motionless. This is false, for time is not composed of indivisible
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In 2003, Peter Lynds argued that all of Zeno's motion paradoxes are resolved by 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
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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 the paradoxes, however, one needs to show what is wrong with the argument, not just the conclusions. Throughout history several solutions have been
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have provided 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
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appears to propose 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
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According to Angie Hobbs of
Sheffield university, this paradox 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.
1839:, while the distances decrease geometrically, such as: 1/2 s for 1/2 m gain, 1/3 s for next 1/4 m gain, 1/4 s for next 1/8 m gain, 1/5 s for next 1/16 m gain, 1/6 s for next 1/32 m gain, etc. In this case, the distances form a convergent series, but the times form a
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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 a quarter of the way there. Before traveling a quarter, she must travel one-eighth; before an eighth, one-sixteenth; and so on.
504:) first distance could be divided in half, and hence would not be first after all. Hence, 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
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of believing in multiple existences, and several arguments against motion and change. Of these, only a few are definitively known today, including the renowned "Achilles
Paradox", which illustrates the problematic concept of infinite divisibility in
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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"?
300:. Thus Plato has Zeno say 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
262:, 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.
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Aristotle's observation that the fractional times also get shorter does not guarantee, in every case, that the task can be completed. One case in which it does not hold is that in which the fractional times decrease in a
887:" 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.
995:, 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
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In 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.
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1056:, describes a paradoxical infinite regress argument in the realm of pure logic. It uses Achilles and the Tortoise as characters in a clear reference to Zeno's paradox of Achilles.
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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.
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Lynds, Peter. Time and
Classical and Quantum Mechanics: Indeterminacy vs. Discontinuity. Foundations of Physics Letter s (Vol. 16, Issue 4, 2003). doi:10.1023/A:1025361725408
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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
225:'s interpretation, suggesting a potential rather than actual infinity, was widely accepted. However, modern solutions leveraging the mathematical framework of
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because other philosophers claimed paradoxes arise when considering
Parmenides' view. Zeno's arguments may then be early examples of a method of proof called
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If the paradoxes are thus stated in the precise mathematical terminology of continuous variables (...) the seeming contradictions resolve themselves.
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2558:"15.6 "Pathological Behavior Classes" in chapter 15 "Hybrid Dynamic Systems: Modeling and Execution" by Pieter J. Mosterman, The Mathworks, Inc."
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has Zeno saying "it is impossible to traverse an infinite number of things in a finite time". This presents Zeno's problem not with finding the
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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.
2564:. Chapman & Hall/CRC Computer and Information Science (hardcover ed.). Boca Raton, Florida, USA: CRC Press. pp. 15–22 to 15–23.
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provides a mathematical solution. Infinite processes remained theoretically troublesome in mathematics until the late 19th century. With the
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developed a rigorous formulation of the logic and calculus involved. These works resolved the mathematics involving infinite processes.
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makes no sound upon falling, but a thousand grains make a sound. Hence a thousand nothings become something, an absurd conclusion.
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these behaviours will also often be excluded from system models, since they cannot be implemented with a digital controller.
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Whereas the first two paradoxes divide space, this paradox starts by dividing time—and not into segments, but into points.
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claim that Zeno and
Parmenides were essentially arguing exactly the same point. They are also credited as a source of the
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Huggett, Nick, "Zeno's Paradoxes", The Stanford Encyclopedia of Philosophy (Winter 2010 Edition), Edward N. Zalta (ed.),
1407:"Why Mathematical Solutions of Zeno's Paradoxes Miss the Point: Zeno's One and Many Relation and Parmenides' Prohibition"
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2095:. Translation 1911 by Nancy Margaret Paul & W. Scott Palmer. George Allen and Unwin. pp. 77–78 of the PDF.
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The origins of the paradoxes are somewhat unclear, but they are generally thought to have been developed to support
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points between those two points for intervening times. In this view motion is just change in position over time.
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This description requires one to complete an infinite number of tasks, which Zeno maintains is an impossibility.
883:, the assumption that space is made of finite and discrete units is subject to a further problem, given by the "
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1843:, the sum of which has no limit. Archimedes developed a more explicitly mathematical approach than Aristotle.
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has argued that the Tile Argument can be resolved, and that discretization can therefore remove the paradox.
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This sequence also presents a second problem in that it contains no first distance to run, for any possible (
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the air as it would move if this part were by itself: for no part even exists otherwise than potentially.
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techniques exclude these behaviours from analysis, if they are not equivalent to non-Zeno behaviour. In
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points, hence there is no infinite sequence of movements, and the paradox is resolved. According to
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934:" as it is strongly reminiscent of Zeno's arrow paradox. This effect was first theorized in 1958.
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2831:. Philosophy and method in the social sciences. Abingdon New York (N.Y.): Routledge. p. 48.
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The Michael Proudfoot, A.R. Lace. Routledge Dictionary of Philosophy. Routledge 2009, p. 445
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That which is in locomotion must arrive at the half-way stage before it arrives at the goal.
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These paradoxes have stirred extensive philosophical and mathematical discussion throughout
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Russell, Bertrand (2002) . "Lecture 6. The Problem of Infinity Considered Historically".
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when he says that objects that occupy the same space as they do at rest must be at rest.
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Khalfin, L.A. (1958). "Contribution to the Decay Theory of a Quasi-Stationary State".
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van Bendegem, Jean Paul (1987). "Discussion:Zeno's Paradoxes and the Tile Argument".
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That which has no thickness cannot be piled up; yet it is a thousand li in dimension.
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if it includes an infinite number of discrete steps in a finite amount of time. Some
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2749:"School of Names > Miscellaneous Paradoxes (Stanford Encyclopedia of Philosophy)"
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The Presocratic Philosophers: A Critical History with a Selection of Texts, 2nd ed.
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Our Knowledge of the External World: As a Field for Scientific Method in Philosophy
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An expanded account of Zeno's arguments, as presented by Aristotle, is given in
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proposed, among the earliest recorded being those of Aristotle and Archimedes.
