Zeno of elea mathematician biography project

1. Life and Writings

The dramatic occasion of Plato’s dialogue, Parmenides, is a visit to Athens by the eminent philosopher Parmenides and Zeno, his younger associate, to attend the festival of the Great Panathenaea. Plato describes Parmenides as about sixty-five years old, Zeno as nearly forty, and Socrates, with whom they converse, as “quite young then,” which is normally taken to mean about twenty. Given that Socrates was a little past seventy when executed by the Athenians in 399 B.C.E., this description suggests that Zeno was born about 490 B.C.E. He would appear to have been active in Magna Graecia, that is, the Greek-speaking regions of southern Italy, during the mid-fifth century B.C.E. There is otherwise little credible information about the circumstances of his life. Diogenes Laertius’s brief “Life of Zeno” (D.L. 9.25–9) is largely taken up with stitching together conflicting reports of his involvement in a brave plot to overthrow one of the local tyrants, but how much truth these reports contain cannot be determined. Although Diogenes also says that Zeno so loved his native Elea that he had no interest in immigrating to Athens, this report is not inconsistent with his having spent some time there; and Plutarch’s report that Pericles heard Zeno expounding on the nature of things in the manner of Parmenides (Plu. Pericles 4.5) suggests that Zeno may indeed have visited Athens and read his famous book, as Plato’s Parmenides implies, to a group of intellectually keen Athenians. Vivid evidence of the cultural impact of Zeno’s arguments is to be found in the interior of a red-figure drinking cup (Rome, Mus. Villa Giulia, inv. 3591) discovered in the Etrurian city of Falerii and dated to the mid-fifth century B.C.E. It depicts a heroic figure racing nimbly ahead of a large tortoise and has every appearance of being the first known “response” to the Achilles paradox.

Zeno of Elea should not be 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 of southern Italy and a member of the Eleatic School, which began with Xenophanes and was developed by Parmenides. Called by Aristotle the inventor of the dialectic, he is best known for his paradoxes.

Zeno presented paradoxes in order to support the claims of Parmenides: that real existence is indivisible, which means it is immobile, immutable, and permanent; the movement, changes, and multiplicity of the world are illusory perceptions based upon sense experiences; truth is accessible by reason alone.

Zeno’s best known paradoxes are: “a flying arrow is stopping,” and “Achilles can never pass over a tortoise in a race.” These paradoxes are contrary to everyday experiences and look absurd. Zeno’s paradoxes were, however, thought-provoking and a number of philosophers and mathematicians, including Plato, Aristotle, Descartes, Bergson, Peirce, Russell, Whitehead, Hilbert, and Bernays, analyzed the issues involved and tried to answer them. There is, however, little agreement on how to resolve them.

His paradoxes include questions concerning: concepts of space and time; relationships between logical reasoning and sense experience; the meaning of reality; and concepts of the infinite and finite.

Life

Little is known for certain about Zeno's life. Although written nearly a century after Zeno's death, the primary source for biographical information on Zeno is the dialogue of Plato called the Parmenides[1]. In this dialogue, Plato describes a visit to Athens by Zeno and Parmenides, at a time when Parmenides is "about 65," Zeno is "nearly 40" and Socrates is "a very young man" (Parmenides 127). Assuming an age for Socrates of around 20, and taking the date of Socrates birth as 470 B.C.E., gives an approximate date of birth for Zeno of 490 B.C.E.

Plato says that Zen

"Arrow paradox" redirects here. For other uses, see Arrow paradox (disambiguation).

Set of philosophical problems

Zeno's paradoxes are a series of philosophicalarguments presented by the ancient Greek philosopher Zeno of Elea (c. 490–430 BC), primarily known through the works of Plato, Aristotle, and later commentators like Simplicius of Cilicia. Zeno devised these paradoxes to support his teacher Parmenides's philosophy of monism, which posits that despite our sensory experiences, reality is singular and unchanging. The paradoxes famously challenge the notions of plurality (the existence of many things), motion, space, and time by suggesting they lead to logical contradictions.

Zeno's work, primarily known from second-hand accounts since his original texts are lost, comprises forty "paradoxes of plurality," which argue against the coherence of believing in multiple existences, and several arguments against motion and change. Of these, only a few are definitively known today, including the renowned "Achilles Paradox", which illustrates the problematic concept of infinite divisibility in space and time. In this paradox, Zeno argues that a swift runner like Achilles cannot overtake a slower moving tortoise with a head start, because the distance between them can be infinitely subdivided, implying Achilles would require an infinite number of steps to catch the tortoise.

These paradoxes have stirred extensive philosophical and mathematical discussion throughout history, particularly regarding the nature of infinity and the continuity of space and time. Initially, Aristotle's interpretation, suggesting a potential rather than actual infinity, was widely accepted. However, modern solutions leveraging the mathematical framework of calculus have provided a different perspective, highlighting Zeno's signi