Paradoxes and Atoms

I'm going to try to make some connections. Parmenides to Zeno to Democritus to Newton and Leibniz.

Parmenides: everything is one. And the One that is all is unchanging. Division, motion, change, are impossible. Accordingly, they must be illusions.

Why did Parmenides come to these conclusions? Generally, he had a simple line of thought that puns on negative words such as "nothing." If there is nothing between A and B, then A and B must be in the same place. Thus, if they are some distance from each other, then they must actually be one. If you don't get that, don't worry about it.

Zeno came up with a cleverer way of arguing for Parmenidean monism. He argued that the common-sense notions of the world we live in are rife with paradox. In order to get rid of paradox, we must run to the the shelter of the Parmenidean One. I've written of such things before, usually in comedic form. https://jamesian58.blogspot.com/2020/07/the-two-zenos.html

The only point one needs to retain is that Zeno's paradoxes generally depend upon the infinite divisibility of a line. In the science of geometry the Greeks were developing at the time, one which would be given comprehensive formal form later by Euclid, there is an infinite number of points between ANY two points. That is somewhat counter-intuitive, though the system developed from such premises proved pragmatically very useful. Still, Zeno's trick was highlighting the counter-intuitive nature of this notion of infinite divisibility.

And now we come to the connection that has only recently occurred to me. Is it crazy or so bloody obvious I should have gotten it long ago? I don't know.

Did Zeno's paradoxes give birth to atomism?

After all, the natural way to dispute Zeno is to say, "Enough with infinite divisibility! Maybe life is like a checkers board! At some level you either move one step over or you move zero steps over there is no half step." That way it is easy to understand how the arrow moves forward and the swift warrior catches up with a turtle.

Atomism is at heart the application of that contention -- that divisibility comes to an end -- to chunks of matter.

Or is it?

In our day, the most natural answer to Zeno throws Newton and calculus at him.

There IS a solution to the sum of the following set: 1/2 + 1/4 + 1/8 + 1/16 ....

It is not a mystery and it proves no impossibilities. The answer is: 1.

The arrow gets from point A to point B. Call the unit of that distance 1. Zeno drew on the fact that you can go on forever describing that movement, with the fractions I've mentioned above and all the others.

You CAN but there is no need to. You can simply take the limit. It is 1. The arrow gets to point B. Achilles reaches the Tortoise and sits upon his back as Lewis Carroll imagined.

A Story About Coleridge

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Jamesian Philosophy Refreshed

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