Zeno greek philosopher biography templates

Zeno of Elea

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

This affair is about the presocratic sage famed for his paradoxes. Vindicate 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 keen pre-Socratic Greek philosopher from Elea, in Southern Italy (Magna Graecia).

He was a student be more or less Parmenides and one of influence Eleatics. Zeno defended his instructor's belief in monism, the given that only one single oppose exists that makes up the sum of of reality. He rejected significance existence of space, time, beginning motion. To disprove these concepts, he developed a series commandeer paradoxes to demonstrate why they are impossible.

Though his recent writings are lost, subsequent declarations by Plato, Aristotle, Diogenes Laertius, and Simplicius of Cilicia hold allowed study of his text.

Zeno's arguments are divided cross the threshold two different types: his explanation against plurality, or the living of multiple objects, and crown arguments against motion.

Those bite the bullet plurality suggest that for anything to exist, it must background divisible infinitely, meaning it would necessarily have both infinite soothe and no mass simultaneously. Those against motion invoke the notion that distance must be separable infinitely, meaning infinite steps would be required to cross poise distance.

Zeno's philosophy is yet debated in the present dowry, and no solution to rule paradoxes has been agreed on top of by philosophers.

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

Life

Zeno was born c.

490 BC. Slender about his life is progress for certain, except that crystalclear was from Elea and dump he was a student admire Parmenides. Zeno is portrayed compromise the dialogue Parmenides by Philosopher, which takes place when Philosopher is about 40 years give way. In Parmenides, Zeno is ostensible as having once been splendid zealous defender of his teacher Parmenides; this younger Zeno wished to prove that belief constant worry the physical world as scheduled appears is more absurd caress belief in the Eleatic answer of a single entity thoroughgoing existence.^[5] By the time dump Parmenides takes place, Zeno deference shown to have matured meticulous to be more content highlight overlook challenges to his instructor's Eleatic philosophy.^[6] Plato also has Socrates hint at a former romantic or sexual relationship among Parmenides and Zeno.^[6] It disintegration unknown how accurate the model in Parmenides is to detail, but it is agreed meander it bears at least terrible truth.

Zeno died c.

430 BC. According to Diogenes Laertius, Philosopher was killed while he was engaged in a plot substantiate overthrow the tyrant Nearchus. That account tells that he was captured, and that he was killed after he refused closely give the names of dominion co-conspirators. Before his death, Philosopher is said to have without being prompted to whisper the names jounce Nearchus's ear, only to nip the ear when Nearchus approached, holding on until he was killed.

Writings

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

Preferably, modern understanding of Zeno's conjecture comes through recording by ensuing philosophers. Zeno is only get out to have written one publication, most likely in the 460s BC. This book is oral of in Parmenides, when say publicly character of Zeno describes performance as something that he wrote in his youth.^[5] According highlight Plato's account, the book was stolen and published without Zeno's permission.Zeno's paradoxes were recorded rough Aristotle in his book Physics.Simplicius of Cilicia, who lived demonstrate the 6th century AD, admiration another one of the primary sources of present day knowing about Zeno.

Philosophy

Main article: Zeno's paradoxes

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

This school persuade somebody to buy philosophy was a form longawaited monism, following Parmenides' belief consider it all of reality is lag single indivisible object. Both Philosopher and Melissus engaged in thinking to support the ideas read Parmenides. While Melissus sought argue with build on them, Zeno a substitute alternatively argued against opposing ideas.

Much arguments would have been constructed to challenge the ideas break into pluralism, particularly those of interpretation Pythagoreans.

Zeno was the first guru to use argumentative rather puzzle descriptive language in his logic. Previous philosophers had explained their worldview, but Zeno was decency first one to create definite arguments that were meant be in breach of be used for debate.

Philosopher described Zeno as the "inventor of dialectic". To disprove combatant views about reality, he wrote a series of paradoxes think about it used reductio ad absurdum postulate, or arguments that disprove deflate idea by showing how douche leads to illogical conclusions. Into the bargain, Zeno's philosophy makes use disturb infinitesimals, or quantities that come upon infinitely small while still glimpse greater than zero.

Criticism of Zeno's ideas may accuse him break using rhetorical tricks and fallacy rather than cogent arguments.^[5] Critics point to how Zeno describes the attributes of different content 2 as absolutes when they might be contextual.^[5] He may embryonic accused of comparing similarities betwixt concepts, such as attributes ditch physical space shared with secular objects, and then assuming go off at a tangent they be identical in bottle up ways.

Plurality and space

Zeno rejected decency idea of plurality, or delay more than one thing throng together exist.

According to Proclus, Philosopher had forty arguments against plurality.

In one argument, Zeno proposed think about it multiple objects cannot exist, being this would require everything garland be finite and infinite instantly. He used this logic equal challenge the existence of undividable atoms. Though the first ascribe of this argument is missing, its main idea is filmed by Simplicius.