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If everything that exists has a place, place too will have a place, and so on
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Three of the strongest and most famous—that of Achilles and the tortoise, the
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between them can be infinitely subdivided, implying Achilles would require an
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Many of these paradoxes argue that contrary to the evidence of one's senses,
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are lost, comprises forty "paradoxes of plurality," which argue against the
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286:(128a–d), Zeno is characterized as taking on the project of creating these
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argument, and that of an arrow in flight—are presented in detail below.
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2124:(1st ed.). Durham, NC: Duke University Press Books. pp. 5–6.
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as the same instant or continuous instant of time then it is in motion.
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moments any more than any other magnitude is composed of indivisibles.
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1191:(Spring 2024 ed.), Metaphysics Research Lab, Stanford University
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Zhang, Jun; Johansson, Karl; Lygeros, John; Sastry, Shankar (2001).
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of many things), motion, space, and time by suggesting they lead to
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1781:. Ancient commentators on Aristotle. Ithaca N.Y: Cornell Univ. Pr.
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Clarity and confusion in social theory: taking concepts seriously
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Franck, Cassez; Henzinger, Thomas; Raskin, Jean-Francois (2002).
3186:
2021:
Lee, Harold (1965). "Are Zeno's Paradoxes Based on a Mistake?".
1280:"Physics" by Aristotle translated by R. P. Hardie and R. K. Gaye
531:"Achilles and the Tortoise" redirects here. For other uses, see
195:
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W.M.Itano; D.J. Heinsen; J.J. Bokkinger; D.J. Wineland (1990).
809:, however, say that Zeno's paradoxes and their variations (see
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398:
25:
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A Comparison of Control Problems for Timed and Hybrid Systems
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Plato: Cratylus. Parmenides. Greater Hippias. Lesser Hippias
840:, is that, while the path is divisible, the motion is not.
3050:
This article incorporates material from Zeno's paradox on
1983:
The History of the Calculus and Its Conceptual Development
1913:(1 ed.). Cambridge Scholars Publishing. p. 19.
1481:(2nd ed.). University of Chicago Press. p. 33.
1052:"What the Tortoise Said to Achilles", written in 1895 by
1141:"Zeno's Paradoxes | Internet Encyclopedia of Philosophy"
198:. In this paradox, Zeno argues that a swift runner like
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History of Ancient Philosophy, University of Washington
2947:(1983). "Zeno's Paradox of Measure". In Cohen, R. S.;
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MĂĽller, Max, ed. (1891). "The Writings of Kwang Tse".
2654:
International Journal for Robust and Nonlinear Control
1899:
Aquinas. Commentary on Aristotle's Physics, Book 6.861
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http://plato.stanford.edu/entries/paradox-zeno/#GraMil
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and B. Misra discovered that the dynamical evolution (
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Some of Zeno's nine surviving paradoxes (preserved in
158:. Zeno devised these paradoxes to support his teacher
146:(c. 490–430 BC), primarily known through the works of
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Parables for the Virtual: Movement, Affect, Sensation
1807:
The University of Sheffield Kaltura Digital Media Hub
1447:"Zeno's Paradoxes: 5. Zeno's Influence on Philosophy"
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ancient thought and modern scientific understanding.
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Lewis Carroll's "What the Tortoise Said to Achilles"
16:"Arrow paradox" redirects here. For other uses, see
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3450:
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1980:
1312:The Moment of Proof : Mathematical Epiphanies
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1911:A Critical Investigation into Precognitive Dreams
1536:"Zeno's Paradoxes: 3.2 Achilles and the Tortoise"
3056:Creative Commons Attribution/Share-Alike License
1777:Simplikios; Konstan, David; Simplikios (1989).
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540:Infinity § Zeno: Achilles and the tortoise
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3032:Kevin Brown on Zeno and the Paradox of Motion
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1316:. New York: Oxford University Press. p.
1187:, in Zalta, Edward N.; Nodelman, Uri (eds.),
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942:In the field of verification and design of
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1610:Lives and Opinions of Eminent Philosophers
533:Achilles and the Tortoise (disambiguation)
3021:Zeno's Paradox: Achilles and the Tortoise
2293:Van Bendegem, Jean Paul (17 March 2010).
2031:(296). Oxford University Press: 563–570.
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116:Learn how and when to remove this message
3009:, Ludwig-Maximilians-Universität München
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3007:Introduction to Mathematical Philosophy
2955:. Dordrecht: Reidel. pp. 223–254.
2953:Physics, Philosophy, and Psychoanalysis
1189:The Stanford Encyclopedia of Philosophy
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830:An alternative conclusion, proposed by
676:The argument is that a single grain of
641:Aristotle gives three other paradoxes.
246:, that all of reality is one, and that
214:number of steps to catch the tortoise.
2932:, 2nd ed. Cambridge University Press.
2401:"The Zeno's paradox in quantum theory"
1926:
1852:Aristotle. Physics 6.9; 6.2, 233a21-31
52:Please improve this article by adding
2556:Paul A. Fishwick, ed. (1 June 2007).
2146:"Zeno's Paradoxes: A Timely Solution"
1868:. Vol. VI. Part 9 verse: 239b5.
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1504:"Zeno's Paradoxes: 3.1 The Dichotomy"
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1005:suggests knowledge of infinitesimals:
983:Roughly contemporaneously during the
930:. This effect is usually called the "
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2888:Stanford Encyclopedia of Philosophy
2562:Handbook of dynamic system modeling
2299:Stanford Encyclopedia of Philosophy
2064:in "The World of Mathematics" (ed.
1953:"Commentary on Aristotle's Physics"
1803:"Zeno's Paradoxes: The Moving Rows"
1779:Simplicius on Aristotle's Physics 6
1655:Stanford Encyclopedia of Philosophy
1541:Stanford Encyclopedia of Philosophy
1509:Stanford Encyclopedia of Philosophy
1452:Stanford Encyclopedia of Philosophy
3431:What the Tortoise Said to Achilles
2062:Mathematics and the metaphysicians
1048:What the Tortoise Said to Achilles
1001:. The second of the Ten Theses of
979:Diagram of Hui Shi's stick paradox
670:Routledge Dictionary of Philosophy
177:Zeno's work, primarily known from
14:
1650:"Zeno's Paradoxes: 3.3 The Arrow"
1479:The Beginnings of Western Science
950:, the system behaviour is called
3784:
3783:
3773:
2323:Cohen, Marc (11 December 2000).
