Zeno of Elea (490-430 a. C.) was introduced by Plato as "beautifully built, handsome, a favorite of Parmenides." Indeed, Zeno defended the ideas of his master, Parmenides, against criticism. It is known that he wrote a book in which he elaborated forty paradoxes: his argumentative strategy, known as reduction to the absurd, established situations in which the consequences of an opposition that he wanted to refute were exposed.
This book has very little left, about nine paradoxes. For the rest, what we can say about Zeno starts from what Plato, Simplicio and Aristotle said. His best-known arguments were those that refuted movement and plurality. Let's go to them:
Zeno of Elea's arguments against the movement:
1. "The first is the impossibility of moving, as the mobile must reach the middle rather than the end." (Aristotle, Physics, 239b 12)*
This is the first argument, called "From Dichotomy". This means that it is not possible for a body, moving from one point to another, to reach the point it has set as its goal. Before reaching it, the body has to go half the way it has to go, and first half of the half, and so on. What the argument wants to make explicit is that half of half of half will never be equivalent to zero, that is, to the contrary to what experience tells us, reason shows that movement does not exist: what we perceive is a illusion.
2. "The second is the call of Achilles. It is this: The slowest will never be reached by the one who runs the fastest; first, the pursuer must arrive, from where the fugitive moved. This way the slowest will always be a little ahead." (Aristotle, Physics, 239b 14-16)*
Achilles, known for its speed, let a turtle, an animal known for its sluggishness, drop ahead of him in a run for a ten-metre lead.
However, Achilles would not be able to reach the turtle, as he would have to travel the distance of the advantage given to him. As the distance is divisible to infinity, it can never be covered.
The distance between them can be reduced, but not bridged.
Let's understand: in a short time, Achilles manages to reach the ten meters that the turtle had the advantage, as expected. But in the time it took to cover the ten meters, the tortoise advanced one meter. When Achilles surpasses that meter, the turtle has already advanced 1/10 of a meter.
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3. “The third (argument) says that the arrow, when set in motion, is immobile. This stems from the fact that time is made up of instants. But if this is not presupposed, there will be no argument." (Aristotle, Physics, VI, 9. 239b 30)*
Suppose an archer shoots an arrow. The common opinion is that the thrown arrow acquires movement. Zeno contradicts this opinion, showing that the arrow is actually stopped.
For him, the arrow occupies a space that is equal to its volume and, therefore, is stopped at that moment. As the arrow will always occupy a space that is equal to its volume, this applies at all times.
This is because in each of the instants in which the flight time is divisible, the arrow occupied an identical space. Everything that occupies an identical space is at rest. So the arrow is at rest and this means that space and time are not a whole made up of real parts, its parts are only imagined.
4. “The fourth argument supposes two opposed series of bodies of equal number and magnitude, arranged from a and another from the ends of a stadium to its midpoint, and which move in the opposite direction to it velocity. This argument, thinks Zeno, leads to the conclusion that half a time is equal to twice that time.” (Aristotle, Physics, VII, 239 b)*
This is considered one of the most complex arguments.
To try to understand it, let's think of a football stadium. Two darts are thrown in opposite directions. When moving, the darts travel a spatial unit at each temporal unit, that is, we are assuming that time and space can be divided into parts that have a size and a duration minimum.
When paired, darts are two paired space units. For this to happen, they would need to go through a situation where only one unit was paired. The instant that this would happen would be half of a temporal unit that we thought was a minimal unit.
With this, we realized that the unity was not minimal as we supposed, but divisible.
The distance covered in this half temporal unit in the stadium would be half of that temporal unit that we also thought was minimal.
For Zeno, as for his master, Parmenides, perceived movement is just an appearance, an aspect superficial reality and, therefore, the senses cannot be considered adequate instruments for knowledge real.
*Aristotle's quotes are taken from: ARISTOTLE. Physics. Trans. Guillermo R. of Echandia. Madrid: Gredos, 1998
By Wigvan Pereira
Graduated in Philosophy
