Zeno

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david familian

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Sep 1, 2011, 1:24:57 PM9/1/11
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hi david

i think i understand your description of Zeno's faulty logic. I am
writing a short essay using the arrow paradox which i think differs
slightly from achilles and the tortoise. What confuses me is your
idea that a abstract attribute doesn't match with a physical one. Of
course that is what is at play here. But his abstract attribute was
not a mathematical one, was it? He abstraction was a form of logic
which is a kind of math, but that logic was based on a world view of
400bc not one of modern science that knows that this can happen. But
was he really making a mistake or was he pointing at the the
intrinsic paradoxes of logic itself.
df

David Deutsch

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Sep 1, 2011, 3:20:38 PM9/1/11
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On 1 Sep 2011, at 6:24pm, david familian wrote:

> hi david
>
> i think i understand your description of Zeno's faulty logic. I am
> writing a short essay using the arrow paradox which i think differs
> slightly from achilles and the tortoise. What confuses me is your
> idea that a abstract attribute doesn't match with a physical one. Of
> course that is what is at play here. But his abstract attribute was
> not a mathematical one, was it?

I had in mind the attribute of being infinite. And I claimed that his mistake was to assume that something that is infinite in the sense of being a sequence of infinitely many entities (in this case, processes of moving from place to place), must also be infinite physically. I think the 'sequence of infinitely many entities' is a mathematical infinity.

> He abstraction was a form of logic
> which is a kind of math, but that logic was based on a world view of
> 400bc not one of modern science that knows that this can happen. But
> was he really making a mistake or was he pointing at the the
> intrinsic paradoxes of logic itself.

Surely logic has no paradoxes. Only misuses of logic could.

-- David Deutsch


Abraham Lewis

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Sep 2, 2011, 10:34:46 AM9/2/11
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This is a *very* interesting article on Zeno's paradox and relativity. I highly recommend it and would be especially interested in David Deutsch thoughts on it:

http://www.mathpages.com/rr/s3-07/3-07.htm

Elliot Temple

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Sep 2, 2011, 2:45:24 PM9/2/11
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On Sep 2, 2011, at 7:34 AM, Abraham Lewis wrote:

> http://www.mathpages.com/rr/s3-07/3-07.htm

The main topic of the article is interesting.

However it's really misleading about some of the contextual details it provides about Xenophanes and Parmenides. He should be more careful before making such strong claims.

The first thing to know is there is *very little information* available, some of which is ancient secondary sources, and a lot of which has been translated badly. A lot of guesswork is involved. He writes some of this like a factual, known history, which is misleading.

My guess is that Xenophanes was the founder of the Eleatic school but even that much is in a fair amount of doubt. It's not something to just assert as a historical fact without comment. Note that Galen wrote, "In a malicious and slanderous way some commentators on Xenophanes have lied about him" (WoP p 42) You have to be really careful with this stuff.

The description of Xenophanes as "religious thinker and poet" is grossly misleading. He was those things but also a scientist and philosopher. He wrote a science book, "On Nature", which we sadly do not have. He knew something about, for example, water evaporating from the ocean to form clouds, which is pretty good for a 570 BC religious poet type... he also (accurately) said rainbows were made of water like clouds.

What we do have from Xenophanes is less than 50 "fragments" -- little pieces of text, which we generally get because some later author quoted them. The article claims:

> whose main teaching was that the universe is singular, eternal, and unchanging.

but this is false. Even if we assume the fragments are representative, that is in no way his main teaching. His fragments cover a lot of ground. A bunch have to do with epistemology and one of his arguments is against parochialism and anthropocentrism. Xenophanes was also, "a historian, perhaps the real father of history" (WoP p 33, p 54-56)

But even worse, was that his teaching at all? Most translations I've read have him saying that *God* is singular, eternal, and too badass to ever have to walk around which isn't fitting for God. He was an early monotheist.

Here's his fragments (do not consider these translations reliable):

http://history.hanover.edu/texts/presoc/Xenophan.html

and in particular about this:

> 1. God is one, supreme among gods and men, and not like mortals in body or in mind. [Zeller, Vorsokrastische Philosophie, p. 530, n. 3.]
>
> 3. But without effort he sets in motion all things by mind and thought.
>
> 4. It [i.e. being] always abides in the same place, not moved at all, nor is it fitting that it should move from one place to another.


so there's one God and he does everything with his mind and it's not fitting that he'd have to move around, says Xenophanes.

but where does xenophanes say the universe was unchanging? well there's this, sort of (same link):

> Theophrastos, Fr. 5 ; Simpl. Phys. 5v : 22, 36 ; Dox. 480. Theophrastos says that Xenophanes of Kolophon, teacher of Parmenides, asserted that the first principle is one, and that being is one and all-embracing, and is neither limited nor infinite, neither moving nor at rest. Theophrastos admits, however, that the record of his opinion is derived from some other source than the investigation of nature. This all-embracing unity Xenophanes called god;

some other guy, not Xenophanes, who claims Xenophanes as the first Eleatic and teacher of Parmenides also attributes to Xenophanes some of Parmenides' ideas. true or false? very hard to know. but even still, he still says Xenophanes called this "god" rather than it being the universe.

Popper comments on this issue further, btw.

back to the zeno article it says:

> "The all is one."


so now it's using quotation makes for xenophanes. which fragment is it quoting? search for "The all is one." on the webpage of xenophanes fragments I gave and you will not find it.


> The greatest of the Eleatic philosophers was Parmenides (born c. 539 BC). In addition to developing the theme of unchanging oneness, he is also credited with originating the use of logical argument in philosophy.

this neglects that Parmenides was a scientist, as previously the article neglected that Xenophanes was a scientist.

evidence is very scanty -- a little bit more than with Xenopahnes -- but Popper credits Parmenides with understanding the phases of the moon: it's just shadow that's changing, not a real change.

in this way his scientific progress may be relevant to his philosophy. the illusion of the moon changing helped inspire Parmenides to consider what else is illusion.


the phrasing about "logical argument" is very sloppy, too. he didn't invent logic. nor did he invent critical argument -- Thales and successors beat him to that. so who credits him with originating the use of "logical argument" and why?

> His habit was to accompany each statement of belief with some kind of logical argument for why it must be so.


you can't tell what his "habit" is from just a few fragments on a particular topic. this implies we have rather more information about Parmenides than we do have, and then makes stuff up about it.

> It's possible that this was a conscious innovation, but it seems more likely that the habitual rationalization was simply a peculiar aspect of his intellect.

why is that "more likely"? this is, again, just plain making stuff up, outside the author's field, and without any arguments. it's also an abuse of probability: it's not a matter of likeliness.

> A continuous function (as emphasized by Weierstrass) is a staticcompleted entity, so by invoking this model we are essentially agreeing with Parmenides that physical motion does not truly exist, and is just an illusion, i.e., "opinions", arising from our psychological experience of a static unchanging reality.

this bit about "psychological" is a distortion with, again, no basis in the available evidence. Parmenides wasn't some subjectivist. he was concerned with 1) what is true 2) mistakes people can (understandably) make. Parmenides argued about objective reality.

btw the word "opinions", here found in quotes for some reason, is a bad translation. long story short, you can't translate non-justificationist epistemology when you take justificationism for granted. btw justificationism basically began with Aristotle and Parmenides predates him.


for more on these topics see especially _The World of Parmenides_ (WoP) by Karl Popper.

-- Elliot Temple
http://fallibleideas.com/

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