1350:"Zeno and the Paradox of Motion"
1029:, chapter 33 (Legge translation)
601:other paradoxes of the same name
266:attribute the paradox to Zeno.
202:cannot overtake a slower moving
30:
2895:from the original on 2022-03-01
2809:from the original on 2020-07-20
2759:from the original on 2016-12-11
2627:from the original on 2010-11-16
2578:from the original on 2023-12-29
2445:from the original on 2013-05-14
2408:Journal of Mathematical Physics
2305:from the original on 2008-05-12
2275:from the original on 2023-12-29
2152:from the original on 2012-08-13
2102:from the original on 2019-10-15
1882:from the original on 2008-05-15
1662:from the original on 2022-03-01
1627:from the original on 2011-08-22
1578:from the original on 2008-05-15
1548:from the original on 2022-03-01
1516:from the original on 2022-03-01
1459:from the original on 2022-03-01
1427:from the original on 2012-06-09
693:Description from Nick Huggett:
206:with a head start, because the
3054:, which is licensed under the
3026:Wolfram Demonstrations Project
1987:. Dover Publications. p.
664:Paradox of the grain of millet
154:, and later commentators like
18:Arrow paradox (disambiguation)
1:
2913:, H. N. Fowler (Translator),
2827:Tsilipakos, Leonidas (2021).
2777:Carroll, Lewis (1895-04-01).
1933:: CS1 maint: date and year (
1909:Kiritsis, Paul (2020-04-01).
1572:The Internet Classics Archive
511:This argument is called the "
250:, that is, that nothing ever
54:secondary or tertiary sources
23:Set of philosophical problems
1613:. Vol. IX. passage 72.
1405:Papa-Grimaldi, Alba (1996).
1076:Philosophy of space and time
706:The moving rows (or stadium)
2995:Encyclopedia of Mathematics
2229:Space From Zeno to Einstein
3851:
2867:Cambridge University Press
2206:. Routledge. p. 169.
2037:10.1093/mind/LXXIV.296.563
1308:Benson, Donald C. (1999).
1066:Incommensurable magnitudes
1045:
903:
597:
537:
530:
519:. It is also known as the
15:
3769:
3014:Zeno meets modern science
2258:Causality and Explanation
1414:The Review of Metaphysics
1354:Reflections on Relativity
575:Achilles and the tortoise
548:Achilles and the tortoise
527:Achilles and the tortoise
308:method used by Socrates.
254:or in any other respect.
2731:Sacred Books of the East
2494:10.1103/PhysRevA.41.2295
1477:Lindberg, David (2007).
598:Not to be confused with
248:all change is impossible
3815:Philosophical paradoxes
3350:Paradoxes of set theory
2928:Sainsbury, R.M. (2003)
2735:Oxford University Press
2610:. Addison-Wesley: 128.
2361:(2). Belgium: 295–302.
2120:Massumi, Brian (2002).
1086:Ross–Littlewood paradox
851:assuming the conclusion
3825:Mathematical paradoxes
2915:Loeb Classical Library
2881:Huggett, Nick (2010).
2862:, M. Schofield (1984)
2795:10.1093/mind/IV.14.278
2295:"Finitism in Geometry"
2227:Huggett, Nick (1999).
1825:Aristotle. Physics 6.9
1648:Huggett, Nick (2010).
1534:Huggett, Nick (2010).
1502:Huggett, Nick (2010).
1445:Huggett, Nick (2010).
1244:(, Diogenes Laërtius.
1183:Huggett, Nick (2024),
1032:
991:philosophers from the
980:
912:E. C. George Sudarshan
889:Jean Paul Van Bendegem
747:In classical antiquity
732:On Aristotle's Physics
724:
715:
703:
691:
684:Aristotle's response:
682:
661:
627:
595:
571:
549:
488:
388:
366:
298:proof by contradiction
172:logical contradictions
41:relies excessively on
3830:Paradoxes of infinity
3037:Palmer, John (2008).
2647:"Zeno hybrid systems"
2465:"Quantum Zeno effect"
2355:Philosophy of Science
985:Warring States period
978:
861:Based on the work of
774:In modern mathematics
713:
593:
547:
489:
364:
156:Simplicius of Cilicia
3716:Kavka's toxin puzzle
3488:Income and fertility
2601:"Specifying Systems"
2399:; Misra, B. (1977).
1979:Boyer, Carl (1959).
1383:Moorcroft, Francis.
910:In 1977, physicists
410:
293:reductio ad absurdum
179:second-hand accounts
3810:Eponymous paradoxes
3375:Temperature paradox
3298:Free choice paradox
3162:Fitch's knowability
2543:1958JETP....6.1053K
2486:1990PhRvA..41.2295I
2420:1977JMP....18..756M
2397:Sudarshan, E. C. G.
2179:Time’s Up, Einstein
1207:Diogenes Laërtius,
956:formal verification
932:Quantum Zeno effect
906:Quantum Zeno effect
900:Quantum Zeno effect
345:Paradoxes of motion
252:changes in location
3835:Physical paradoxes
3751:Prisoner's dilemma
3437:Heat death paradox
3425:Unexpected hanging
3390:Chicken or the egg
3012:Silagadze, Z. K. "
2977:Dowden, Bradley. "
2883:"Zeno's Paradoxes"
2753:plato.stanford.edu
2683:on August 11, 2011
2608:Microsoft Research
2184:2012-12-30 at the
2084:Matière et Mémoire
1761:2008-05-15 at the
1739:2022-03-01 at the
1720:2008-05-11 at the
1689:2008-05-09 at the
1601:Laërtius, Diogenes
1276:2011-01-06 at the
1255:25ff and VIII 57).
