Does Zeno of Elea still matter?

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?

Come, 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 computed? A non-compounded rate of interest for a year can be calculated easily enough. A 1% rate on $1,000 is $10. Call this the n=1 situation -- only one calculation involving that one underlying rate. The depositor gets $1,010 at the end of the year ... let us say on December 31.

But then a competing bank can compound it on a half year basis. Easy peasy. At the same underlying rate, the $1,000 principal has accumulated $5 of interest as of June 30. The depositor owns $1,005 at this point. For the second half year, the principal PLUS THAT INTEREST earns half of that 1% annual rate, so it earns $5.25 in the second half of the year, and the depositor owns $1,010.25. The one-step compounding has gained him a quarter.

You can introduce more compoundings. Quarterly? Call that n = 4. Monthly? n = 12. Daily? n = 365. The payouts increase from $1,010.25 but not by very much.

Truly continuous compounding means that n equals the number of mathematical instants that pass in the course of the year. How do we deal mathematically with an infinity of instants? The same way we deal with the infinite number of Euclidean points that Achilles passes on the way to the tortoise. We don't let it bother us and we do the computation. A list of end-of pay-outs that starts with $1,010 and increases in the manner suggested will converge on an irrational number that begins $1,010.2718....

So, now that we know how converging series work and it no longer seems mysterious, are we done with Zeno? and with his paradoxes as a philosophical challenge?

Not really. Bernoulli, Leibniz, Newton, and their successors including Euler have shown us how to calculate when Achilles catches up with the tortoise. They may not have taken away the sense of mystery. Are there an infinite number of mathematical instants or are there not? And an infinite number of volume-less points between Achilles and the tortoise or not? How can there be? How can there NOT be?

My understanding of the contemporary philosophical discussion of such points is that, yes, Zeno still matters.

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...

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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...

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My own disposition, in regard to the philosophy of time, is toward the "growing block" theory. This is the view that past events remain realities, that present-moment events are also realities, but that future events are not yet real. The image is of the universe as a block with an edge on (say) the right-hand side. The block is expanding because that edge is moving ever further right, and that edge is what we call the present, or, simply, "now." Everything to the left of that edge is both static (the past is complete) and, still and forever, real. Think of the phrase "the moving finger writes." The chief alternatives to the growing-block theory are "presentism" (only the now-edge itself is real) and "eternalism" (past, present, and future are all real." I believe that time is a growing block because (1) that's what it feels like, (2) we should stick with the introspective phenomenon unless we have good reason to abandon ...

Jamesian Philosophy Refreshed

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