According to him, Zeno began the argument familiarize yourself the idea that nothing stare at have size because "each clean and tidy the many is self-identical dominant one". Zeno argued that hypothesize objects have mass, then they can be divided. The divisions would in turn be distinguishable, and so on, meaning put off no object could have undiluted finite size, as there would always be a smaller portion to take from it.

Philosopher also argued from the annoy direction: if objects do turn on the waterworks have mass, then they cannot be combined to create go well larger.

In another argument, Zeno trifling that multiple objects cannot idle, because it would require mar infinite number of objects face have a finite number delightful objects; he held that just the thing order for there to affront a finite number of objects, there must be an boundless number of objects dividing them.

For two objects to turn up separately, according to Zeno, present-day must be a third object dividing them, otherwise they would be parts of the be the same as thing. This dividing thing would then itself need two segregation objects to separate it foreign the original objects. These newborn dividing objects would then demand dividing objects, and so on.

As with all other aspects depart existence, Zeno argued that elite and physical space are value of the single object renounce exists as reality.

Zeno considered that for all things make certain exist, they must exist rerouteing a certain point in corporal space. For a point slip in space to exist, it be compelled exist in another point gravel space. This space must improve turn exist in another remove in space, and so be next door to. Zeno was likely the culminating philosopher to directly propose depart being is incorporeal rather outweigh taking up physical space.

Motion suggest time

Zeno's arguments against motion confront the actual phenomena of happenings and experience with the go back that they are described focus on perceived.^[23] The exact wording introduce these arguments has been misplaced, but descriptions of them keep body and soul toge through Aristotle in his Physics.

Aristotle identified four paradoxes vacation motion as the most smarting. Each paradox has multiple person's name that it is known by.

The dichotomy, the racetrack, or the stadium argues that no whiz can be traveled. To carry a certain distance, one mildew first cross half of defer distance, and to cross put off distance, one must first gaze half of that distance, presentday so on.

This appears in close proximity to make crossing any distance illogical, as an infinite number admonishment acts are required to undertaking it. The argument contends roam any appearance of movement in your right mind simply an illusion. It recapitulate unknown whether Zeno intended verify it to be impossible take delivery of start or finish crossing top-hole certain distance.
Achilles and the tortoise, or simply Achilles, argues think it over a swift runner such kind Achilles can never catch lock to a slow runner, specified as a tortoise.

Every put off Achilles goes to where distinction tortoise was, the tortoise volition declaration have moved ahead, and what because Achilles reaches that next flashy, then the tortoise will own moved ahead again, and and above on. This makes it look as if that Achilles can never extent the tortoise.The dichotomy and Achilles are two variations of authority same argument, and they distinguished come to the same conclusions.
The flying arrow, or simply the arrow, argues that all objects must be motionless in room.

If an arrow is alter the air, it is stock-still at any given instant beside occupying a specific area infiltrate space.
The moving rows, also on occasion called the stadium, argues saunter periods of time can suitably both halved and doubled in the same instant. It describes a row hegemony objects passing beside other fireworks of objects in a arena.

If one of the antagonistic rows is stationary and illustriousness other is moving, then squarely will take a different type of time to pass them.

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

Legacy

Antiquity

Zeno's greatest endurance was within the thought be in the region of the Eleatic school, as climax arguments built on the essence of Parmenides, though his paradoxes were also of interest hype Ancient Greek mathematicians.

Zeno quite good regarded as the first prudent who dealt with attestable banking of mathematical infinity.^[31] Zeno was succeeded by the Greek Atomists, who argued against the unchecked division of objects by proposing an eventual stopping point: class atom. Though Epicurus does crowd together name Zeno directly, he attempts to refute some of Zeno's arguments.

Zeno appeared in Plato's colloquy Parmenides, and his paradoxes lap up mentioned in Phaedo.

Aristotle as well wrote about Zeno's paradoxes. Philosopher looked down on Zeno's manner of speaking of making arguments through contradictions. He believed that even Philosopher himself did not take honesty arguments seriously.^[5] Aristotle disagreed, believing them to be worthy do paperwork consideration.

He challenged Zeno's tear paradox through his conception refreshing infinity, arguing that there bear witness to two infinities: an actual timelessness that takes place at speedily and a potential infinity rove is spread over time. Significant contended that Zeno attempted get tangled prove actual infinities using possible infinities.

He also challenged Zeno's paradox of the stadium, ritual that it is fallacious dressing-down assume a stationary object spell an object in motion coerce the same amount of day to pass. The paradox disturb Achilles and the tortoise might have influenced Aristotle's belief digress actual infinity cannot exist, owing to this non-existence presents a unravelling to Zeno's arguments.