1251:2010-12-12 at the
1185:"Zeno's Paradoxes"
981:
813:) remain relevant
757:Diogenes the Cynic
742:Proposed solutions
716:
596:
573:In the paradox of
550:
484:
367:
336:, but rather with
273:is nothing but an
65:"Zeno's paradoxes"
3797:
3796:
3468:Arrow information
2838:978-1-032-09883-8
2571:978-1-58488-565-8
2531:Soviet Phys. JETP
2473:Physical Review A
2268:978-0-19-510864-4
2253:Salmon, Wesley C.
2089:Matter and Memory
1998:978-0-486-60509-8
1788:978-0-8014-2238-6
1488:978-0-226-48205-7
1101:List of paradoxes
966:Similar paradoxes
837:Matter and Memory
834:in his 1896 book
471:
458:
445:
432:
357:Dichotomy paradox
256:Diogenes Laërtius
162:'s philosophy of
138:presented by the
126:
125:
118:
100:
3842:
3787:
3786:
3777:
3776:
3588:Service recovery
3442:Olbers's paradox
3142:Buridan's bridge
3115:
3108:
3101:
3092:
3087:
3085:
3084:
3075:. Archived from
3065:"Zeno's Paradox"
3046:
3024:by Jon McLoone,
3003:
2981:." Entry in the
2979:Zeno’s Paradoxes
2966:
2903:
2901:
2900:
2843:
2842:
2824:
2818:
2817:
2815:
2814:
2774:
2768:
2767:
2765:
2764:
2745:
2739:
2738:
2726:
2720:
2719:
2717:
2716:
2707:. Archived from
2698:
2692:
2691:
2689:
2688:
2682:
2676:. Archived from
2651:
2642:
2636:
2635:
2633:
2632:
2626:
2605:
2593:
2587:
2586:
2584:
2583:
2553:
2547:
2546:
2526:
2520:
2519:
2517:
2516:
2510:
2504:. Archived from
2480:(5): 2295–2300.
2469:
2460:
2454:
2453:
2451:
2450:
2444:
2428:10.1063/1.523304
2405:
2393:
2387:
2386:
2350:
2344:
2343:
2341:
2340:
2335:on July 12, 2010
2331:. Archived from
2320:
2314:
2313:
2311:
2310:
2290:
2284:
2283:
2281:
2280:
2249:
2243:
2242:
2224:
2218:
2217:
2199:
2193:
2176:
2170:
2167:
2161:
2160:
2158:
2157:
2148:. January 2003.
2142:
2136:
2135:
2117:
2111:
2110:
2108:
2107:
2101:
2094:
2075:
2069:
2068:), pp 1576-1590.
2055:
2049:
2048:
2018:
2012:
2011:
2006:
2005:
1986:
1976:
1967:
1966:
1964:
1963:
1945:
1939:
1938:
1932:
1924:
1906:
1900:
1897:
1891:
1890:
1888:
1887:
1859:
1853:
1850:
1844:
1841:divergent series
1832:
1826:
1823:
1817:
1816:
1814:
1813:
1799:
1793:
1792:
1774:
1765:
1749:
1743:
1730:
1724:
1708:
1702:
1699:
1693:
1677:
1671:
1670:
1668:
1667:
1645:
1636:
1635:
1633:
1632:
1597:
1591:
1590:
1584:
1583:
1563:
1557:
1556:
1554:
1553:
1531:
1525:
1524:
1522:
1521:
1499:
1493:
1492:
1474:
1468:
1467:
1465:
1464:
1442:
1436:
1435:
1433:
1432:
1426:
1411:
1402:
1393:
1392:
1387:. Archived from
1385:"Zeno's Paradox"
1380:
1369:
1368:
1366:
1365:
1356:. Archived from
1345:
1332:
1331:
1315:
1305:
1299:
1298:
1293:. Archived from
1287:
1281:
1265:
1256:
1242:
1236:
1230:
1224:
1218:
1212:
1211:, 9.23 and 9.29.
1205:
1199:
1198:
1197:
1196:
1180:
1151:
1150:
1148:
1147:
1137:
1071:Infinite regress
1035:The Mohist canon
1030:
867:Bertrand Russell
857:Bertrand Russell
718:From Aristotle:
649:From Aristotle:
645:Paradox of place
625:
614:as recounted by
569:
558:as recounted by
493:
491:
490:
485:
483:
479:
472:
464:
459:
451:
446:
438:
433:
425:
386:
375:as recounted by
296:, also known as
264:Modern academics
131:are a series of
129:Zeno's paradoxes
121:
114:
110:
107:
101:
99:
58:
34:
26:
3850:
3849:
3845:
3844:
3843:
3841:
3840:
3839:
3800:
3799:
3798:
3793:
3765:
3676:Decision-making
3622:Decision theory
3617:
3446:
3370:Hilbert's Hotel
3303:Grelling–Nelson
3246:
3125:
3119:
3082:
3080:
3062:
3036:
2988:
2974:
2969:
2963:
2943:
2898:
2896:
2880:
2851:
2846:
2839:
2826:
2825:
2821:
2812:
2810:
2789:(14): 278–280.
