Zeno of Elea (/ˈziːnoʊ ... ˈɛliə/; Ancient Greek: Ζήνων ὁ Ἐλεᾱ́της; c. 490 – c. 430 BC) was a pre-Socratic Greek philosopher from Elea, in Southern Italy (Magna Graecia). He was a student of Parmenides and one of the Eleatics. Zeno defended his instructor's belief in monism, the idea that only one single entity exists that makes up all of reality. He rejected the existence of space, time, and motion. To disprove these concepts, he developed a series of paradoxes to demonstrate why they are impossible. Though his original writings are lost, subsequent descriptions by Plato, Aristotle, Diogenes Laertius, and Simplicius of Cilicia have allowed study of his ideas.
Zeno's arguments are divided into two different types: his arguments against plurality, or the existence of multiple objects, and his arguments against motion. Those against plurality suggest that for anything to exist, it must be divisible infinitely, meaning it would necessarily have both infinite mass and no mass simultaneously. Those against motion invoke the idea that distance must be divisible infinitely, meaning infinite steps would be required to cross any distance.
Zeno's philosophy is still debated in the present day, and no solution to his paradoxes has been agreed upon by philosophers. His paradoxes have influenced philosophy and mathematics, both in ancient and modern times. Many of his ideas have been challenged by modern developments in physics and mathematics, such as atomic theory, mathematical limits, and set theory.
Zeno was born c. 490 BC. Little about his life is known for certain, except that he was from Elea and that he was a student of Parmenides. Zeno is portrayed in the dialogue Parmenides by Plato, which takes place when Zeno is about 40 years old. In Parmenides, Zeno is described as having once been a zealous defender of his instructor Parmenides; this younger Zeno wished to prove that belief in the physical world as it appears is more absurd than belief in the Eleatic idea of a single entity of existence. By the time that Parmenides takes place, Zeno is shown to have matured and to be more content to overlook challenges to his instructor's Eleatic philosophy. Plato also has Socrates hint at a previous romantic or sexual relationship between Parmenides and Zeno. It is unknown how accurate the depiction in Parmenides is to reality, but it is agreed that it bears at least some truth.
Zeno died c. 430 BC. According to Diogenes Laertius, Zeno was killed while he was engaged in a plot to overthrow the tyrant Nearchus. This account tells that he was captured, and that he was killed after he refused to give the names of his co-conspirators. Before his death, Zeno is said to have asked to whisper the names into Nearchus's ear, only to bite the ear when Nearchus approached, holding on until he was killed.
The writings of Zeno have been lost; no fragments of his original thoughts exist. Instead, modern understanding of Zeno's philosophy comes through recording by subsequent philosophers. Zeno is only known to have written one book, most likely in the 460s BC. This book is told of in Parmenides, when the character of Zeno describes it as something that he wrote in his youth. According to Plato's account, the book was stolen and published without Zeno's permission. Zeno's paradoxes were recorded by Aristotle in his book Physics. Simplicius of Cilicia, who lived in the 6th century AD, is another one of the main sources of present day knowledge about Zeno.
Zeno is one of three major philosophers in the Eleatic school, along with Parmenides and Melissus of Samos. This school of philosophy was a form of monism, following Parmenides' belief that all of reality is one single indivisible object. Both Zeno and Melissus engaged in philosophy to support the ideas of Parmenides. While Melissus sought to build on them, Zeno instead argued against opposing ideas. Such arguments would have been constructed to challenge the ideas of pluralism, particularly those of the Pythagoreans.
Zeno was the first philosopher to use argumentative rather than descriptive language in his philosophy. Previous philosophers had explained their worldview, but Zeno was the first one to create explicit arguments that were meant to be used for debate. Aristotle described Zeno as the "inventor of dialectic". To disprove opposing views about reality, he wrote a series of paradoxes that used reductio ad absurdum arguments, or arguments that disprove an idea by showing how it leads to illogical conclusions. Furthermore, Zeno's philosophy makes use of infinitesimals, or quantities that are infinitely small while still being greater than zero.
Criticism of Zeno's ideas may accuse him with using rhetorical tricks and sophistry rather than cogent arguments. Critics point to how Zeno describes the attributes of different ideas as absolutes when they may be contextual. He may be accused of comparing similarities between concepts, such as attributes that physical space shared with physical objects, and then assuming that they be identical in other ways.