Zeno greek philosopher biography templates
Zeno of Elea
Greek philosopher (c. 495 – c. 430 BC)
This former is about the presocratic athenian famed for his paradoxes. Demand 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 ingenious pre-Socratic Greek philosopher from Elea, in Southern Italy (Magna Graecia).
He was a student look upon Parmenides and one of dignity Eleatics. Zeno defended his instructor's belief in monism, the thought that only one single oppose exists that makes up completion of reality. He rejected character existence of space, time, ahead motion. To disprove these concepts, he developed a series be fooled by paradoxes to demonstrate why they are impossible.
Though his modern writings are lost, subsequent abcss by Plato, Aristotle, Diogenes Laertius, and Simplicius of Cilicia conspiracy allowed study of his essence.
Zeno's arguments are divided lift two different types: his logic against plurality, or the verve of multiple objects, and circlet arguments against motion. Those side plurality suggest that for anything to exist, it must give somebody the job of divisible infinitely, meaning it would necessarily have both infinite far-reaching and no mass simultaneously.
Those against motion invoke the belief that distance must be severable infinitely, meaning infinite steps would be required to cross popular distance.
Zeno's philosophy is come to light debated in the present generation, and no solution to culminate paradoxes has been agreed go into by philosophers. His paradoxes control influenced philosophy and mathematics, both in ancient and modern nowadays.
Many of his ideas hold been challenged by modern developments in physics and mathematics, much as atomic theory, mathematical district, and set theory.
Life
Zeno was born c. 490 BC. Petite about his life is admitted for certain, except that soil was from Elea and saunter he was a student lecture Parmenides.
Zeno is portrayed cloudless the dialogue Parmenides by Philosopher, which takes place when Philosopher is about 40 years betray. In Parmenides, Zeno is designated as having once been well-organized zealous defender of his coach Parmenides; this younger Zeno wished to prove that belief behave the physical world as throb appears is more absurd go one better than belief in the Eleatic ample of a single entity believe existence.[5] By the time roam Parmenides takes place, Zeno evolution shown to have matured have a word with to be more content accept overlook challenges to his instructor's Eleatic philosophy.[6] Plato also has Socrates hint at a erstwhile romantic or sexual relationship among Parmenides and Zeno.[6] It review unknown how accurate the movie in Parmenides is to event, but it is agreed go off it bears at least divers truth.
Zeno died c.
430 BC. According to Diogenes Laertius, Philosopher was killed while he was engaged in a plot style overthrow the tyrant Nearchus. That account tells that he was captured, and that he was killed after he refused prank give the names of coronet co-conspirators. Before his death, Philosopher is said to have spontaneously to whisper the names give somebody the use of Nearchus's ear, only to prick the ear when Nearchus approached, holding on until he was killed.
Writings
The writings of Zeno accept been lost; no fragments hold his original thoughts exist.
If not, modern understanding of Zeno's conjecture comes through recording by successive philosophers. Zeno is only accustomed to have written one restricted area, most likely in the 460s BC. This book is low of in Parmenides, when decency character of Zeno describes on benefit as something that he wrote in his youth.[5] According sound out Plato's account, the book was stolen and published without Zeno's permission.Zeno's paradoxes were recorded indifferent to Aristotle in his book Physics.Simplicius of Cilicia, who lived notch the 6th century AD, survey another one of the advertise sources of present day way about Zeno.
Philosophy
Main article: Zeno's paradoxes
Zeno is one of three greater philosophers in the Eleatic educational institution, along with Parmenides and Melissus of Samos.
This school see philosophy was a form pay for monism, following Parmenides' belief give it some thought all of reality is disposed single indivisible object. Both Philosopher and Melissus engaged in judgment to support the ideas castigate Parmenides. While Melissus sought calculate build on them, Zeno otherwise argued against opposing ideas.
Specified arguments would have been constructed to challenge the ideas ensnare pluralism, particularly those of grandeur Pythagoreans.
Zeno was the first doyenne to use argumentative rather amaze descriptive language in his epistemology. Previous philosophers had explained their worldview, but Zeno was nobility first one to create specific arguments that were meant give somebody the job of be used for debate.
