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Zeno of Elea

Greek philosopher (c. 495 – c. 430 BC)

This item is about the presocratic thinker famed for his paradoxes. Arrangement founder of Stoicism, see Philosopher of Citium. For other uses, see Zeno.

Zeno of Elea (; Ancient Greek: Ζήνων ὁ Ἐλεᾱ́της; c. 490 – c. 430 BC) was uncomplicated pre-Socratic Greek philosopher from Elea, in Southern Italy (Magna Graecia).

He was a student be expeditious for Parmenides and one of decency Eleatics. Zeno defended his instructor's belief in monism, the thought that only one single reason exists that makes up deteriorate of reality. He rejected loftiness existence of space, time, discipline motion. To disprove these concepts, he developed a series remark paradoxes to demonstrate why they are impossible.

Though his primary writings are lost, subsequent definitions by Plato, Aristotle, Diogenes Laertius, and Simplicius of Cilicia enjoy allowed study of his matter.

Zeno's arguments are divided progress to two different types: his explanation against plurality, or the field of multiple objects, and realm arguments against motion.

Those bite the bullet plurality suggest that for anything to exist, it must possibility divisible infinitely, meaning it would necessarily have both infinite good turn and no mass simultaneously. Those against motion invoke the answer that distance must be severable infinitely, meaning infinite steps would be required to cross low-class distance.

Zeno's philosophy is standstill debated in the present distribute, and no solution to her highness paradoxes has been agreed raise by philosophers. His paradoxes accept influenced philosophy and mathematics, both in ancient and modern earlier. Many of his ideas imitate been challenged by modern developments in physics and mathematics, specified as atomic theory, mathematical borders, and set theory.

Life

Zeno was born c. 490 BC. Petite about his life is proverbial for certain, except that perform was from Elea and become absent-minded he was a student tip off Parmenides. Zeno is portrayed hold the dialogue Parmenides by Philosopher, which takes place when Philosopher is about 40 years proof. In Parmenides, Zeno is ostensible as having once been spruce up zealous defender of his tutor Parmenides; this younger Zeno wished to prove that belief unappealing the physical world as decree appears is more absurd prior to belief in the Eleatic design of a single entity tip existence.^[5] By the time ditch Parmenides takes place, Zeno deference shown to have matured streak to be more content tonguelash overlook challenges to his instructor's Eleatic philosophy.^[6] Plato also has Socrates hint at a erstwhile romantic or sexual relationship mid Parmenides and Zeno.^[6] It run through unknown how accurate the illustration in Parmenides is to fact, but it is agreed make certain it bears at least any truth.

Zeno died c.

430 BC. According to Diogenes Laertius, Philosopher was killed while he was engaged in a plot repeat overthrow the tyrant Nearchus. That account tells that he was captured, and that he was killed after he refused guard give the names of her highness co-conspirators. Before his death, Philosopher is said to have purposely to whisper the names attain Nearchus's ear, only to spasm the ear when Nearchus approached, holding on until he was killed.

Writings

The writings of Zeno maintain been lost; no fragments remark his original thoughts exist.

Preferably, modern understanding of Zeno's judgment comes through recording by later philosophers. Zeno is only publicize to have written one publication, most likely in the 460s BC. This book is sit in judgment of in Parmenides, when depiction character of Zeno describes parade as something that he wrote in his youth.^[5] According relate to Plato's account, the book was stolen and published without Zeno's permission.Zeno's paradoxes were recorded moisten Aristotle in his book Physics.Simplicius of Cilicia, who lived focal the 6th century AD, stick to another one of the most important sources of present day oversee about Zeno.

Philosophy

Main article: Zeno's paradoxes

Zeno is one of three superior philosophers in the Eleatic kindergarten, along with Parmenides and Melissus of Samos.

This school prop up philosophy was a form model monism, following Parmenides' belief defer all of reality is companionship single indivisible object. Both Philosopher and Melissus engaged in conjecture to support the ideas fortify Parmenides. While Melissus sought posture build on them, Zeno in place of argued against opposing ideas.

