Date: Mon, 1 Apr 2002 10:16:18 +0200
From: Avi Sion (*)
To: Ralph Kenyon
Subject: Zeno paradoxes

Hello,

Wow - I want to congratulate you on your detailed study of the Zeno paradoxes. I've only so far glossed through it, but have printed it all out for careful study and will write to you if I have specific comments.

I here just want to recommend you look into the work of Buddhist philosopher Nagarjuna, among other Orientals. Here too there are both interesting and fallacious arguments about motion, etc. which need to be closely analyzed.

I also want to recommend to you my own website on Logic:

Dear Friends,

Avi Sion is pleased to inform you that his philosophy Website is up and running. Click below to go to it:

www.TheLogician.net (*)

In this site you will find the complete text of the following two works already published in hardcover:

• Future Logic - about Categorical and Conditional Deduction and Induction of the Natural, Temporal, Extensional and Natural Modalities.
• Judaic Logic - A Formal Analysis of Biblical, Talmudic and Rabbinic Logic.

You will also find extracts of my forthcoming work:

• Causal Logic - about Definition, Deduction and Induction of Causation, Volition and Allied Cause-Effect Relations.
• And various other essays on Logic, Epistemology and other issues in Philosophy.

Do visit this site, rich in new thought. And pass the message to your acquaintances!

Best regards,
Avi.

Date: Tue, 02 Apr 2002 21:20:07 -0500
From: Ralph Kenyon
Subject: Re: Zeno paradoxes
To: Avi Sion

Hi Avi,

Thank you for your generous comments on my work.

Regards, and best wishes,

Ralph E. Kenyon, Jr.

Date: Sun, 21 Apr 2002 10:55:24 +0200
From: Avi Sion
To: Ralph Kenyon
Subject: RE: Zeno paradoxes

Dear Ralph,

just a couple of words in partial reply to your kind mail.

Regarding your work on the Zeno paradoxes. I have so far read only the first four chapters, but can confirm my initial "wow!". I find so far your analysis very thorough and instructive. Not only do you ably review various classical and modern answers to the questions involved, but you bring the matter up to date with applications of Relativity theory and Quantum Mechanics as well as your own original insights. I have always wanted to devote time and thought to the Zeno paradoxes, in view of their philosophical importance, but have always been restrained by my ignorance of advanced mathematics and physics. You save me a lot of work - hence my gratitude to you. I shall certainly refer to your text in my future writings. I am looking forward to reading the rest of it, as you seem to there analyze in detail the concept of atomistic, in contrast to 'divisionist', motion.

>From my very first acquaintance with the Zeno paradoxes nearly 30 years ago in Aristotle's work, I realized that they could be regarded as a critique of divisionism, and a call for the construction of an alternative, atomistic hypothesis. (I note that you have gone further than that, and show that the various paradoxes taken together leave both questions open.) I tried to imagine what atomism would mean specifically, and in an Appendix (#2) to my Judaic Logic I briefly mention the concept, saying:

"We could regard space and/or time as composed of discrete segments, extremely but not infinitely minuscule, within which bodies are invariably stationary (though not locked). A moving body would pass from one station to another, by instantly disappearing from the first, and instantly reappearing in the second, without any of its parts having at all traveled within either station. The instantaneous change of place takes no time, only the static existence at each place has an extension in time."

(You can find this and other references to the Zeno paradoxes in my website by clicking on the Search facility in the bottom left-hand corner of the home page, and typing Zeno.) By the way, with regard to terminology, I like to reserve the word "instant" for a 'point' or boundary of time, and "moment" for an 'atom' or duration of time (whatever its minimum size might be). This is close to colloquial usage. I find your use of the same word instant in both cases a bit confusing; but that is of course no big deal.

At this time, I am writing a series of essays (eventually a book) on phenomenology, and the Zeno paradoxes are issues arising in that context for me. I guess you would class me as having an epistemological approach to them. In one of these essays, I say by way of introduction:

"The Zeno paradoxes cannot be conceived as proofs that motion is impossible, but only as evidence that our (or Zeno’s) initial concepts of motion are problematic; for motion is experientially manifest before and irrespective of any conceptual deliberation concerning it and all discussion concerning motion arises only in reaction to such experience of it as an attempt to rationally interpret and explicate it."

For it occurred to me, reading your work, that we had to consider and not ignore the order of things in the development of knowledge. The Zeno paradoxes are a conceptual issue, not an experiential one. It is only after motion is experienced that we can at all wonder about it and formulate theories (like atomism or divisionism) about it. Any inconsistencies such theories give rise to can never erase the fact that motion was experienced (even if such experience is illusory in some way or mentally generated). With this insight, the Zeno paradoxes become less of a Philosophical issue, and are relegated to the specialized sphere of Mathematics and Physics.

I shall no doubt return to you later, when I've read the rest of your treatment. I realized 3-4 years ago that if atomism is true, or at least a possible alternative to divisionist assumptions of Pythagorean mathematics and their Euclidean and modern offshoots, then many of the theorems of geometry and number-theory would have to be reviewed, or at least considered as true only within a more restricted hypothetical domain. That is, we would need to conceive continuous space-time as one possible "axiom" leading to existing theorems, and construct an alternative atomist maths based on the opposite "axiom". Has this already been done by mathematicians, I wonder (do you know)? I am hoping that the chapters of your work I have not yet read will advance this issue for me, as I see many interesting diagrams seemingly to that effect in them.

Again thanks, and well done.
Best regards,
Avi.

Avi Sion, 306, route d'Hermance, 1247 Anières (GE), Switzerland
Phone: +41 22 7514950
E-mail: avi_sion@thelogician.net
Website: www.TheLogician.net

From: Avi Sion
To: Ralph Kenyon
Subject: About Zeno Paradoxes
Date: Wed, 28 Aug 2002 11:58:23 +0200