2776:
2775:
2771:
2762:
2760:
2747:
2746:
2742:
2728:
2727:
2723:
2714:
2712:
2711:on May 28, 2008
2700:
2699:
2695:
2686:
2684:
2680:
2666:10.1002/rnc.592
2649:
2644:
2643:
2639:
2630:
2628:
2624:
2618:
2603:
2597:Lamport, Leslie
2595:
2594:
2590:
2581:
2579:
2572:
2555:
2554:
2550:
2528:
2527:
2523:
2514:
2512:
2508:
2467:
2462:
2461:
2457:
2448:
2446:
2442:
2403:
2395:
2394:
2390:
2352:
2351:
2347:
2338:
2336:
2322:
2321:
2317:
2308:
2306:
2292:
2291:
2287:
2278:
2276:
2269:
2251:
2250:
2246:
2239:
2226:
2225:
2221:
2214:
2201:
2200:
2196:
2188:, Josh McHugh,
2186:Wayback Machine
2177:
2173:
2168:
2164:
2155:
2153:
2144:
2143:
2139:
2132:
2119:
2118:
2114:
2105:
2103:
2099:
2092:
2077:
2076:
2072:
2056:
2052:
2020:
2019:
2015:
2003:
2001:
1999:
1978:
1977:
1970:
1961:
1959:
1949:Aquinas, Thomas
1947:
1946:
1942:
1925:
1921:
1908:
1907:
1903:
1898:
1894:
1885:
1883:
1876:
1861:
1860:
1856:
1851:
1847:
1837:harmonic series
1833:
1829:
1824:
1820:
1811:
1809:
1801:
1800:
1796:
1789:
1776:
1775:
1768:
1763:Wayback Machine
1750:
1746:
1741:Wayback Machine
1731:
1727:
1722:Wayback Machine
1709:
1705:
1700:
1696:
1691:Wayback Machine
1678:
1674:
1665:
1663:
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1646:
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1630:
1628:
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1598:
1594:
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1579:
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1551:
1549:
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1528:
1519:
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1501:
1500:
1496:
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1471:
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1444:
1443:
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1430:
1428:
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1409:
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1403:
1396:
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1372:
1363:
1361:
1347:
1346:
1335:
1328:
1307:
1306:
1302:
1289:
1288:
1284:
1278:Wayback Machine
1266:
1259:
1253:Wayback Machine
1243:
1239:
1231:
1227:
1219:
1215:
1206:
1202:
1194:
1192:
1182:
1181:
1154:
1145:
1143:
1139:
1138:
1113:
1109:
1081:Renormalization
1062:
1050:
1044:
1031:
1025:
1022:
993:School of Names
989:ancient Chinese
987:(475–221 BCE),
973:
971:School of Names
968:
940:
908:
902:
897:
876:
859:
846:
828:
820:Rorschach image
776:
749:
744:
714:The moving rows
708:
666:
647:
639:
637:Other paradoxes
626:
613:
605:
588:
570:
557:
542:
536:
529:
417:
413:
408:
407:
401:
399:
387:
374:
359:
347:
314:
236:
122:
111:
105:
102:
59:
57:
51:
47:primary sources
35:
24:
21:
12:
11:
5:
3848:
3846:
3838:
3837:
3832:
3827:
3822:
3817:
3812:
3802:
3801:
3795:
3794:
3792:
3791:
3781:
3770:
3767:
3766:
3764:
3763:
3758:
3753:
3748:
3743:
3738:
3733:
3728:
3723:
3718:
3713:
3708:
3703:
3698:
3693:
3688:
3683:
3678:
3673:
3668:
3663:
3658:
3653:
3652:
3651:
3646:
3641:
3631:
3625:
3623:
3619:
3618:
3616:
3615:
3610:
3605:
3600:
3595:
3593:St. Petersburg
3590:
3585:
3580:
3575:
3570:
3565:
3560:
3555:
3550:
3545:
3540:
3535:
3530:
3525:
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3515:
3510:
3505:
3500:
3495:
3490:
3485:
3480:
3475:
3470:
3465:
3460:
3454:
3452:
3448:
3447:
3445:
3444:
3439:
3434:
3427:
3422:
3417:
3412:
3407:
3402:
3397:
3392:
3387:
3382:
3377:
3372:
3367:
3362:
3357:
3352:
3347:
3342:
3341:
3340:
3335:
3330:
3325:
3320:
3310:
3305:
3300:
3295:
3290:
3285:
3280:
3275:
3270:
3265:
3260:
3254:
3252:
3248:
3247:
3245:
3244:
3239:
3234:
3229:
3224:
3222:Rule-following
3219:
3214:
3209:
3204:
3199:
3194:
3189:
3184:
3179:
3174:
3169:
3164:
3159:
3154:
3149:
3147:Dream argument
3144:
3139:
3133:
3131:
3127:
3126:
3120:
3118:
3117:
3110:
3103:
3095:
3089:
3088:
3063:Grime, James.
3060:
3047:
3039:"Zeno of Elea"
3034:
3029:
3017:
3010:
3004:
2986:
2973:
2972:External links
2970:
2968:
2967:
2961:
2941:
2926:
2904:
2878:
2852:
2850:
2847:
2845:
2844:
2837:
2819:
2769:
2740:
2721:
2693:
2637:
2616:
2588:
2570:
2548:
2521:
2455:
2414:(4): 756–763.
2388:
2367:10.1086/289379
2345:
2315:
2285:
2267:
2244:
2237:
2219:
2212:
2194:
2190:Wired Magazine
2171:
2162:
2137:
2131:978-0822328971
2130:
2112:
2079:Bergson, Henri
2070:
2050:
2013:
1997:
1968:
1940:
1920:978-1527546332
1919:
1901:
1892:
1874:
1854:
1845:
1827:
1818:
1794:
1787:
1766:
1744:
1725:
1703:
1694:
1672:
1637:
1619:
1592:
1558:
1526:
1494:
1487:
1469:
1437:
1394:
1391:on 2010-04-18.
1370:
1348:Brown, Kevin.
1333:
1327:978-0195117219
1326:
1300:
1297:on 2008-05-16.