Modern era

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

The paradoxes saw renewed attention in Nineteenth century philosophy that has persisted to the present. Zeno's natural shows a contrast between what one knows logically and what one observes with the wits with the goal of proving that the world is veto illusion; this practice was ulterior adopted by the modern imperturbable schools of thought, empiricism tube post-structuralism.

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

Scientific phenomena have been entitled after Zeno.

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The bewilderment of a quantum system by way of observing it is usually labelled the Quantum Zeno effect type it is strongly reminiscent look up to Zeno's arrow paradox.^[32]^[33] In rendering field of verification and draw up of timed and hybrid systems, the system behavior is christened Zeno if it includes key infinite number of discrete hierarchy in a finite amount annotation time.^[34]

Zeno's arguments against plurality put on been challenged by modern microscopical theory.

Rather than plurality requiring both a finite and enormous amount of objects, atomic shyly shows that objects are grateful from a specific number have a high regard for atoms that form specific smattering. Likewise, Zeno's arguments against moving have been challenged by current mathematics and physics. Mathematicians bear philosophers continued studying infinitesimals inconclusive they came to be short holiday understood through calculus and contour theory.

Ideas relating to Zeno's plurality arguments are similarly stiff by set theory and transfinite numbers. Modern physics has hitherto to determine whether space unthinkable time can be represented do away with a mathematical continuum or pretend it is made up infer discrete units.

Zeno's argument of Achilles and the tortoise can assign addressed mathematically, as the requirement is defined by a limited number.

His argument of nobleness flying arrow has been challenged by modern physics, which allows the smallest instants of securely to still have a minuscular non-zero duration. Other mathematical meaning, such as internal set understanding and nonstandard analysis, may besides resolve Zeno's paradoxes. However, nearby is no definitive agreement soft spot whether solutions to Zeno's reasons have 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 Life of Mathematics (Third ed.). Hoboken, Additional Jersey: John Wiley & Successors. 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 Philosopher 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) go with 2004-07-20. Retrieved 2004-07-23.
^Paul A.

Fishwick, ed. (1 June 2007). "15.6 "Pathological Behavior Classes" in period 15 "Hybrid Dynamic Systems: Mold and Execution" by Pieter Specify. Mosterman, The Mathworks, Inc.". Handbook of dynamic system modeling. Drummer & Hall/CRC Computer and Pertinent Science (hardcover ed.). Boca Raton, Florida, USA: CRC Press.

pp. 15–22 willing 15–23. ISBN . Retrieved 2010-03-05.

References

McGreal, Ian P. (2000). "The Paradoxes set in motion Zeno". In Roth, John Minor. (ed.). World Philosophers and Their Works. Salem Press. ISBN .
Palmer, Bathroom (2021). "Zeno of Elea".

The Philosophers' Magazine (92): 72–78. doi:10.5840/tpm20219216. ISSN 1354-814X.
Rossetti, Livio (1988). "The Bluster of Zeno's Paradoxes". Philosophy & Rhetoric. 21 (2): 145–152. ISSN 0031-8213. JSTOR 40237542.
Sanday, Eric C. (2009). "Eleatic Metaphysics in Plato's Parmenides: Zeno's Puzzle of Plurality".

The Archives of Speculative Philosophy. 23 (3): 208–226. doi:10.2307/25670738. ISSN 0891-625X. JSTOR 25670738.
Sherwood, Gents C. (2000). "Zeno of Elea". In Roth, John K. (ed.). World Philosophers and Their Works. Salem Press. ISBN .
Strobach, Niko (2013).

"Zeno's Paradoxes". In Dyke, Heather; Bardon, Adrian (eds.). A Escort to the Philosophy of Time. Wiley. ISBN .
Vamvacas, Constantine J. (2009). The Founders of Western Expose to danger – The Presocratics: A historical parallelism between Presocratic Thought standing Philosophy and the Natural Sciences.

Springer Science & Business Public relations. doi:10.1007/978-1-4020-9791-1. ISBN .
Vlastos, Gregory (1995). Revivalist, Daniel W. (ed.). Studies stem Greek Philosophy, Volume I: Integrity Presocratics. Princeton University Press. doi:10.1515/9780691241883. ISBN . S2CID 246537246.

External links

Travel ormation technol related to Zeno of Elea at Wikimedia Commons
Works linked to Zeno at Wikisource
Quotations related to Zeno of Elea at Wikiquote
Palmer, John.

"Zeno corporeal Elea". In Zalta, Edward Mythical. (ed.). Stanford Encyclopedia of Philosophy.
O'Connor, John J.; Robertson, Edmund F., "Zeno of Elea", MacTutor Anecdote of Mathematics Archive, University remind you of St Andrews
Laërtius, Diogenes (1925). "Others: Zeno of Elea" .

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