And half again, Zeno?*

A post by a new contributor, Bobby V., in response to yesterday’s post, Well, What Would Jesus Do?.

I remember long ago sitting in an educational administration class in graduate school and blurting out, “Aristotle won, didn’t he?” I don’t even remember what the class was about, but it was being taught by Sherry Vaughan who would later become the Dean of the College of Education at Washington State University. “Yes, I suppose you’re right; why don’t you elaborate,” she said. As usual, I wasn’t really paying attention and bird-walked off on a tangent about Aristotle and Plato. At the time, I was amazed that none of the other students in the class – mostly doctoral candidate administrator types – had any apparent interest in either Aristotle or Plato. I neglected to consider that this disinterest might have had something to do with the fact that I was very young, totally inexperienced, and that I had derailed the existing topic of conversation. I’m sure that was part of it.

However, after 20 some years in the business, I know now that these folks don’t have conversations about Aristotle or Plato. They have no knowledge of them, either. They have no knowledge of Seneca, or St. Thomas, or Kant, or Descartes, or Goethe or even of Emerson and Thoreau. They certainly know nothing of the Upanishads or the Four Noble Truths or the Prophet Dance. Some might profess a knowledge of Jesus, but as you say, this knowledge is generally nothing more than a set of talking points distributed by whatever church they belong to.

These are our public school leaders. Our leaders are taught to be this way

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. They are taught that knowledge is easy and that children are little empty vessels to be filled with “cream.” This “cream” is described by simple qualities: the ability to do arithmetic, to fluently sound out words and phrases, to accept authority, and to quietly tolerate boredom.

What could be easier, and why are American schools so bad at this? Perhaps breaking the system down into its smallest constituent parts and carefully measuring those and evaluating them could solve the problem? This methodology has worked since the Enlightenment and it’s the source of all of our scientific and technological achievement, isn’t it?

Indeed, science would not exist without Aristotelian universals, but Aristotle was not a reductionist. However, Socrates via Plato with his shadows on the cave wall wouldn’t have led to Descrates without Aristotle in the middle. Aristotle won and the world isn’t shadows and all we have to do is teach kids reading and arithmetic and make damn sure teachers are accountable. The reward for doing the hard work of holding teachers’ feet to the fire will be a renewed America where a competitive entrepreneurial spirit leads to expanding growth and prosperity.

What would Jesus have to say about all this? The scriptural evidence doesn’t support the notion that Jesus was a key proponent of a mechanistic world view or of the primacy of material wealth and well being. To say the least. Of course many important people throughout Christian history have argued that my understanding is misguided and a misrepresentation of God’s plan for the righteous on Earth. And so here we are in America in 2012 with shadows on the wall. There is something to this about light and darkness that I can’t quite put my finger on. Epistemology is a bitch.

*Zeno’s Paradox


Editor’s Appendix (I.e., not Bobby V’s fault): What the Tortoise Said to Achilles, by Lewis Carroll (Mind, Vol. 4, No. 14 (Apr. 1895), 278-280)

Achilles had overtaken the Tortoise, and had seated himself comfortably on its back.

So you’ve got to the end of our race-course? said the Tortoise. Even though it does consist of an infinite series of distances? I thought some wiseacre or another had proved that the thing couldn’t be done?

It can be done, said Achilles; It has been done! Solvitur ambulando. You see, the distances were constantly diminishing; and so—

But if they had been constantly increasing? the Tortoise interrupted. How then?

Then I shouldn’t be here, Achilles modestly replied; and you would have got several times round the world, by this time!

You flatter me—flatten, I mean, said the Tortoise; for you are a heavy weight, and no mistake! Well now, would you like to hear of a race-course, that most people fancy they can get to the end of in two or three steps, while it really consists of an infinite number of distances, each one longer than the previous one?

Very much indeed! said the Grecian warrior, as he drew from his helmet (few Grecian warriors prossessed pockets in those days) an enormous note-book and a pencil. Proceed! And speak slowly, please. Short-hand isn’t invented yet!

That beautiful First Proposition of Euclid! the Tortoise murmured dreamily. You admire Euclid?

Passionately! So far, at least, as one can admire a treatise that wo’n’t be published for some centuries to come!

Well, now, let’s take a little bit of the argument in that First Proposition—just two steps, and the conclusion drawn from them. Kindly enter them in your note-book. And in order to refer to them conveniently, let’s call them A, B, and Z:—
(A) Things that are equal to the same are equal to each other.
(B) The two sides of this Triangle are things that are equal to the same.
(Z) The two sides of this Triangle are equal to each other.
Readers of Euclid will grant, I suppose, that Z follows logically from A and B, so that any one who accepts A and B as true, must accept Z as true?