1282:
1257:
1237:
1225:
1213:
1200:
1152:
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1108:
1105:
1104:
1103:
1098:
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1073:
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1061:
1058:
1046:Main article:
1043:
1040:
1023:
1018:
998:Gongsun Longzi
972:
969:
967:
964:
960:systems design
948:hybrid systems
939:
938:Zeno behaviour
936:
920:quantum system
904:Main article:
901:
898:
896:
893:
875:
872:
858:
855:
845:
842:
827:
824:
811:Thomson's lamp
790:definition of
775:
772:
768:Thomas Aquinas
748:
745:
743:
740:
707:
704:
665:
662:
646:
643:
638:
635:
611:
587:
584:
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346:
343:
313:
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242:' doctrine of
235:
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183:original texts
124:
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38:
36:
29:
22:
13:
10:
9:
6:
4:
3:
2:
3847:
3836:
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3780:
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3768:
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3747:
3744:
3742:
3739:
3737:
3734:
3732:
3729:
3727:
3724:
3722:
3721:Morton's fork
3719:
3717:
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3712:
3709:
3707:
3704:
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3699:
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3694:
3692:
3689:
3687:
3684:
3682:
3679:
3677:
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3672:
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3667:
3664:
3662:
3661:Buridan's ass
3659:
3657:
3654:
3650:
3647:
3645:
3642:
3640:
3637:
3636:
3635:
3634:Apportionment
3632:
3630:
3627:
3626:
3624:
3620:
3614:
3611:
3609:
3606:
3604:
3601:
3599:
3596:
3594:
3591:
3589:
3586:
3584:
3581:
3579:
3576:
3574:
3571:
3569:
3566:
3564:
3561:
3559:
3556:
3554:
3551:
3549:
3546:
3544:
3541:
3539:
3536:
3534:
3531:
3529:
3526:
3524:
3521:
3519:
3516:
3514:
3511:
3509:
3506:
3504:
3501:
3499:
3496:
3494:
3493:Downs–Thomson
3491:
3489:
3486:
3484:
3481:
3479:
3476:
3474:
3471:
3469:
3466:
3464:
3461:
3459:
3456:
3455:
3453:
3449:
3443:
3440:
3438:
3435:
3432:
3428:
3426:
3423:
3421:
3418:
3416:
3413:
3411:
3410:Plato's beard
3408:
3406:
3403:
3401:
3398:
3396:
3393:
3391:
3388:
3386:
3383:
3381:
3378:
3376:
3373:
3371:
3368:
3366:
3363:
3361:
3358:
3356:
3353:
3351:
3348:
3346:
3343:
3339:
3336:
3334:
3331:
3329:
3326:
3324:
3321:
3319:
3316:
3315:
3314:
3311:
3309:
3308:Kleene–Rosser
3306:
3304:
3301:
3299:
3296:
3294:
3291:
3289:
3286:
3284:
3281:
3279:
3276:
3274:
3271:
3269:
3266:
3264:
3261:
3259:
3256:
3255:
3253:
3249:
3243:
3240:
3238:
3235:
3233:
3232:Theseus' ship
3230:
3228:
3225:
3223:
3220:
3218:
3215:
3213:
3210:
3208:
3205:
3203:
3200:
3198:
3195:
3193:
3192:Mere addition
3190:
3188:
3185:
3183:
3180:
3178:
3175:
3173:
3170:
3168:
3165:
3163:
3160:
3158:
3155:
3153:
3150:
3148:
3145:
3143:
3140:
3138:
3135:
3134:
3132:
3130:Philosophical
3128:
3124:
3116:
3111:
3109:
3104:
3102:
3097:
3096:
3093:
3079:on 2018-10-03
3078:
3074:
3070:
3066:
3061:
3059:
3057:
3053:
3048:
3044:
3040:
3035:
3033:
3030:
3027:
3023:
3022:
3018:
3015:
3011:
3008:
3005:
3001:
2997:
2996:
2991:
2987:
2984:
2980:
2976:
2975:
2971:
2964:
2962:90-277-1533-5
2958:
2954:
2950:
2946:
2945:Skyrms, Brian
2942:
2939:
2938:0-521-48347-6
2935:
2931:
2927:
2924:
2923:0-674-99185-0
2920:
2916:
2912:
2908:
2905:
2894:
2890:
2889:
2884:
2879:
2876:
2875:0-521-27455-9
2872:
2868:
2865:
2861:
2857:
2854:
2853:
2848:
2840:
2834:
2830:
2823:
2820:
2808:
2804:
2800:
2796:
2792:
2788:
2784:
2780:
2773:
2770:
2758:
2754:
2750:
2744:
2741:
2736:
2732:
2725:
2722:
2710:
2706:
2705:
2697:
2694:
2679:
2675:
2671:
2667:
2663:
2659:
2655:
2648:
2641:
2638:
2623:
2619:
2617:0-321-14306-X
2613:
2609:
2602:
2598:
2592:
2589:
2577:
2573:
2567:
2563:
2559:
2552:
2549:
2544:
2540:
2536:
2532:
2525:
2522:
2511:on 2004-07-20
2507:
2503:
2499:
2495:
2491:
2487:
2483:
2479:
2475:
2474:
2466:
2459:
2456:
2441:
2437:
2433:
2429:
2425:
2421:
2417:
2413:
2409:
2402:
2398:
2392:
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2372:
2368:
2364:
2360:
2356:
2349:
2346:
2334:
2330:
2326:
2319:
2316:
2304:
2300:
2296:
2289:
2286:
2274:
2270:
2264:
2260:
2259:
2254:
2248:
2245:
2240:
2238:0-262-08271-3
2234:
2231:. MIT Press.
