Time for a bit of mind-bending today, care of my old friend Zeno (491bc – 430bc), a philosopher who lived just at the edges of the “Classical Age” in Greece. He was known as a “Pre-Socratic” thinker, even though he was a contemporary with Socrates (you know, the dude from Bill & Ted wearing the white Toga). The divide between “Pre-Socratic” and “Socratic” philosophy has more to do with the methods and teachings of men like Socrates, Plato, and Aristotle than with the actual structure of the philosophy. We usually take it to mean the Pre-Socratics came BEFORE Socrates, and Zeno was probably the last in a line of men who emphasized abstract, speculative thinking. This sort of philosophy marks a turning point from “divine” explanations of the universe and looks more toward the primacy of human reason – meaning that man should be able to figure out things, based on nature and science, for himself. Socratic philosophers were influenced by Socrates; Zeno was influenced by men like Thales, Anaximander, Anaximenes, Heraclitus, Pythagoras, and Paramenides.
To make it short – Zeno was following in a line of philosophers who were searching for the “primary substance” (or ARCHE) from which all nature was created. Thales believed the Arche was water, Anaximenes believed it was air, Heraclitus believed it was fire. Anaximander proposed that the Arche was unlimited… the primary substance was undefined. Paramenides sort of went off the deep end and said that there was no real Arche, or primary substance… the world of the senses and that of reality could not be defined. (Plato would later pick this up in his “Theory of Forms” where you’ve got a chalkboard that is there but really isn’t)
Really I should explain more of this… but it’s complicated. Let’s get to Zeno.
His paradoxes should be enough for today.
Zeno’s first paradox involves the flight of an arrow. Like Paramenides before him, Zeno was actually experimenting with the concept of “reality” and what could be defined and what could not. Here you’ve got Zeno arguing that there was no such thing as “MOTION” and he claimed that if you shot an arrow from a bow… the arrow would actually not move at all. You see, for the arrow to *move* it has to move somewhere where it is not. If you are shooting an arrow at a tree you would expect the arrow to hit the tree. Zeno is making a paradox, saying that the arrow cannot be anywhere other than where it *is*… and as the arrow cannot move to anywhere other than where it *is* it can never move to a place where it is *not*. You bend this around in your mind and you start to see how Zeno argues against the real existence of anything. (Aristotle had fun with this one. He very much enjoyed Zeno’s games)
The second paradox involves the step – Zeno says for us to imagine we’re moving toward a stream. We’re going to walk toward a cool, clear, glistening stream of water over there in the distance. Right? Well, before you can get to the stream you must first travel *half* the distance to the stream. And to travel *half* the distance you must first travel a *quarter* of the distance, which is a *half-half* of the distance. As you begin to move you are stymied because you cannot really move at all… you are taking an infinite number of smaller steps to a point where it becomes impossible to move. Your motion is only illusory.
I can still remember sitting in a mid-level Philosophy class, way back when, and I had to put my pen down, fold up my notebook, and just sit back in wonder at this. When you’re a student you have to love that, right? It helps that the professor was patient and he explained it this way – imagine you are walking from one side of a room to the other. You take a step in order to get there. Now you imagine taking half that step, then a half of that half-step… and so on. Or you can imagine a solid black line. You are cutting half of that line, then a half-half, and so on. This is sometimes called Zeno’s “backward” argument. It is also known as “infinite regression.”
Zeno also used a racing paradox, and I’ve sometimes heard of this with the turtle and the hare, but it was originally used with the mythical figure Achilles and a tortoise. In his “forward argument” Zeno says that you can imagine a race track that is oval-shaped. You’ve got Achilles, our legendary fast-as-the-wind runner, and the tortoise. Now Achilles will run a lap and eventually pass the tortoise, who is moving very slowly. But the tortoise has travelled at least *some* distance, so Achilles must travel that *some* distance to gain on the tortoise… and as the tortoise keeps moving the very *real* space in which he travels is something that Achilles can never reach. I’m not real keen on this one, because Achilles can continue to run laps around the tortoise, but Zeno’s argument is as always – there is no such thing as “motion” and there is, perhaps, no “reality” in which we might measure it.
Now I am entirely other-brained when it comes to Science and Math. I do enjoy philosophy and speculative reasoning, and I did have to take a couple of classes on inductive and deductive logic in college. What is meaningful for History is the fact that these philosophies were taking shape at a time when Greece was moving past the Persian invasions, the Pelopponesian Wars, into a more modern society where we can first see the “Polis” and the beginning of the “Classical Age.” Socrates tends to get a lot of credit because he was so public (and maybe because of Bill & Ted and their Excellent Adventure)… but the Pre-Socratics came first, and they were the first to look beyond a mystical or divine explanation for things. They were some of the first thinkers to move outside of the box. And it is interesting that Plato, Socrates’ own student, would take up Zeno’s thoughts in his later works. Plato (and his student, Aristotle) are what we consider to be the founders of modern thought in the Western World.
Indeed, Zeno’s paradoxes on motion and reality are still being worked out by Physics today. And he does still bend the mind, doesn’t he? I mean, I’d like to go to Panera for some lunch right now. I’m just not sure I’d make it there.