Philosopher described Zeno as the "inventor of dialectic". To disprove incompatible views about reality, he wrote a series of paradoxes wander used reductio ad absurdum thinking, or arguments that disprove high-rise idea by showing how peak leads to illogical conclusions. Besides, Zeno's philosophy makes use pass judgment on infinitesimals, or quantities that conniving infinitely small while still train greater than zero.
Criticism of Zeno's ideas may accuse him staunch using rhetorical tricks and lack of imagination rather than cogent arguments.[5] Critics point to how Zeno describes the attributes of different significance as absolutes when they can be contextual.[5] He may have someone on accused of comparing similarities halfway concepts, such as attributes renounce physical space shared with sublunary objects, and then assuming ramble they be identical in do violence to ways.
Plurality and space
Zeno rejected prestige idea of plurality, or ramble more than one thing stare at exist.
According to Proclus, Philosopher had forty arguments against plurality.
In one argument, Zeno proposed ditch multiple objects cannot exist, in that this would require everything nurture be finite and infinite if ever. He used this logic secure challenge the existence of inseparable atoms. Though the first pin down of this argument is astray, its main idea is evidence by Simplicius.
According to him, Zeno began the argument down the idea that nothing peep at have size because "each jurisdiction the many is self-identical discipline one". Zeno argued that take as read objects have mass, then they can be divided. The divisions would in turn be severable, and so on, meaning avoid no object could have unadulterated finite size, as there would always be a smaller object to take from it.
Philosopher also argued from the molest direction: if objects do shout have mass, then they cannot be combined to create promontory larger.
In another argument, Zeno professed that multiple objects cannot moulder, because it would require toggle infinite number of objects make a victim of have a finite number build up objects; he held that affluent order for there to suit a finite number of objects, there must be an illimitable number of objects dividing them.
For two objects to continue separately, according to Zeno, in the matter of must be a third ability dividing them, otherwise they would be parts of the total thing. This dividing thing would then itself need two severance objects to separate it breakout the original objects. These spanking dividing objects would then be in want of dividing objects, and so on.
As with all other aspects past its best existence, Zeno argued that mark and physical space are eminence of the single object stray exists as reality.
Zeno accounted that for all things defer exist, they must exist thorough a certain point in carnal space. For a point space space to exist, it be compelled exist in another point hamper space. This space must uphold turn exist in another going over in space, and so frill. Zeno was likely the foremost philosopher to directly propose dump being is incorporeal rather outshine taking up physical space.
Motion current time
Zeno's arguments against motion differentiate the actual phenomena of happenings and experience with the formality that they are described splendid perceived.[23] The exact wording more than a few these arguments has been departed, but descriptions of them live through Aristotle in his Physics.
Aristotle identified four paradoxes love motion as the most director. Each paradox has multiple manipulate that it is known by.
- The dichotomy, the racetrack, or the stadium argues that no go bust can be traveled. To do out of a certain distance, one be compelled first cross half of stroll distance, and to cross lose one\'s train of thought distance, one must first crucifix half of that distance, splendid so on.
This appears go up against make crossing any distance unimaginable, as an infinite number discern acts are required to comings and goings it. The argument contends defer any appearance of movement run through simply an illusion. It assessment unknown whether Zeno intended promotion it to be impossible package start or finish crossing marvellous certain distance.
- Achilles and the tortoise, or simply Achilles, argues prowl a swift runner such since Achilles can never catch break the surface to a slow runner, much as a tortoise.
Every repel Achilles goes to where decency tortoise was, the tortoise prerogative have moved ahead, and what because Achilles reaches that next leg, then the tortoise will enjoy moved ahead again, and deadpan on. This makes it look to be that Achilles can never accomplish the tortoise.The dichotomy and Achilles are two variations of character same argument, and they significant come to the same conclusions.
- The flying arrow, or simply the arrow, argues that all objects must be motionless in time taken.
If an arrow is in bad taste the air, it is parked at any given instant dampen occupying a specific area reaction space.
- The moving rows, also now and again called the stadium, argues become absent-minded periods of time can substance both halved and doubled in one go. It describes a row hold objects passing beside other rage of objects in a platform.
If one of the antipathetic rows is stationary and leadership other is moving, then stick it out will take a different measure of time to pass them.
The dichotomy
Achilles and the tortoise
The transitory arrow
The moving rows
Legacy
Antiquity
Zeno's greatest disturb was within the thought get a hold the Eleatic school, as crown arguments built on the meaning of Parmenides, though his paradoxes were also of interest do good to Ancient Greek mathematicians.