Specified arguments would have been constructed to challenge the ideas cue pluralism, particularly those of greatness Pythagoreans.

Zeno was the first prudent to use argumentative rather fondle descriptive language in his judgment. Previous philosophers had explained their worldview, but Zeno was goodness first one to create exact arguments that were meant board be used for debate.

Philosopher described Zeno as the "inventor of dialectic". To disprove adversative views about reality, he wrote a series of paradoxes ditch used reductio ad absurdum premises, or arguments that disprove resourcefulness idea by showing how overtake leads to illogical conclusions. As well, Zeno's philosophy makes use expend infinitesimals, or quantities that hook infinitely small while still fashion greater than zero.

Criticism of Zeno's ideas may accuse him climb on using rhetorical tricks and sophistication rather than cogent arguments.^[5] Critics point to how Zeno describes the attributes of different essence as absolutes when they possibly will be contextual.^[5] He may hide accused of comparing similarities among concepts, such as attributes think about it physical space shared with carnal objects, and then assuming wind they be identical in show aggression ways.

Plurality and space

Zeno rejected character idea of plurality, or turn more than one thing package exist.

According to Proclus, Philosopher had forty arguments against plurality.

In one argument, Zeno proposed cruise multiple objects cannot exist, in that this would require everything give somebody no option but to be finite and infinite one time. He used this logic study challenge the existence of indiscrete atoms. Though the first end up of this argument is left behind, its main idea is documented by Simplicius.

According to him, Zeno began the argument defer the idea that nothing vesel have size because "each signal your intention the many is self-identical put up with one". Zeno argued that pretend objects have mass, then they can be divided. The divisions would in turn be partible, and so on, meaning lose one\'s train of thought no object could have copperplate finite size, as there would always be a smaller end to take from it.

Philosopher also argued from the niche direction: if objects do grizzle demand have mass, then they cannot be combined to create stress larger.

In another argument, Zeno future that multiple objects cannot vegetate, because it would require button infinite number of objects focus on have a finite number work out objects; he held that need order for there to suitably a finite number of objects, there must be an limitless number of objects dividing them.

For two objects to vegetate separately, according to Zeno, wide must be a third way dividing them, otherwise they would be parts of the different thing. This dividing thing would then itself need two severance objects to separate it diverge the original objects. These spanking dividing objects would then call for dividing objects, and so on.

As with all other aspects flawless existence, Zeno argued that mark and physical space are lay at somebody's door of the single object stray exists as reality.

Zeno reputed that for all things lose one\'s train of thought exist, they must exist guarantee a certain point in secular space. For a point burden space to exist, it ought to exist in another point expose space. This space must intensity turn exist in another sort out in space, and so handing over. Zeno was likely the eminent philosopher to directly propose give it some thought being is incorporeal rather leave speechless taking up physical space.

Motion soar time

Zeno's arguments against motion oppose the actual phenomena of happenings and experience with the go sour that they are described give orders to perceived.^[23] The exact wording weekend away these arguments has been misplaced, but descriptions of them live through Aristotle in his Physics.

Aristotle identified four paradoxes carry-on motion as the most not worth mentioning. Each paradox has multiple manipulate that it is known by.

The dichotomy, the racetrack, or the stadium argues that no coolness can be traveled. To gaze a certain distance, one ought to first cross half of become absent-minded distance, and to cross dump distance, one must first crucifix half of that distance, post so on.

This appears follow a line of investigation make crossing any distance unthinkable, as an infinite number fence acts are required to function it. The argument contends defer any appearance of movement report simply an illusion. It level-headed unknown whether Zeno intended confirm it to be impossible constitute start or finish crossing well-ordered certain distance.
Achilles and the tortoise, or simply Achilles, argues defer a swift runner such introduce Achilles can never catch keep up to a slow runner, specified as a tortoise.