2230:
2223:
2220:
2215:
2213:0-415-09605-7
2209:
2205:
2198:
2195:
2191:
2187:
2183:
2180:
2175:
2172:
2166:
2163:
2151:
2147:
2141:
2138:
2133:
2127:
2123:
2116:
2113:
2098:
2090:
2086:
2085:
2080:
2074:
2071:
2067:
2063:
2059:
2054:
2051:
2046:
2042:
2038:
2034:
2030:
2026:
2025:
2017:
2014:
2010:
2000:
1994:
1990:
1985:
1984:
1975:
1973:
1969:
1958:
1954:
1950:
1944:
1941:
1936:
1930:
1922:
1916:
1912:
1905:
1902:
1896:
1893:
1881:
1877:
1875:0-585-09205-2
1871:
1867:
1866:
1858:
1855:
1849:
1846:
1842:
1838:
1831:
1828:
1822:
1819:
1808:
1804:
1798:
1795:
1790:
1784:
1780:
1773:
1771:
1767:
1764:
1760:
1757:
1755:
1748:
1745:
1742:
1738:
1735:
1729:
1726:
1723:
1719:
1716:
1715:VII:5, 250a20
1714:
1707:
1704:
1698:
1695:
1692:
1688:
1685:
1683:
1676:
1673:
1661:
1657:
1656:
1651:
1644:
1642:
1638:
1626:
1622:
1620:1-116-71900-2
1616:
1612:
1611:
1606:
1602:
1596:
1593:
1589:
1577:
1573:
1569:
1562:
1559:
1547:
1543:
1542:
1537:
1530:
1527:
1515:
1511:
1510:
1505:
1498:
1495:
1490:
1484:
1480:
1473:
1470:
1458:
1454:
1453:
1448:
1441:
1438:
1423:
1419:
1415:
1408:
1401:
1399:
1395:
1390:
1386:
1379:
1377:
1375:
1371:
1360:on 2012-12-05
1359:
1355:
1351:
1344:
1342:
1340:
1338:
1334:
1329:
1323:
1319:
1314:
1313:
1304:
1301:
1296:
1292:
1286:
1283:
1279:
1275:
1272:
1271:
1264:
1262:
1258:
1254:
1250:
1247:
1241:
1238:
1234:
1229:
1226:
1222:
1217:
1214:
1210:
1204:
1201:
1190:
1186:
1179:
1177:
1175:
1173:
1171:
1169:
1167:
1165:
1163:
1161:
1159:
1157:
1153:
1142:
1136:
1134:
1132:
1130:
1128:
1126:
1124:
1122:
1120:
1118:
1116:
1112:
1106:
1102:
1099:
1097:
1094:
1092:
1089:
1087:
1084:
1082:
1079:
1077:
1074:
1072:
1069:
1067:
1064:
1063:
1059:
1057:
1055:
1054:Lewis Carroll
1049:
1039:
1036:
1028:
1021:
1016:
1014:
1013:
1008:
1004:
1000:
999:
994:
990:
986:
977:
970:
965:
963:
961:
957:
953:
949:
945:
937:
935:
933:
929:
925:
921:
917:
913:
907:
899:
894:
892:
890:
886:
885:tile argument
882:
873:
871:
868:
864:
856:
854:
852:
843:
841:
839:
838:
833:
832:Henri Bergson
826:Henri Bergson
825:
823:
821:
816:
812:
808:
803:
801:
797:
793:
789:
788:epsilon-delta
785:
781:
773:
771:
769:
765:
761:
758:
754:
751:According to
746:
741:
739:
735:
733:
729:
723:
719:
712:
705:
702:
700:
694:
690:
685:
681:
679:
673:
671:
663:
660:
658:
657:
650:
644:
642:
636:
634:
631:
623:
622:
617:
610:
603:
602:
592:
586:Arrow paradox
585:
583:
580:
576:
567:
566:
561:
554:
546:
541:
534:
526:
524:
522:
518:
514:
509:
507:
503:
498:
480:
476:
473:
468:
465:
460:
455:
452:
447:
442:
439:
434:
429:
426:
421:
418:
414:
406:
405:
404:
396:
393:
384:
383:
378:
371:
365:The dichotomy
363:
356:
354:
352:
344:
342:
339:
335:
331:
326:
322:
321:
311:
309:
307:
303:
299:
295:
294:
289:
285:
284:
280:
276:
272:
267:
265:
261:
257:
253:
249:
245:
241:
233:
231:
228:
224:
220:
215:
213:
209:
205:
201:
197:
193:
188:
184:
180:
175:
173:
169:
165:
161:
157:
153:
149:
145:
141:
140:ancient Greek
137:
134:
133:philosophical
130:
120:
117:
109:
98:
95:
91:
88:
84:
81:
77:
74:
70:
67: –
66:
62:
61:Find sources:
55:
49:
48:
44:
39:This article
37:
33:
28:
27:
19:
3741:Preparedness
3573:Productivity
3553:Mandeville's
3345:Opposite Day
3273:Burali-Forti
3268:Bhartrhari's
3241:
3081:. Retrieved
3077:the original
3068:
3049:
3042:
3019:
2993:
2952:
2929:
2910:
2897:. Retrieved
2886:
2863:
2828:
2822:
2811:. Retrieved
2786:
2782:
2772:
2761:. Retrieved
2752:
2743:
2730:
2724:
2713:. Retrieved
2709:the original
2703:
2696:
2685:. Retrieved
2678:the original
2657:
2653:
2640:
2629:. Retrieved
2607:
2591:
2580:. Retrieved
2561:
2551:
2534:
2530:
2524:
2513:. Retrieved
2506:the original
2477:
2471:
2458:
2447:. Retrieved
2411:
2407:
2391:
2358:
2354:
2348:
2337:. Retrieved
2333:the original
2328:
2318:
2307:. Retrieved
2298:
2288:
2277:. Retrieved
2257:
2247:
2228:
2222:
2203:
2197:
2174:
2165:
2154:. Retrieved
2140:
2121:
2115:
2104:. Retrieved
2088:
2083:
2073:
2061:
2053:
2028:
2022:
2016:
2008:
2002:. Retrieved
1982:
1960:. Retrieved
1956:
1943:
1910:
1904:
1895:
1884:. Retrieved
1864:
1857:
1848:
1830:
1821:
1810:. Retrieved
1806:
1797:
1778:
1756:VI:9, 239b33
1753:
1747:
1728:
1712:
1706:
1697:
1684:IV:1, 209a25
1681:
1675:
1664:. Retrieved
1653:
1629:. Retrieved
1609:
1595:
1586:
1580:. Retrieved
1571:
1561:
1550:. Retrieved
1539:
1529:
1518:. Retrieved
1507:
1497:
1478:
1472:
1461:. Retrieved
1450:
1440:
1429:. Retrieved
1417:
1413:
1389:the original
1362:. Retrieved
1358:the original
1353:
1311:
1303:
1295:the original
1285:
1269:
1268:Aristotle's
1240:
1232:
1228:
1220:
1216:
1208:
1203:
1193:, retrieved
1188:
1144:. Retrieved
1096:Zeno machine
1051:
1033:
1026:
1019:
1011:
1006:
997:
982:
951:
941:
909:
895:Applications
881:Hermann Weyl
877:
874:Hermann Weyl
863:Georg Cantor
860:
847:
835:
829:
815:metaphysical
807:philosophers
804:
777:
762:
750:
736:
731:
728:Simplicius's
725:
721:
717:
696:
692:
687:
683:
675:
669:
667:
656:ad infinitum
654:
652:
648:
640:
632:
628:
620:
607:
600:
574:
572:
568:VI:9, 239b15
564:
552:
520:
510:
499:
496:
402:
389:
385:VI:9, 239b10
381:
369:
348:
337:
333:
325:Simplicius's
319:
318:Aristotle's
315:
291:
282:
268:
247:
237:
216:
176:
144:Zeno of Elea
142:philosopher
128:
127:
112:
103:
93:
86:
79:
72:
60:
40:
3671:Condorcet's
3523:Giffen good
3483:Competition
3237:White horse
3212:Omnipotence
3073:Brady Haran
3069:Numberphile
2860:J. E. Raven
2856:Kirk, G. S.
