Jamesian Philosophy Refreshed

  To my mind, one of the most intriguing of the ancient Greek philosophers is the second of the great Eleatics, Zeno of Elea.  But ... does he still matter?  C ome, let us reason together.  If the fastest of warriors, Achilles, can not catch up with a tortoise, then something is of course very wrong with the way we understand our life in the world.  That is of course Zeno's point.  He was defending an Eleatic monism, a sort of Hellenic gaslighting that told the world nothing is as it seems, so he was committed to saying that since the apparent world is illusory, something crazy must be true.  Maybe this is irrelevant now, because we live in the thought world that Leibniz and Newton gave us with the development of calculus. The central idea is that of a converging series.   Consider continuously compounding interest.  You probably have bank accounts that earn it.  You do not regard this as a mystery.  But how can that be compute...

  Yesterday I paid tribute here to a great mathematician. Today I offer a quote from him.  "To those who ask what the infinitely small quantity in mathematics is, we answer that it is actually zero.  Hence there are not so many mysteries hidden in this concept as there are usually believed to be."  The significance of that observation may not be obvious outside of some consideration of the history of math, the development of calculus in particular.  But once we do a little grappling with that history, we see that Euler is making a point here that takes us back to ancient Greece.  Back to Zeno, Achilles and tortoise.  If Achilles is to catch up with the tortoise there must be a moment at which the difference between them is zero. One way of looking at the problem is to ask what is the next lower number -- one really really close to zero but still a positive number!  Euler here is saying "That is the wrong way of looking at it." Or, "don't create my...

Let us take this from the top.  Just think of two creatures: one notoriously swift of foot, the other not so.  Then think that the slower creature has a short head-start in a race.  Of course the former will catch up with and pass the later.  That is inherent in what we mean by such notions as slow and fast.  But ... what if we assume with ancient geometers that space, and so every possible distance, is infinitely divisible?  Does that throw a wrench into things?  Fast creature (Achilles) starts ten meters behind slow creature (Turtle). Achilles moves ten times as fast.  Within some period of time (we will call it a nonce), Achilles has advanced those ten meters. Ah, but Turtle has now advanced one meter, and so is still ahead.  Achilles advances THAT distance in one-tenth of a nonce.  Yet he still has not caught up, for the Turtle has by now advanced one-hundredth of a meter.  And so forth, depressingly, on and on. It is impossible...

 How does continuous compound interest work?  Well, suppose the magical "Bank of Bernoulli" offers you 100 percent interest per annum. Or, in decimal terms, a return of 1.0.  Great. You put a dollar in the bank and the bank gives you two dollars at the end of the year, one dollar representing the principal, the other the yield. Only one simple computation has to be made, so we can say of this situation that n = 1. It gets better.  Bank of Bernoulli [so named after the great 17th century mathematician Jacob Bernoulli] decides to compound semi-annually.  You put in one dollar, and on June 30 you are credited with 100 percent interest for half a year, or $0.50. In the second half of the year, you earn the same 1/2 of the underlying annual rate, for the redefined principal amount, this time on $1.50.  So you earn $0.75 between June 30 and December 31. This means you have $2.25 waiting for you at the end of the year. You can keep this up, presuming a calculation...

Our chronicler of classical philosophers, Diogenes Laertius, a source at once indispensable and unreliable, deserves one more blog post from us.  This is so that we can settle the account between Laertius and Zeno of Elea.  I earlier quoted a passage from the Book Six in which there is an account of Diogenes of Sinope and juxtaposition of two observations his biographer namesake attributes to him. "A man once proved to him syllogistically that he has horns, so he put his hand to his forehead and said, 'I do not see them.' And in a similar manner he replied to one who had been asserting  that there was no such thing as motion, by getting up and walking away."  As we've discussed, the sophism of the "horns" arose in the context of Stoicism, and its preference for the hypothetical syllogism rather than the categorical syllogism beloved by Aristotle. The denial of motion is famously due to one Zeno of Elea, although it takes Laertius a looong time to get aro...

 So, what's it all about, Alfie? Is it just for the tee shirt we live?  I have written of late in this blog about Alfred North Whitehead's book, Process and Reality. But I have written chiefly of what he says there about other philosophers.  Plato, Locke, Hume....Now I hope to get to the core of Whitehead's original thought. What does he say about ... process and reality? What is his cosmology?  I have to bring one more historic figure, Leibniz, into the mix even to say this next bit, though. Because you can think of Whitehead's core supposition as a monadology. Any one of us is a society of society of societies ... all the way down. The ultimate bottom level, the individual nuggets (or monads, if you will) at the bottom of this hierarchy of societies? Whitehead seems to think there is a bottom, and he does give it a name: occasions. A lot of unconscious and brief occasions, conceived of as independent of content, might constitute the bottom building block. Sort of...

So, it turns out the two famous Greek philosophers names Zeno were roomies. They lived in a high-rise apartment in downtown Athens. They didn't always get along, although I would not go so far as to say that they were an odd couple. Here's a bit of dialog from a possible television sitcom: "Zeno, did you drink all of the orange juice from this jug?" "No." "Oh, come one. Who else could have done it?" "The question you ought to be asking yourself is how could ANYONE have done it After all, first one would have to drink the first half of it. And to do that, one would have to drink the first quarter of it. And to do that ... you get the idea? infinite repetition suggests the process could never get started." "I don't want to discuss paradoxes now, Zeno. I want you to admit you took the orange juice. I'm not going to be angry. I'm a stoic, after all." "I think I'll buy some from Parmenides th...