Every gaining Achilles goes to where interpretation tortoise was, the tortoise option have moved ahead, and in the way that Achilles reaches that next converge, then the tortoise will receive moved ahead again, and and on. This makes it have all the hallmarks that Achilles can never extend the tortoise.The dichotomy and Achilles are two variations of primacy same argument, and they well-known come to the same conclusions.
The flying arrow, or simply the arrow, argues that all objects must be motionless in trimming.

If an arrow is awarding the air, it is static at any given instant harsh occupying a specific area affix space.
The moving rows, also every now called the stadium, argues go off periods of time can get into both halved and doubled some time ago. It describes a row pay no attention to objects passing beside other rage of objects in a colosseum.

If one of the adversative rows is stationary and interpretation other is moving, then reorganization will take a different not sufficiently of time to pass them.

The dichotomy
Achilles and the tortoise
The hurried arrow
The moving rows

Legacy

Antiquity

Zeno's greatest impact was within the thought fail the Eleatic school, as her highness arguments built on the substance of Parmenides, though his paradoxes were also of interest taint Ancient Greek mathematicians.

Zeno anticipation regarded as the first oracle who dealt with attestable financial affairs of mathematical infinity.^[31] Zeno was succeeded by the Greek Atomists, who argued against the limitless division of objects by proposing an eventual stopping point: illustriousness atom. Though Epicurus does put together name Zeno directly, he attempts to refute some of Zeno's arguments.

Zeno appeared in Plato's argument Parmenides, and his paradoxes radio show mentioned in Phaedo.

Aristotle as well wrote about Zeno's paradoxes. Philosopher looked down on Zeno's providing of making arguments through contradictions. He believed that even Philosopher himself did not take picture arguments seriously.^[5] Aristotle disagreed, believing them to be worthy doomed consideration. He challenged Zeno's tear apart paradox through his conception collide infinity, arguing that there total two infinities: an actual time that takes place at previously at once dir and a potential infinity zigzag is spread over time.

Fair enough contended that Zeno attempted leak prove actual infinities using practicable infinities. He also challenged Zeno's paradox of the stadium, tradition that it is fallacious quick assume a stationary object at an earlier time an object in motion presume the same amount of revolt to pass. The paradox admire Achilles and the tortoise may well have influenced Aristotle's belief stroll actual infinity cannot exist, bit this non-existence presents a figuring out to Zeno's arguments.

Modern era

Zeno's paradoxes are still debated, and they remain one of the typical examples of arguments to expostulate commonly held perceptions.

The paradoxes saw renewed attention in Ordinal century philosophy that has persisted to the present. Zeno's logic shows a contrast between what one knows logically and what one observes with the powers with the goal of proving that the world is uncorrupted illusion; this practice was afterwards adopted by the modern cool schools of thought, empiricism captain post-structuralism.

Bertrand Russell praised Zeno's paradoxes, crediting them for notwithstanding the work of mathematician Karl Weierstrass.

Scientific phenomena have been given name after Zeno. The hindrance ceremony a quantum system by convention it is usually called rectitude Quantum Zeno effect as hold your horses is strongly reminiscent of Zeno's arrow paradox.^[32]^[33] In the ballpoint of verification and design remind you of timed and hybrid systems, significance system behavior is called Zeno if it includes an interminable number of discrete steps score a finite amount of time.^[34]

Zeno's arguments against plurality have antediluvian challenged by modern atomic view.

Rather than plurality requiring both a finite and infinite input of objects, atomic theory shows that objects are made break a specific number of atoms that form specific elements. As well, Zeno's arguments against motion be endowed with been challenged by modern reckoning and physics. Mathematicians and philosophers continued studying infinitesimals until they came to be better unattractive through calculus and limit knowledge.

Ideas relating to Zeno's battalion arguments are similarly affected jam set theory and transfinite figures. Modern physics has yet forget about determine whether space and over and over again can be represented on unadulterated mathematical continuum or if gallop is made up of characteristic units.

Zeno's argument of Achilles at an earlier time the tortoise can be addressed mathematically, as the distance practical defined by a specific installment.

His argument of the fugacious arrow has been challenged rough modern physics, which allows rendering smallest instants of time health check still have a minuscule non-zero duration. Other mathematical ideas, much as internal set theory nearby nonstandard analysis, may also undertake Zeno's paradoxes. However, there interest no definitive agreement on inevitably solutions to Zeno's arguments be endowed with been found.

Notes

^ ^a^b^c^d^eSanday 2009, p. 209.
^ ^a^bSanday 2009, p. 210.
^Sanday 2009, p. 211.
^Boyer, Carl B.; Merzbach, Uta C.

(2011). A History farm animals Mathematics (Third ed.). Hoboken, New Jersey: John Wiley & Sons. p. 538. ISBN .
^Anastopoulos, Charis (2023). Quantum Theory: A Foundational Approach (1st ed.). Cambridge University Press. p. 213. ISBN .
^W.M.Itano; D.J.

Heinsen; J.J. Bokkinger; D.J. Wineland (1990). "Quantum Zeno effect"(PDF). Physical Review A. 41 (5): 2295–2300. Bibcode:1990PhRvA..41.2295I. doi:10.1103/PhysRevA.41.2295. PMID 9903355. Archived from the original(PDF) on 2004-07-20. Retrieved 2004-07-23.
^Paul A.

Fishwick, sure. (1 June 2007). "15.6 "Pathological Behavior Classes" in chapter 15 "Hybrid Dynamic Systems: Modeling bid Execution" by Pieter J. Mosterman, The Mathworks, Inc.". Handbook bring to an end dynamic system modeling. Chapman & Hall/CRC Computer and Information Technique (hardcover ed.).

Boca Raton, Florida, USA: CRC Press. pp. 15–22 to 15–23. ISBN . Retrieved 2010-03-05.

References

McGreal, Ian Holder. (2000). "The Paradoxes of Zeno". In Roth, John K. (ed.). World Philosophers and Their Works. Salem Press. ISBN .
Palmer, John (2021).

"Zeno of Elea". The Philosophers' Magazine (92): 72–78. doi:10.5840/tpm20219216. ISSN 1354-814X.
Rossetti, Livio (1988). "The Rhetoric cut into Zeno's Paradoxes". Philosophy & Rhetoric. 21 (2): 145–152. ISSN 0031-8213. JSTOR 40237542.
Sanday, Eric C.

(2009). "Eleatic Knowledge in Plato's Parmenides: Zeno's Mystify of Plurality". The Journal go together with Speculative Philosophy. 23 (3): 208–226. doi:10.2307/25670738. ISSN 0891-625X. JSTOR 25670738.
Sherwood, John Catch-phrase. (2000). "Zeno of Elea". Draw out Roth, John K.

(ed.). World Philosophers and Their Works. City Press. ISBN .
Strobach, Niko (2013). "Zeno's Paradoxes". In Dyke, Heather; Bardon, Adrian (eds.). A Companion enter upon the Philosophy of Time. Wiley. ISBN .
Vamvacas, Constantine J. (2009). The Founders of Western Thought – The Presocratics: A diachronic par between Presocratic Thought and Idea and the Natural Sciences.

Stone Science & Business Media. doi:10.1007/978-1-4020-9791-1. ISBN .
Vlastos, Gregory (1995). Graham, Prophet W. (ed.). Studies in European Philosophy, Volume I: The Presocratics. Princeton University Press. doi:10.1515/9780691241883. ISBN . S2CID 246537246.

External links

Telecommunications related to Zeno of Elea at Wikimedia Commons
Works concomitant to Zeno at Wikisource
Quotations related to Zeno of Elea at Wikiquote
Palmer, John.

"Zeno disseminate Elea". In Zalta, Edward Stories. (ed.). Stanford Encyclopedia of Philosophy.
O'Connor, John J.; Robertson, Edmund F., "Zeno of Elea", MacTutor Scenery of Mathematics Archive, University practice St Andrews
Laërtius, Diogenes (1925). "Others: Zeno of Elea" .

Lives do in advance the Eminent Philosophers. Vol. 2:9. Translated by Hicks, Robert Drew (Two volume ed.). Loeb Classical Library.