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

This is a quote from a memoir by Dorothy Wordsworth, reflecting on a trip she took with two famous poets, her brother, William Wordsworth, and their similarly gifted companion, Samuel Taylor Coleridge. We sat upon a bench, placed for the sake of one of these views, whence we looked down upon the waterfall, and over the open country ... A lady and gentleman, more expeditious tourists than ourselves, came to the spot; they left us at the seat, and we found them again at another station above the Falls. Coleridge, who is always good-natured enough to enter into conversation with anybody whom he meets in his way, began to talk with the gentleman, who observed that it was a majestic waterfall. Coleridge was delighted with the accuracy of the epithet, particularly as he had been settling in his own mind the precise meaning of the words grand, majestic, sublime, etc., and had discussed the subject with William at some length the day before. “Yes, sir,” says Coleridge, “it is a maj...

Searle: The Chinese Room

John Searle has become the object of accusations of improper conduct. These accusations even have some people in the world of academic philosophy saying that instructors in that world should try to avoid teaching Searle's views. That is an odd contention, and has given rise to heated exchanges in certain corners of the blogosphere. At Leiter Reports, I encountered a comment from someone describing himself as "grad student drop out." GSDO said: " This is a side question (and not at all an attempt to answer the question BL posed): How important is John Searle's work? Are people still working on speech act theory or is that just another dead end in the history of 20th century philosophy? My impression is that his reputation is somewhat inflated from all of his speaking engagements and NYRoB reviews. The Chinese room argument is a classic, but is there much more to his work than that?" I took it upon myself to answer that on LR. But here I'll tak...

Recent Controversies Involving Nassim Taleb, Part I

I've written about Nassim Taleb on earlier occasions in this blog. I'll let you do the search yourself, dear reader, for the full background. The short answer to the question "who is Taleb?" is this: he is a 57 year old man born in Lebanon, educated in France, who has been both a hedge fund manager and a derivatives trader. He retired from active participation from the financial world sometime between 2004 and 2006, and has been a full-time writer and provocateur ever since. Taleb's writings for the general public began where one might expect -- in the field where he had made his money -- and he explained certain financial issues to a broad audiences in a very dramatic non-technical way. Since then, he has widened has fields of study, writing about just about everything, applying the intellectual tools he honed in that earlier work. As you might have gather from the above, I respect Taleb, though I have sometimes been critical of him when my own writing ab...

Jamesian Philosophy Refreshed

Search This Blog