2192:, June 2005
1862:Aristotle.
1566:Aristotle.
1420:: 299–314.
1038:interpret.
924:observation
844:Peter Lynds
796:Weierstrass
730:commentary
699:Parmenidean
624:VI:9, 239b5
521:Race Course
3820:Supertasks
3804:Categories
3746:Prevention
3736:Parrondo's
3726:Navigation
3711:Inventor's
3706:Hedgehog's
3666:Chainstore
3649:Population
3644:New states
3578:Prosperity
3558:Mayfield's
3400:Entailment
3380:Barbershop
3293:Epimenides
3083:2013-04-13
3052:PlanetMath
2990:"Antinomy"
2949:Laudan, L.
2899:2011-03-07
2849:References
2813:2020-07-20
2763:2020-01-30
2715:2010-03-02
2687:2010-02-28
2660:(5): 435.
2631:2010-03-06
2582:2010-03-05
2515:2004-07-23
2449:2018-04-20
2339:2012-01-03
2309:2012-01-03
2279:2020-11-21
2156:2012-07-02
2106:2019-10-15
2066:J R Newman
2004:2010-02-26
1962:2024-03-25
1957:aquinas.cc
1886:2008-08-11
1812:2024-06-28
1751:Aristotle
1710:Aristotle
1679:Aristotle
1666:2011-03-07
1631:2011-03-05
1603:(c. 230).
1582:2012-08-21
1552:2011-03-07
1520:2011-03-07
1463:2011-03-07
1431:2012-03-06
1364:2010-06-06
1233:Parmenides
1221:Parmenides
1195:2024-03-25
1146:2024-03-25
780:Carl Boyer
753:Simplicius
697:This is a
538:See also:
330:Simplicius
283:Parmenides
240:Parmenides
181:since his
160:Parmenides
106:March 2023
76:newspapers
43:references
3761:Willpower
3756:Tolerance
3731:Newcomb's
3696:Fredkin's
3583:Scitovsky
3503:Edgeworth
3498:Easterlin
3463:Antitrust
3360:Russell's
3355:Richard's
3328:Pinocchio
3283:Crocodile
3202:Newcomb's
3172:Goodman's
3167:Free will
3152:Epicurean
3123:paradoxes
3000:EMS Press
2930:Paradoxes
2803:0026-4423
2383:224840314
2325:"ATOMISM"
2058:B Russell
1929:cite book
1568:"Physics"
1091:Supertask
764:Aristotle
616:Aristotle
594:The arrow
560:Aristotle
523:paradox.
517:asymptote
513:Dichotomy
419:⋯
377:Aristotle
351:Dichotomy
338:finishing
312:Paradoxes
306:dialectic
288:paradoxes
260:Favorinus
258:, citing
223:Aristotle
187:coherence
168:existence
152:Aristotle
136:arguments
3789:Category
3686:Ellsberg
3538:Leontief
3518:Gibson's
3513:European
3508:Ellsberg
3478:Braess's
3473:Bertrand
3451:Economic
3385:Catch-22
3365:Socratic
3207:Nihilism
3177:Hedonism
3137:Analysis
3121:Notable
2951:(eds.).
2893:Archived
2807:Archived
2757:Archived
2622:Archived
2599:(2002).
2576:Archived
2537:: 1053.
2440:Archived
2303:Archived
2273:Archived
2255:(1998).
2182:Archived
2150:Archived
2097:Archived
2081:(1896).
1880:Archived
1759:Archived
1737:Archived
1718:Archived
1687:Archived
1660:Archived
1625:Archived
1605:"Pyrrho"
1576:Archived
1546:Archived
1514:Archived
1457:Archived
1422:Archived
1274:Archived
1249:Archived
1060:See also
1027:Zhuangzi
1024:—
1012:Zhuangzi
784:calculus
612:—
579:Achilles
556:—
506:illusion
392:Atalanta
390:Suppose
373:—
302:Socrates
275:illusion
227:calculus
212:infinite
208:distance
204:tortoise
200:Achilles
3691:Fenno's
3656:Arrow's
3639:Alabama
3629:Abilene
3608:Tullock
3563:Metzler
3405:Lottery
3395:Drinker
3338:Yablo's
3333:Quine's
3288:Curry's
3251:Logical
3227:Sorites
3217:Preface
3197:Moore's
3182:Liberal
3157:Fiction
3002:, 2001
2909:(1926)
2674:2057416
2539:Bibcode
2502:9903355
2482:Bibcode
2436:7342282
2416:Bibcode
2060:(1956)
2045:2251675
1865:Physics
1754:Physics
1713:Physics
1682:Physics
1270:Physics
1003:Hui Shi
926:of the
918:) of a
621:Physics
565:Physics
382:Physics
320:Physics
279:Plato's
234:History
219:history
90:scholar
3598:Thrift
3568:Plenty
3543:Lerner
3533:Jevons
3528:Icarus
3458:Allais
3420:Ross's
3258:Barber
3242:Zeno's
3187:Meno's
2959:
2936:
2921:
2873:
2835:
2801:
2672:
2614:
2568:
2500:
2434:
2381:
2375:187807
2373:
2265:
2235:
2210:
2128:
2091:]
2043:
1995:
1917:
1872:
1785:
1617:
1485:
1324:
1235:128a–b
928:system
916:motion
800:Cauchy
678:millet
502:finite
271:motion
244:monism
164:monism
92:
85:
78:
71:
63:
3701:Green
3681:Downs
3613:Value
3548:Lucas
3415:Raven
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