Undoubtedly! The youngest child in High School—as soon as High Schools are invented, which wlil not be till some two thousand years later—will grant that.

And if some reader had not yet accepted A and B as true, he might still accept the sequence as a valid one, I suppose?

No doubt such a reader might exist. He might say, I accept as true the Hypothetical Proposition that, if A and B be true, Z must be true; but, I don’t accept A and B as true. Such a reader would do wisely in abandoning Euclid, and taking to football.

And might there not also be some reader who would say, I accept A and B as true, but I don’t accept the Hypothetical?

Certainly there might. He, also, had better take to football.

And neither of these readers, the Tortoise continued, is as yet under any logical necessity to accept Z as true?

Quite so, Achilles assented.

Well, now, I want you to consider me as a reader of the second kind, and to force me, logically, to accept Z as true.

A tortoise playing football would be— Achilles was beginning

—an anomaly, of course, the Tortoise hastily interrupted. Don’t wander from the point. Let’s have Z first, and football afterwards!

I’m to force you to accept Z, am I? Achilles said musingly. And your present position is that you accept A and B, but you don’t accept the Hypothetical—

Let’s call it C, said the Tortoise.

—but you don’t accept
(C) If A and B are true, Z must be true.

That is my present position, said the Tortoise.

Then I must ask you to accept C.

I’ll do so, said the Tortoise, as soon as you’ve entered it in that note-book of yours. What else have you got in it?

Only a few memoranda, said Achilles, nervously fluttering the leaves: a few memoranda of—of the battles in which I have distinguished myself!

Plenty of blank leaves, I see! the Tortoise cheerily remarked. We shall need them all! (Achilles shuddered.) Now write as I dictate:—
(A) Things that are equal to the same are equal to each other.
(B) The two sides of this Triangle are things that are equal to the same.
(C) If A and B are true, Z must be true.
(Z) The two sides of this Triangle are equal to each other.

You should call it D, not Z, said Achilles. It comes next to the other three. If you accept A and B and C, you must accept Z.

And why must I?

Because it follows logically from them. If A and B and C are true, Z must be true. You don’t dispute that, I imagine?

If A and B and C are true, Z must be true, the Tortoise thoughtfully repeated. That’s another Hypothetical, isn’t it? And, if I failed to see its truth, I might accept A and B and C, and still not accept Z, mightn’t I?

You might, the candid hero admitted; though such obtuseness would certainly be phenomenal. Still, the event is possible. So I must ask you to grant one more Hypothetical.

Very good. I’m quite willing to grant it, as soon as you’ve written it down. We will call it
(D) If A and B and C are true, Z must be true.
Have you entered that in your notebook?

I have! Achilles joyfully exclaimed, as he ran the pencil into its sheath. And at last we’ve got to the end of this ideal race-course! Now that you accept A and B and C and D, of course you accept Z.

Do I? said the Tortoise innocently. Let’s make that quite clear. I accept A and B and C and D. Suppose I still refused to accept Z?

Then Logic would take you by the throat, and force you to do it! Achilles triumphantly replied. Logic would tell you, You ca’n’t help yourself. Now that you’ve accepted A and B and C and D, you must accept Z! So you’ve no choice, you see.

Whatever Logic is good enough to tell me is worth writing down, said the Tortoise. So enter it in your note-book, please. We will call it
(E) If A and B and C and D are true, Z must be true. Until I’ve granted that, of course I needn’t grant Z. So it’s quite a necessary step, you see?

I see, said Achilles; and there was a touch of sadness in his tone.

Here the narrator, having pressing business at the Bank, was obliged to leave the happy pair, and did not again pass the spot until some months afterwards. When he did so, Achilles was still seated on the back of the much-enduring Tortoise, and was writing in his note-book, which appeared to be nearly full. The Tortoise was saying, Have you got that last step written down? Unless I’ve lost count, that makes a thousand and one. There are several millions more to come. And would you mind, as a personal favour, considering what a lot of instruction this colloquy of ours will provide for the Logicians of the Nineteenth Century—would you mind adopting a pun that my cousin the Mock-Turtle will then make, and allowing yourself to be re-named Taught-Us?

As you please! replied the weary warrior, in the hollow tones of despair, as he buried his face in his hands. Provided that you, for your part, will adopt a pun the Mock-Turtle never made, and allow yourself to be re-named A Kill-Ease!


photo credit: romantech

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