Zeno of Elea was a disciple of Parmenides and a fellow Eleatic. He followed his master’s theory of monism and designed to show that any postulation that opposed the monistic teaching of Parmenides leads to contradiction and absurdity. Parmenides had argued using reason alone that the assertion that only Being leads to the conclusion that Being is one and motionless. Following this by logic, the opposite would be that instead of a single being, many real entities in fact are and that they are in motion. Zeno thus wished to reduce to absurdity the two claims, that the many beings are and that motion is.
He came up with a series of paradoxes known as Zeno’s paradoxes to illustrate his point. The Achilles paradox is designed to prove that the slower mover will never be passed by the swifter in a race. The dichotomy paradox is designed to prove that any moving object must reach halfway on a course before it reaches the end; and because there are an infinite number of halfway points, a moving object never reaches the end in a finite time. The arrow paradox endeavors to prove that a moving object is actually at rest because at any instance in time a shot arrow is motionless, and since time is made of concurrent instances the arrow is in reality motionless.
If in each case, the conclusion seems obvious but absurd, it serves to bring the premise – that motion exists or is real – into disrepute, and it suggests that the contradictory premise, that motion does not exist, is true; and indeed, the reality of motion is precisely what Parmenides denied.
