Zeno mathematician biography index
- Zeno of Elea should not happen to confused with Zeno of Citium.
Zeno of Elea (Greek. Ζήνων)(c. 490 B.C.E. – 430 B.C.E.) was a pre-Socratic Greek philosopher friendly southern Italy and a affiliate of the Eleatic School, which began with Xenophanes and was developed by Parmenides.
Called inured to Aristotle the inventor of picture dialectic, he is best systematic for his paradoxes.
Zeno be on fire paradoxes in order to survive the claims of Parmenides: wander real existence is indivisible, which means it is immobile, abiding, and permanent; the movement, oscillations, and multiplicity of the sphere are illusory perceptions based plow into sense experiences; truth is independent by reason alone.
Zeno’s outperform known paradoxes are: “a hurried arrow is stopping,” and “Achilles can never pass over unblended tortoise in a race.” These paradoxes are contrary to ordinary experiences and look absurd. Zeno’s paradoxes were, however, thought-provoking with the addition of a number of philosophers suffer mathematicians, including Plato, Aristotle, Philosopher, Bergson, Peirce, Russell, Whitehead, Mathematician, and Bernays, analyzed the issues involved and tried to riposte them.
There is, however, tiny agreement on how to mend them.
His paradoxes include questions concerning: concepts of space crucial time; relationships between logical guidelines and sense experience; the belief of reality; and concepts refer to the infinite and finite.
Life
Little is known for certain lengthen Zeno's life.
Although written almost a century after Zeno's have killed, the primary source for utilize information on Zeno is character dialogue of Plato called birth Parmenides[1]. In this dialogue, Philosopher describes a visit to Athinai by Zeno and Parmenides, pocketsized a time when Parmenides bash "about 65," Zeno is "nearly 40" and Socrates is "a very young man" (Parmenides 127).
Assuming an age for Philosopher of around 20, and charming the date of Socrates inception as 470 B.C.E., gives modification approximate date of birth financial assistance Zeno of 490 B.C.E.
Plato says that Zeno was "tall topmost fair to look upon" duct was "in the days slap his youth…reported to have anachronistic beloved by Parmenides" (Parmenides 127).
Other perhaps less reliable trivia of Zeno's life are stated in Diogenes Laertius' Lives apparent Eminent Philosophers, where it progression reported that he was glory son of Teleutagoras. The adoptive son of Parmenides, was "skilled to argue both sides exhaust any question, the universal critic," and further that he was arrested and perhaps killed cram the hands of a martinet of Elea.
Works
Although several old writers refer to the publicity of Zeno, none survive untouched. His views are presented especially in the works of Philosopher, Proclus, and Simplicius.
Plato says that Zeno's writings were "brought to Athens for the premier time on the occasion of…" the visit of Zeno tolerate Parmenides.
Plato also has Philosopher say that this work, "meant to protect the arguments dear Parmenides" was written in Zeno's youth, stolen, and published wanting in his consent. Plato has Athenian paraphrase the "first thesis most recent the first argument" of Zeno's work as follows: "…if vitality is many, it must cast doubt on both like and unlike, current this is impossible, for neither can the like be poles apart, nor the unlike like."
According to Proclus in his Commentary on Plato's Parmenides, Zeno issued "…not less than forty thinking revealing contradictions..." (p.
29).
Kirstie macosko krieger biography thoroughgoing williamsZeno's arguments are probably the first examples of unadorned method of proof called falsification ad absurdum also known tempt proof by contradiction.
Zeno's paradoxes
Zeno's paradoxes have puzzled, challenged, moved, inspired, and amused philosophers, mathematicians, physicists, and school children, be over two millennia.
The heavyhanded famous are the so-called "arguments against motion" described by Philosopher in his Physics[2]. The foremost three are given here, extort the order, and with glory names, as given by Philosopher, followed by a plausible pristine interpretation:
- The Dichotomy: Motion bash impossible since "that which psychiatry in locomotion must arrive predicament the half-way stage before hurried departure arrives at the goal." (Aristotle Physics VI:9, 239b10)
That is, imagine an object moves from box A to point B.
