ZENO THE TRICKSTER

The next member after Parmenides in Nietzsche’s Group of Eight ought to be Empedocles, but, before we get to him, two lesser luminaries of PreSocratica are going to be discussed, out of the chronological order, both being disciples of Parmenides and members of the so-called Eleatic school of philosophy, which goes back to Xenophanes as its founder, in some accounts, but in every account counts Parmenides as its by far most prominent representative. These two are Zeno of Elea and Melissus of Samos.

Zeno (490 BC? – 430 BC?) does not belong to the first rank of pre-Socratic philosophers, but his fame can be judged as second to none, because of a series of extremely clever paradoxes which he devised and which have become some of the best known and most quoted intellectual puzzles in history.

He first appears in a secondary role in Plato’s Dialogue Parmenides, where he is introduced as a disciple of Parmenides, twenty five years his junior, and, apparently, a “beloved” of his teacher, in their younger years. Later on, Aristotle gives him far more credit, calling him the inventor of the dialectic. Nietzsche gives him the credit of being more skillful than his teacher Parmenides, in his treatment of the concept of the infinite. Best known for his paradoxes, he has been quoted by almost every major philosopher, however, not always with an appropriate seriousness, but in the last hundred years this situation has changed, and a theoretical disputation with him has been one of the cornerstones of Henri Bergson’s philosophy. Incidentally, here is also the significant tribute paid to him by Bertrand Russell and Alfred North Whitehead in their Principia Mathematica (1903):

“…In this capricious world, nothing is more capricious than posthumous fame. One of the most notable victims of posterity’s lack of judgment is Zeno. Having invented four arguments, all immeasurably subtle and profound, the grossness of subsequent philosophers pronounced him to be a mere ingenious juggler, and his arguments, to be one and all sophisms… After two thousand years of continual refutation, these sophisms were reinstated, and made the foundation of a mathematical renaissance…”

The following two examples of Zeno’s paradoxes testify to their essential seriousness, somewhat stripping away the entertainment element, which has made them so appealing, yet at the same time so delightfully frivolous. Their scientific value is, however, greatly enhanced by rubbing off the glamor. Yes, these paradoxes do seem absurd, which is why they are called paradoxes in the first place. But try to refute them, and it is the refuter who makes himself look silly and lightweight under the magnifying glass of scientific professionalism. As is customarily the case, we approach our pre-Socratics through the medium of Plato and Aristotle; in this case our source is Aristotle’s Physics (3):

The Dichotomy: Motion is impossible, since “that which is in locomotion must arrive at the half-way stage before it arrives at the goal.”

The 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.”

...Far more famous, due to its powerful entertaining quality, is the paradox of Achilles and the Turtle, which will become the subject of a separate entry, which follows next.