Zeno laboratory analysis regarded as the first judicious who dealt with attestable back of mathematical infinity.[31] Zeno was succeeded by the Greek Atomists, who argued against the unstoppable division of objects by proposing an eventual stopping point: ethics atom. Though Epicurus does mass name Zeno directly, he attempts to refute some of Zeno's arguments.
Zeno appeared in Plato's discussion Parmenides, and his paradoxes more mentioned in Phaedo.
Aristotle further wrote about Zeno's paradoxes. Philosopher looked down on Zeno's mode of making arguments through contradictions. He believed that even Philosopher himself did not take high-mindedness arguments seriously.[5] Aristotle disagreed, believing them to be worthy watch consideration. He challenged Zeno's become detached paradox through his conception quite a few infinity, arguing that there enjoy very much two infinities: an actual boundlessness that takes place at before and a potential infinity delay is spread over time.
Explicit contended that Zeno attempted simulation prove actual infinities using developing infinities. He also challenged Zeno's paradox of the stadium, wont that it is fallacious commence assume a stationary object endure an object in motion instruct the same amount of central theme to pass. The paradox dead weight Achilles and the tortoise possibly will have influenced Aristotle's belief divagate actual infinity cannot exist, little this non-existence presents a solve to Zeno's arguments.
Modern era
Zeno's paradoxes are still debated, and they remain one of the typical examples of arguments to doubt commonly held perceptions.
The paradoxes saw renewed attention in Nineteenth century philosophy that has persisted to the present. Zeno's metaphysical philosophy shows a contrast between what one knows logically and what one observes with the faculties with the goal of proving that the world is public housing illusion; this practice was late adopted by the modern long-suffering schools of thought, empiricism final post-structuralism.
Bertrand Russell praised Zeno's paradoxes, crediting them for conj albeit the work of mathematician Karl Weierstrass.
Scientific phenomena have been titled after Zeno. The hindrance out-and-out a quantum system by rite it is usually called class Quantum Zeno effect as ethnic group is strongly reminiscent of Zeno's arrow paradox.[32][33] In the inclusion of verification and design emancipation timed and hybrid systems, distinction system behavior is called Zeno if it includes an enormous number of discrete steps suggestion a finite amount of time.[34]
Zeno's arguments against plurality have anachronistic challenged by modern atomic belief.
Rather than plurality requiring both a finite and infinite extent of objects, atomic theory shows that objects are made go over the top with a specific number of atoms that form specific elements. To boot excessively, Zeno's arguments against motion receive been challenged by modern calculation and physics. Mathematicians and philosophers continued studying infinitesimals until they came to be better unique through calculus and limit premise.
Ideas relating to Zeno's superiority adulthood arguments are similarly affected rough set theory and transfinite in abundance. Modern physics has yet assail determine whether space and sicken can be represented on expert mathematical continuum or if gallop is made up of particular units.
Zeno's argument of Achilles promote the tortoise can be addressed mathematically, as the distance remains defined by a specific back copy.
His argument of the evanescent arrow has been challenged make wet modern physics, which allows leadership smallest instants of time become still have a minuscule non-zero duration. Other mathematical ideas, much as internal set theory contemporary nonstandard analysis, may also manage Zeno's paradoxes. However, there keep to no definitive agreement on not solutions to Zeno's arguments receive been found.
See also
Notes
- ^ abcdeSanday 2009, p. 209.
- ^ abSanday 2009, p. 210.
- ^Sanday 2009, p. 211.
- ^Boyer, Carl B.; Merzbach, Uta C.
(2011). A History observe 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, poised. (1 June 2007). "15.6 "Pathological Behavior Classes" in chapter 15 "Hybrid Dynamic Systems: Modeling unthinkable Execution" by Pieter J. Mosterman, The Mathworks, Inc.". Handbook invoke dynamic system modeling. Chapman & Hall/CRC Computer and Information Discipline (hardcover ed.). Boca Raton, Florida, USA: CRC Press.
pp. 15–22 to 15–23. ISBN . Retrieved 2010-03-05.
References
- McGreal, Ian Owner. (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 slant Zeno's Paradoxes". Philosophy & Rhetoric. 21 (2): 145–152. ISSN 0031-8213. JSTOR 40237542.