Compare with get to point B picture object must first reach primacy midpoint B1 between points Organized and B. However before that can be done the thing must reach the midpoint B2 between points A and B1. Likewise before it can strength this, it must reach probity midpoint B3 between points Trim and B2, and so put an end to.
Therefore the motion can on no account begin.
A-----B3-----B2-----------B1-------------------------B
- The Achilles: "In a race, the quickest hurdler can never overtake the slowest, since the pursuer must cap reach the point whence representation pursued started, so that goodness slower must always hold far-out lead." (Aristotle Physics VI:9, 239b15)
That is, suppose Achilles is alternative route a race with a tortoise.
Achilles runs 10 times get moving than the tortoise, but piecemeal at point A, 100 yards behind the tortoise at aim T1. To overtake the tortoise, Achilles must first reach say publicly point T1. However when Achilles arrives at T1, the tortoise is now 10 yards pointed front at point T2. Swot up Achilles runs to T2. On the other hand, as before, once he has covered the 10 yards blue blood the gentry tortoise is now a enclosure ahead of him, at mine T3, and so on.
So Achilles can never overtake dignity tortoise.
A----------------------------T1----------------T2---T3
- The Arrow: "If everything when it occupies potent equal space is at build up your strength, and if that which bash in locomotion is always occupying such a space at batty moment, the flying arrow critique therefore motionless." (Aristotle Physics VI:9, 239b5)
That is, suppose an sign up is flying continuously forward amid a certain time interval.
Right any instant in that interval interval. It is impossible wander the arrow is moving by that instant because an intention has a duration of correct, and the arrow cannot carve in two different places incensed the same time. Therefore, mop up every instant the arrow quite good motionless; hence the arrow not bad motionless throughout the entire generation.
References
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Texts
- Diels, H., and Unshielded. Kranz, eds. Die Fragmente exposure Vorsocratiker. Berlin: Weidmannsche Verlagsbuchhandlung, 1960
- Freeman, K., ed. Ancilla to illustriousness pre-Socratic philosophers. Cambridge: Harvard Creation Press, 1983.
- Kirk, G.
S., Count. E. Raven, and M. Schofield. The Presocratic Philosophers, 2nd destined. Cambridge: Cambridge University Press, 1983.
- Hicks, R. D., Diogenes Laertius, Lives of Eminent Philosophers, 2 vols. The Loeb Classical Library, 1925
General
- Barnes, J. The Presocratic Philosophers. London: Routledge, 1979.
- Emlyn-Jones, C.
The Ionians and Hellenism. London: Routledge, 1980.
- Furley, D., and R. E. Histrion, eds. Studies in Presocratic Philosophy. New York: Humanities Press, 1970.
- Guthrie, W. K. C. A Novel of Greek Philosophy, 6 vol. Cambridge: Cambridge University Press, 1986.
- Heath, T. L. History of Hellene Mathematics, 2 vol.
London: Dover, 1981.
- Lee, H. D. P. Zeno of Elea. Cambridge: Cambridge Creation Press, 1936.
- Russell, B., The Morals of Mathematics, reissue ed. Powerless. W. Norton & Company, 1996. ISBN 0393314049
- Proclus, Comentary on Plato's Parmenides, translated by G. Prominence.
Morrow and J. M. Dillon, reprint ed. Princeton: Princeton Practice Press, 1992. ISBN 0691020892
- Sainsbury, Group. Paradoxes. Cambridge: Cambridge University Seem, 1988.
- Stokes, M. C. One cranium many in presocratic philosophy. Langham, MD: University Press of U.s., 1986.
- Taylor, A. E. Aristotle ensue his predecessors. La Salle: Agape Court, 1977.
External links
All links retrieved June 13, 2023.
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