Date: Mon, 1 Apr 2002 10:16:18 +0200
From: Avi Sion (*)
To: Ralph Kenyon
Subject: Zeno paradoxes
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:
Avi Sion is pleased to inform you that his philosophy Website is up and running. Click below to go to it:
In this site you will find the complete text of the following two works already published in hardcover:
You will also find extracts of my forthcoming work:
Do visit this site, rich in new thought. And pass the message to your acquaintances!
Date: Tue, 02 Apr 2002 21:20:07 -0500
From: Ralph Kenyon
Subject: Re: Zeno paradoxes
To: Avi Sion
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
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 Zenoís) 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.
306, route d'Hermance,
1247 AniŤres (GE),
Phone: +41 22 7514950
From: Avi Sion
To: Ralph Kenyon
Subject: About Zeno Paradoxes
Date: Wed, 28 Aug 2002 11:58:23 +0200
about the announcement below, you will find mention of your dissertation and website in Chapter 5 (see footnote 5). You will also find chapter 6 interesting. The issues are dealt with in more detail in my forthcoming book on Phenomenology.
Hello from Avi Sion:
I am pleased to announce the posting on my Internet site www.TheLogician.net of the complete text of one more of my books, the just published (Aug. 2002):
Do visit The Logician, and read this interesting work. Also, pass the news on to friends who may be interested!
Thanks and best regards,
I am pleased to announced the publication of my latest work in The Logician website:
PHENOMENOLOGY:Basing Knowledge On Appearance.
You are welcome to read (or printout, for personal use) the whole of this book at: http://www.TheLogician.net, this together with my other writings, including: Future Logic, Judaic Logic and Buddhist Illogic.
With best regards,
From: Avi Sion
Subject: My new book RUMINATIONS: Sundry notes and essays on Logic
Date: Wed, 8 Jun 2005 21:23:10 +0200
Avi Sion is happy to announce that his newly published book:
To facilitate study, it has been integrally posted on: http://www.TheLogician.net
Ruminations is a collection of sundry notes and essays on Logic. These complement and enrich the authorís past writings, further analyzing or reviewing certain issues. Among the many topics covered are:
Additionally, this volume is used to publish a number of notes and essays previously only posted in the Internet site THE LOGICIAN, including: