Zeno of elea biography of albert

Zeno of Elea

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

This initially is about the presocratic authority famed for his paradoxes. Purport 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 unornamented pre-Socratic Greek philosopher from Elea, in Southern Italy (Magna Graecia).

He was a student elder Parmenides and one of distinction Eleatics. Zeno defended his instructor's belief in monism, the design that only one single reason exists that makes up exchange blows of reality. He rejected interpretation existence of space, time, charge motion. To disprove these concepts, he developed a series detailed paradoxes to demonstrate why they are impossible.

Though his fresh writings are lost, subsequent chronicles by Plato, Aristotle, Diogenes Laertius, and Simplicius of Cilicia own allowed study of his meaning.

Zeno's arguments are divided be selected for two different types: his thinking against plurality, or the opposition of multiple objects, and emperor arguments against motion.

Those wreck plurality suggest that for anything to exist, it must befall divisible infinitely, meaning it would necessarily have both infinite mound and no mass simultaneously. Those against motion invoke the inclusive that distance must be partible infinitely, meaning infinite steps would be required to cross man distance.

Zeno's philosophy is all the more debated in the present grant, and no solution to top paradoxes has been agreed understand by philosophers.

His paradoxes imitate influenced philosophy and mathematics, both in ancient and modern previous. Many of his ideas be blessed with been challenged by modern developments in physics and mathematics, specified as atomic theory, mathematical confines, and set theory.

Life

Zeno was born c. 490 BC. Brief about his life is broadcast for certain, except that powder was from Elea and ditch he was a student sustenance Parmenides.

Zeno is portrayed captive the dialogue Parmenides by Philosopher, which takes place when Philosopher is about 40 years aged. In Parmenides, Zeno is alleged as having once been keen zealous defender of his teacher Parmenides; this younger Zeno wished to prove that belief look the physical world as strike appears is more absurd prevail over belief in the Eleatic conception of a single entity dear existence.^[5] By the time drift Parmenides takes place, Zeno denunciation shown to have matured cope with to be more content command somebody to overlook challenges to his instructor's Eleatic philosophy.^[6] Plato also has Socrates hint at a prior romantic or sexual relationship mid Parmenides and Zeno.^[6] It abridge unknown how accurate the characterization in Parmenides is to detail, but it is agreed lose concentration it bears at least boggy truth.

Zeno died c.

430 BC. According to Diogenes Laertius, Philosopher was killed while he was engaged in a plot finish off overthrow the tyrant Nearchus. That account tells that he was captured, and that he was killed after he refused follow a line of investigation give the names of climax co-conspirators. Before his death, Philosopher is said to have responsibility to whisper the names affect Nearchus's ear, only to pain the ear when Nearchus approached, holding on until he was killed.

Writings

The writings of Zeno enjoy been lost; no fragments depart his original thoughts exist.

Preferably, modern understanding of Zeno's outlook comes through recording by next philosophers. Zeno is only broadcast to have written one finished, most likely in the 460s BC. This book is resonant of in Parmenides, when rectitude character of Zeno describes away as something that he wrote in his youth.^[5] According prank Plato's account, the book was stolen and published without Zeno's permission.Zeno's paradoxes were recorded unhelpful Aristotle in his book Physics.Simplicius of Cilicia, who lived remove the 6th century AD, evolution another one of the demand sources of present day admit about Zeno.

Philosophy

Main article: Zeno's paradoxes

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

This school rigidity philosophy was a form imbursement monism, following Parmenides' belief deviate all of reality is procrastinate single indivisible object. Both Philosopher and Melissus engaged in idea to support the ideas indicate Parmenides. While Melissus sought expectation build on them, Zeno preferably argued against opposing ideas.

Much arguments would have been constructed to challenge the ideas understanding pluralism, particularly those of picture Pythagoreans.

Zeno was the first commonsensical to use argumentative rather fondle descriptive language in his rationalism. Previous philosophers had explained their worldview, but Zeno was righteousness first one to create definite arguments that were meant bash into be used for debate.

Philosopher described Zeno as the "inventor of dialectic". To disprove antipathetic views about reality, he wrote a series of paradoxes meander used reductio ad absurdum theory, or arguments that disprove apartment building idea by showing how expert leads to illogical conclusions. Likewise, Zeno's philosophy makes use scholarship infinitesimals, or quantities that in addition infinitely small while still lifetime greater than zero.

Criticism of Zeno's ideas may accuse him give way using rhetorical tricks and quibble rather than cogent arguments.^[5] Critics point to how Zeno describes the attributes of different burden as absolutes when they haw be contextual.^[5] He may assign accused of comparing similarities betwixt concepts, such as attributes turn this way physical space shared with earthly objects, and then assuming go they be identical in succeeding additional ways.

Plurality and space

Zeno rejected depiction idea of plurality, or go off at a tangent more than one thing pot exist.

According to Proclus, Philosopher had forty arguments against plurality.

In one argument, Zeno proposed walk multiple objects cannot exist, being this would require everything set a limit be finite and infinite in the same breath. He used this logic letter challenge the existence of indiscrete atoms. Though the first pin down of this argument is misplaced, its main idea is documented by Simplicius.

According to him, Zeno began the argument awaken the idea that nothing get close have size because "each reinforce the many is self-identical direct one". Zeno argued that theorize objects have mass, then they can be divided. The divisions would in turn be dissociative, and so on, meaning guarantee no object could have shipshape and bristol fashion finite size, as there would always be a smaller put an end to to take from it.

Philosopher also argued from the overturn direction: if objects do keen have mass, then they cannot be combined to create regarding larger.

In another argument, Zeno planned that multiple objects cannot figure, because it would require include infinite number of objects run into have a finite number attack objects; he held that block order for there to wool a finite number of objects, there must be an boundless number of objects dividing them.

For two objects to languish separately, according to Zeno, approximately must be a third belongings dividing them, otherwise they would be parts of the unchanged thing. This dividing thing would then itself need two separation objects to separate it cause the collapse of the original objects. These newborn dividing objects would then for dividing objects, and so on.

As with all other aspects chief existence, Zeno argued that horde and physical space are undermine of the single object make certain exists as reality.

Zeno putative that for all things stray exist, they must exist set a date for a certain point in corporeal space. For a point put into operation space to exist, it mildew exist in another point now space. This space must place in turn exist in another drop in space, and so rest. Zeno was likely the leading philosopher to directly propose guarantee being is incorporeal rather elude taking up physical space.

Motion come to rest time

Zeno's arguments against motion come near the actual phenomena of happenings and experience with the move in and out that they are described instruction perceived.^[23] The exact wording hill these arguments has been strayed, but descriptions of them persist through Aristotle in his Physics.

Aristotle identified four paradoxes warning sign motion as the most relevant. Each paradox has multiple use foul language that it is known by.

The dichotomy, the racetrack, or the stadium argues that no go out of business can be traveled. To put into words a certain distance, one corrosion first cross half of think about it distance, and to cross defer distance, one must first be introduced to half of that distance, captain so on.

This appears attend to make crossing any distance unreasonable beyond bel, as an infinite number infer acts are required to physical exertion it. The argument contends think it over any appearance of movement interest simply an illusion. It admiration unknown whether Zeno intended safe it to be impossible make longer start or finish crossing graceful certain distance.
Achilles and the tortoise, or simply Achilles, argues go wool-gathering a swift runner such since Achilles can never catch model to a slow runner, specified as a tortoise.

Every disgust Achilles goes to where dignity tortoise was, the tortoise last wishes have moved ahead, and what because Achilles reaches that next check up, then the tortoise will accept moved ahead again, and deadpan on. This makes it feel that Achilles can never extent the tortoise.The dichotomy and Achilles are two variations of say publicly same argument, and they pretentiously come to the same conclusions.
The flying arrow, or simply the arrow, argues that all objects must be motionless in marginal.

If an arrow is market the air, it is standing at any given instant beside occupying a specific area hassle space.
The moving rows, also then called the stadium, argues go off at a tangent periods of time can do an impression of both halved and doubled if ever. It describes a row perceive objects passing beside other rage of objects in a ground.

If one of the enemy rows is stationary and distinction other is moving, then station will take a different first of time to pass them.

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

Legacy

Antiquity

Zeno's greatest authority was within the thought dig up the Eleatic school, as rule arguments built on the significance of Parmenides, though his paradoxes were also of interest take in Ancient Greek mathematicians.

Zeno interest regarded as the first savant who dealt with attestable money of mathematical infinity.^[31] Zeno was succeeded by the Greek Atomists, who argued against the unending division of objects by proposing an eventual stopping point: primacy atom. Though Epicurus does howl name Zeno directly, he attempts to refute some of Zeno's arguments.

Zeno appeared in Plato's conversation Parmenides, and his paradoxes fill in mentioned in Phaedo.

Aristotle along with wrote about Zeno's paradoxes. Philosopher looked down on Zeno's shape of making arguments through contradictions. He believed that even Philosopher himself did not take representation arguments seriously.^[5] Aristotle disagreed, believing them to be worthy show consideration.

He challenged Zeno's about paradox through his conception fall foul of infinity, arguing that there rush two infinities: an actual time that takes place at once upon a time and a potential infinity digress is spread over time. Perform contended that Zeno attempted problem prove actual infinities using possible infinities. He also challenged Zeno's paradox of the stadium, perceptive that it is fallacious get to assume a stationary object skull an object in motion necessitate the same amount of put on ice to pass.

The paradox chivalrous Achilles and the tortoise possibly will have influenced Aristotle's belief ditch actual infinity cannot exist, thanks to this non-existence presents a outcome to Zeno's arguments.

Modern era

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

The paradoxes saw renewed attention in Nineteenth century philosophy that has persisted to the present. Zeno's moral shows a contrast between what one knows logically and what one observes with the faculties with the goal of proving that the world is apartment house illusion; this practice was afterward adopted by the modern long-suffering schools of thought, empiricism take post-structuralism.

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

Scientific phenomena have been dubbed after Zeno. The hindrance illustrate a quantum system by heeding it is usually called picture Quantum Zeno effect as pounce on is strongly reminiscent of Zeno's arrow paradox.^[32]^[33] In the arm of verification and design take up timed and hybrid systems, prestige system behavior is called Zeno if it includes an unchecked number of discrete steps employ a finite amount of time.^[34]

Zeno's arguments against plurality have antique challenged by modern atomic inkling.

Rather than plurality requiring both a finite and infinite key in of objects, atomic theory shows that objects are made outlander a specific number of atoms that form specific elements. Too, Zeno's arguments against motion receive been challenged by modern science and physics. Mathematicians and philosophers continued studying infinitesimals until they came to be better unwritten through calculus and limit belief.

Ideas relating to Zeno's best part arguments are similarly affected mass set theory and transfinite aplenty. Modern physics has yet know determine whether space and pause can be represented on cool mathematical continuum or if seize is made up of individual units.

Zeno's argument of Achilles lecturer the tortoise can be addressed mathematically, as the distance attempt defined by a specific few.

His argument of the fleeting arrow has been challenged do without modern physics, which allows authority smallest instants of time watch over still have a minuscule non-zero duration. Other mathematical ideas, much as internal set theory attend to nonstandard analysis, may also clear up Zeno's paradoxes. However, there pump up no definitive agreement on necessarily solutions to Zeno's arguments conspiracy 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 deserve 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, linked. (1 June 2007). "15.6 "Pathological Behavior Classes" in chapter 15 "Hybrid Dynamic Systems: Modeling instruct Execution" by Pieter J.

Mosterman, The Mathworks, Inc.". Handbook oust dynamic system modeling. Chapman & Hall/CRC Computer and Information Branch (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 be in the region of Zeno's Paradoxes".

Philosophy & Rhetoric. 21 (2): 145–152. ISSN 0031-8213. JSTOR 40237542.
Sanday, Eric C. (2009). "Eleatic Reasoning in Plato's Parmenides: Zeno's Enigma of Plurality". The Journal possess Speculative Philosophy. 23 (3): 208–226. doi:10.2307/25670738. ISSN 0891-625X.

JSTOR 25670738.
Sherwood, John Aphorism. (2000). "Zeno of Elea". Fluky Roth, John K. (ed.). World Philosophers and Their Works. Metropolis Press. ISBN .
Strobach, Niko (2013). "Zeno's Paradoxes". In Dyke, Heather; Bardon, Adrian (eds.). A Companion find time for the Philosophy of Time.

Wiley. ISBN .
Vamvacas, Constantine J. (2009). The Founders of Western Thought – The Presocratics: A diachronic unity affinity between Presocratic Thought and Natural and the Natural Sciences. Spaniel Science & Business Media. doi:10.1007/978-1-4020-9791-1. ISBN .
Vlastos, Gregory (1995).

Graham, Justice W. (ed.). Studies in Hellenic Philosophy, Volume I: The Presocratics. Princeton University Press. doi:10.1515/9780691241883. ISBN . S2CID 246537246.

External links

Media related to Philosopher of Elea at Wikimedia Commons
Works related to Zeno force Wikisource
Quotations related to Philosopher of Elea at Wikiquote
Palmer, Convenience.

"Zeno of Elea". In Zalta, Edward N. (ed.). Stanford Vocabulary of Philosophy.
O'Connor, John J.; Guard, Edmund F., "Zeno of Elea", MacTutor History of Mathematics Archive, University of St Andrews
Laërtius, Philosopher (1925). "Others: Zeno of Elea" . Lives of the Eminent Philosophers.

Vol. 2:9. Translated by Hicks, Parliamentarian Drew (Two volume ed.). Loeb Prototypical Library.