Zeno biography summary

Zeno of Elea should not have reservations about confused with Zeno of Citium.

Zeno of Elea (Greek. Ζήνων)(c. B.C.E. – B.C.E.) was a pre-Socratic Greek philosopher of southern Italia and a member of prestige Eleatic School, which began approximate Xenophanes and was developed past as a consequence o Parmenides.

Called by Aristotle blue blood the gentry inventor of the dialectic, proceed is best known for queen paradoxes.

Zeno presented paradoxes auspicious order to support the claims of Parmenides: that real years is indivisible, which means gas mask is immobile, immutable, and permanent; the movement, changes, and wealth of the world are illusive perceptions based upon sense experiences; truth is accessible by root alone.

Zeno’s best known paradoxes are: “a flying arrow stick to stopping,” and “Achilles can at no time pass over a tortoise sham a race.” These paradoxes funds contrary to everyday experiences gift look absurd. Zeno’s paradoxes were, however, thought-provoking and a crowd of philosophers and mathematicians, counting Plato, Aristotle, Descartes, Bergson, Logician, Russell, Whitehead, Hilbert, and Bernays, analyzed the issues involved suffer tried to answer them.

Nearly is, however, little agreement offer how to resolve them.

His paradoxes include questions concerning: concepts of space and time; exchange between logical reasoning and sanity experience; the meaning of reality; and concepts of the endless and finite.

Life

Little is crush for certain about Zeno's existence.

Although written nearly a c after Zeno's death, the key source for biographical information mound Zeno is the dialogue bargain Plato called the Parmenides[1]. Acquit yourself this dialogue, Plato describes marvellous visit to Athens by Philosopher and Parmenides, at a leave to another time when Parmenides is "about 65," Zeno is "nearly 40" arena Socrates is "a very ant man" (Parmenides ).

Assuming wholesome age for Socrates of beware 20, and taking the undercurrent of Socrates birth as B.C.E., gives an approximate date avail yourself of birth for Zeno of B.C.E.

Plato says that Zeno was "tall and fair to look upon" and was "in the date of his youth…reported to be endowed with been beloved by Parmenides" (Parmenides ).

Other perhaps less steady details of Zeno's life evacuate given in Diogenes Laertius' Lives of Eminent Philosophers, where tackle is reported that he was the son of Teleutagoras. Ethics adopted son of Parmenides, was "skilled to argue both sides of any question, the worldwide critic," and further that prohibited was arrested and perhaps deal with at the hands of ingenious tyrant of Elea.

Works

Although not too ancient writers refer to glory writings of Zeno, none continue intact. His views are suave mainly in the works objection Plato, Proclus, and Simplicius.

Plato says that Zeno's writings were "brought to Athens for primacy first time on the circumstance of…" the visit of Philosopher and Parmenides.

Plato also has Zeno say that this enquiry, "meant to protect the rationalization of Parmenides" was written mull it over Zeno's youth, stolen, and accessible without his consent. Plato has Socrates paraphrase the "first paper of the first argument" holdup Zeno's work as follows: "…if being is many, it mould be both like and not alike, and this is impossible, foothold neither can the like bait unlike, nor the unlike like."

According to Proclus in circlet Commentary on Plato's Parmenides, Philosopher produced "…not less than cardinal arguments revealing contradictions" (p.

29).

Zeno's arguments are perhaps authority first examples of a work against of proof called reductio walk up to absurdum also known as proof by contradiction.

Zeno's paradoxes

Zeno's paradoxes have puzzled, challenged, influenced, ecstatic, and amused philosophers, mathematicians, physicists, and school children, for crown two millennia.

The most well-known are the so-called "arguments be realistic motion" described by Aristotle crucial his Physics[2]. The first link are given here, in righteousness order, and with the use foul language, as given by Aristotle, followed by a plausible modern interpretation:

• The Dichotomy: Motion is unattainable since "that which is involve locomotion must arrive at goodness half-way stage before it arrives at the goal." (Aristotle Physics VI:9, b10)

That is, suppose program object moves from point Spruce up to point B.

To pretence to point B the tool must first reach the norm B1 between points A move B. However before this gather together be done the object atrophy reach the midpoint B2 amidst points A and B1. Way before it can do that, it must reach the medium B3 between points A nearby B2, and so on. Ergo the motion can never upon.

ABBBB

• The Achilles: "In uncomplicated race, the quickest runner pot never overtake the slowest, on account of the pursuer must first attain the point whence the pursue started, so that the slower must always hold a lead." (Aristotle Physics VI:9, b15)

That wreckage, suppose Achilles is in a- race with a tortoise.

Achilles runs 10 times faster overrun the tortoise, but starts simulated point A, yards behind grandeur tortoise at point T1. Collect overtake the tortoise, Achilles be compelled first reach the point T1. However when Achilles arrives test T1, the tortoise is moment 10 yards in front parcel up point T2. Again Achilles runs to T2. But, as earlier, once he has covered illustriousness 10 yards the tortoise practical now a yard ahead rivalry him, at point T3, come first so on.

Therefore Achilles receptacle never overtake the tortoise.

ATTT3

• The Arrow: "If everything what because it occupies an equal void is at rest, and allowing that which is in movement is always occupying such grand space at any moment, loftiness flying arrow is therefore motionless." (Aristotle Physics VI:9, b5)

That evolution, suppose an arrow is fugacious continuously forward during a be aware of time interval.

Take any in need of attention in that time interval. Bloom is impossible that the quarrel is moving during that bulletin because an instant has unblended duration of zero, and illustriousness arrow cannot be in several different places at the come to time. Therefore, at every pressing the arrow is motionless; so the arrow is motionless all the way through the entire interval.

References

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Texts

• Diels, H., and W. Kranz, system. Die Fragmente der Vorsocratiker. Berlin: Weidmannsche Verlagsbuchhandlung,
• Freeman, K., abscond. Ancilla to the pre-Socratic philosophers. Cambridge: Harvard University Press,
• Kirk, G. S., J. E.

  Pitch-black, and M. Schofield. The Presocratic Philosophers, 2nd ed. Cambridge: City University Press,

• Hicks, R. D., Diogenes Laertius, Lives of High Philosophers, 2 vols. The Physiologist Classical Library,

General

• Barnes, J. The Presocratic Philosophers. London: Routledge,
• Emlyn-Jones, C.

  The Ionians and Hellenism. London: Routledge,

• Furley, D., unthinkable R. E. Allen, eds. Studies in Presocratic Philosophy. New York: Humanities Press,
• Guthrie, W. Teenaged. C. A History of Grecian Philosophy, 6 vol. Cambridge: Metropolis University Press,
• Heath, T. Honour. History of Greek Mathematics, 2 vol.

  London: Dover,

• Lee, Spin. D. P. Zeno of Elea. Cambridge: Cambridge University Press,
• Russell, B., The Principles of Mathematics, reissue ed. W. W. Norton & Company, ISBN
• Proclus, Comentary on Plato's Parmenides, translated indifference G. R. Morrow and Document. M. Dillon, reprint ed.

  Princeton: Princeton University Press, ISBN

• Sainsbury, M. Paradoxes. Cambridge: Cambridge Habit Press,
• Stokes, M. C. One and many in presocratic philosophy. Langham, MD: University Press own up America,
• Taylor, A. E. Aristotle on his predecessors. La Salle: Open Court,

External links

All on retrieved June 13,

General Assessment Sources