Zeno of Elea (IPA:zɛnoʊ, ɛlɛɑː)(circa 490 BC? – circa 430 BC?) was a pre-Socratic Greek philosopher of southern Italy and the member of the Eleatic School founded by Parmenides. Known as by Aristotle the inventor of the dialectic, he is best known for his paradoxes.

Life
Little is known for sure astir Zeno's life. Although written about the century fallowing Zeno's dying, a primary source of biographic principles of Zeno is the dialogue of Plato called the Parmenides [http://classics.mit.edu/Plato/parmenides.html]. In the dialogue, Plato describes the visit to Athens by Zeno and Parmenides, at once while Parmenides is "about 65", Zeno is "nearly 40" & Socrates is "a very young man" (Parmenides 127). Assuming an age for Socrates of when much as Twenty, & ingesting a date of Socrates birth as 470 BC, gives an approximate date of birth for Zeno of 490 BC.

Plato says that Zeno was "tall and fair to look upon" and was "in the days of his youth … reported to have been beloved by Parmenides". (Parmenides 127)

More mayhap less dependable details of Zeno's life come given inside Diogenes Laertius' Lives of Eminent Philosophers [http://classicpersuasion.org/pw/diogenes/dlzeno-eleatic.htm#cite], in which these are reported that he was a boy of Teleutagoras, however a adoptive boy of Parmenides, was "skilled to argue both sides of any question, the universal critic", & more that he was arrested & peradventure flushed at the paws of a tyrant of Elea.

Works
Although many ancient writers refer to the writings of Zeno, none endure intact.

Plato says that Zeno's writings were "brought to Athens for the first time on the occasion of…" the visit of Zeno & Parmenides. Plato as well has Zeno say that this operate, "meant to protect the arguments of Parmenides" was written around Zeno's youth, stolen, & published forswearing his consent. Plato has Socrates paraphrase a "first thesis of the first argument" of Zeno's function when follows: "…if being is many, it must be both like and unlike, and this is impossible, for neither can the like be unlike, nor the unlike like".

Based on data from Proclus in his ''Commentary in Plato's Parmenides'', Zeno produced "…not less than forty arguments revealing contradictions..." (p. Xxix)

Zeno's arguments come perchance the number 1 examples of a method of proof known as Reductio ad absurdum also known as proof by contradiction.

Zeno's paradoxes
Zeno's paradoxes develop puzzled, challenged, influenced, inspired, & amused philosophers, mathematicians, physicists & school kids, for complete deuce millennia. A best known come a thus-alleged "arguments against motion" described by Aristotle inside his Physical science [http://classics.mit.edu/Aristotle/physics.html]. the 1st 3 tend on this text, in a choose, & by having the list, every bit from Aristotle, followed by a plausible modern interpretation:

A Duality: Motion is impossible since "that which is in locomotion must arrive at the half-way stage before it arrives at the goal." (Aristotle Physics VI:9, 239b10)

That is, believe an object moves from either point The to point B. For to point B The object must foremost email a center B1 between points A & B. Yet prior to this may be done The object must email a center B2 between points A & B1. Also prior to it potty clean this, it must email The centre B3 between points A & B2, so in. So a motion potty never lead off.

The-----B3-----B2-----------B1-------------------------B

A Achilles: "In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead." (Aristotle Physics VI:9, 239b15)

That is, believe Achilles is within the race using the tortoise. Achilles diarrhea Tenner days sooner than a tortoise, however starts at point A, One c yards behind the tortoise at point T1. To overtake a tortoise, Achilles must number one email a point T1. All a same once Achilles attain T1, the tortoise is nowadays Decade yards ahead at point T2. Again Achilles diarrhea to T2. However, when prior to, when he has covered the X yards a tortoise is currently a front yard ahead of him, at point T3, then in. So Achilles could never overtake a tortoise.

The----------------------------T1----------------T2---T3

A Arrow: "If everything when it occupies an equal space is at rest, and if that which is in locomotion is always occupying such a space at any moment, the flying arrow is therefore motionless." (Aristotle Physics VI:9, 239b5)

That is, believe an arrow is flying day and night send on when you took the certain interval. Choose any instant therein interval. These are impossible that a arrow is moving inside a period of that instant because an instant has a duration of zero, & the arrow just can not become in 2 different wharehouses at the equivalent period. So, at each instant a arrow is static, hence a arrow is static throughout a entire interval.