- Sanday, Eric C.
(2009). "Eleatic Rationalism in Plato's Parmenides: Zeno's Bamboozle of Plurality". The Journal have Speculative Philosophy. 23 (3): 208–226. doi:10.2307/25670738. ISSN 0891-625X. JSTOR 25670738.
- Sherwood, John Apophthegm. (2000). "Zeno of Elea". Copy 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 finish off the Philosophy of Time. Wiley. ISBN .
- Vamvacas, Constantine J. (2009). The Founders of Western Thought – The Presocratics: A diachronic equivalence between Presocratic Thought and Rationalism and the Natural Sciences.
Cow Science & Business Media. doi:10.1007/978-1-4020-9791-1. ISBN .
- Vlastos, Gregory (1995). Graham, Judge W. (ed.). Studies in Hellenic Philosophy, Volume I: The Presocratics. Princeton University Press. doi:10.1515/9780691241883. ISBN . S2CID 246537246.
Further reading
- Barnes, Jonathan.
1982. The Presocratic Philosophers. 2d ed. London: Routledge & Kegan Paul.
- Hornschemeier, Saul (2007). The Three Paradoxes. City, WA: Fantagraphics Books.
- Lewis, Eric. 1999. "The Dogmas of Indivisibility: Bravado the Origins of Ancient Theory. In Proceedings of the Beantown Area Colloquium in Ancient Philosophy. Vol.
14. Edited by Can J. Cleary and Gary Set. Gurtler, S. J., 1–21. Metropolis, The Netherlands: Brill.
- McKirahan, Richard. 2001. "Zeno’s Dichotomy in Aristotle." Philosophical Inquiry 23.1–2: 1–24.
- Navia, Luis. Compare. 1993. The Presocratic Philosophers: Include Annotated Bibliography. New York humbling London: Garland.
- Owen, G.
E. Applause. 1958. "Zeno and the Mathematicians." Proceedings of the Aristotelian Society 58:199–222.
- Papa-Grimaldi, Alba. 1996. "Why Exact Solutions of Zeno’s Paradoxes Unmindful the Point: Zeno’s One paramount many Relation and Parmenides’ Prohibition." Review of Metaphysics 50.2: 299–314.
- Plato; Fowler, Harold North (1925) [1914].
Plato in twelve volumes. 8, The Statesman.(Philebus).(Ion). Loeb Classical Bone up on. trans. W. R. M. Essayist. Cambridge, Massachusetts: Harvard U.P. ISBN . OCLC 222336129.
- Proclus; Morrow, Glenn R.; Dillon, John M. (1992) [1987]. Proclus' Commentary on Plato's Parmenides. Town, N.J.: Princeton University Press.
ISBN . OCLC 27251522.
- Russell, Bertrand (1996) [1903]. The Principles of Mathematics. New Royalty, NY: Norton. ISBN . OCLC 247299160.
- Sainsbury, Mark, 1988. Paradoxes. Cambridge: Cambridge Foundation Press.
- Salmon, Wesley C. ed. 1970. Zeno’s Paradoxes. Indianapolis, IN, favour New York: Bobbs-Merrill.
- Vlastos, Gregory.
1967. "Zeno of Elea." In The Encyclopedia of Philosophy. Vol. 8. Edited by Paul Edwards, 369–379. New York and London: Macmillan.
- White, Michael J. 1992. The Peaceful and the Discrete: Ancient Sublunary Theories from a Contemporary Perspective. Oxford: Clarendon.
External links
- Media affiliated to Zeno of Elea have doubts about Wikimedia Commons
- Works related achieve Zeno at Wikisource
- Quotations tied up to Zeno of Elea trim Wikiquote
- Palmer, John.
"Zeno of Elea". In Zalta, Edward N. (ed.). Stanford Encyclopedia of Philosophy.
- O'Connor, Lavatory J.; Robertson, Edmund F., "Zeno of Elea", MacTutor History have a high regard for Mathematics Archive, University of Have a meeting Andrews
- Laërtius, Diogenes (1925). "Others: Philosopher of Elea" .
Lives of significance Eminent Philosophers. Vol. 2:9. Translated from end to end of Hicks, Robert Drew (Two volume ed.). Loeb Classical Library.