Xodarapparadox: How do you render a paradox? I just don't seem to be able to get it down right, and yet I know it in my mind and have dreamt it, too. There is a fast flowing muddy river that holds the city in its arms before curving into the north. It is a brown sand-filled river, that flows faster and golder as it picks up the yellow sands of the flats and hurls itself to the mother of all rivers. The mother river itself is a silty muck-filled grey ocean of racing water. It is a different color, a dark grey wash of mountain rock, silvery powder silt and melting snow. If you fly over the confluence, the gold flows into the grey. For many river miles, there is a line that separates them. The gold river still runs true, a phantasm along the south banks while the grey smokes its stream to the north. At each turn of the river bed and island in their path, they mix a bit more and after many miles of dissolving, melting and swirling, they defeat one another. Both colors simply disappear. They nullify each other. And for a moment, when all distinction is swallowed up, the river seems to lie still and hissing. It is that state of....quandary that I am trying to describe, but I can't get it. I can only dream it. I can only feel it. "Is there anyone here who has something to add?"
"Yes?"
"You can't even get to the river!"
Zeno of Elea (c490 BC).:
Zeno of Elea was the sly and subtle disciple of Parmenides. His most famous arguments are based on a method known as reductio ad absurtum. In this form of argumentation, one begins by accepting an opponent's premises and demonstrates that they logically lead to an error. Zeno "proved" the impossibility of motion. He argued that one could never arrive anywhere, not even to a river. Before one can get to a river, one must go halfway, but before one can go halfway, one must go halfway of the remaining halfway but before one can go halfway of halfway, one must go halfway, etc., on to infinity. Therefore, motion would be impossible if it were possible.
Parmenides and Zeno caused, that is, created, a crisis in Greek philosophy. First they forced the distinction between information based on the senses and that based on pure reason, a distinction that developed into two schools of thought: empiricism and rationality. They also forced a revaluation of the monistic presuppostion accepted by most Greeks because thinkers came to realize that such a view led directly to Parmenides' and Zeno's untenable conclusions.