The 9 paradoxes of Zeno

[Agent327]

Not if one actually reads them... Those parts are not the center of the dialogue, and in the Parmenides they are not un-natural either, cause the discussion leads Socrates to concede in the first place. I even gave a link to the etext of the 20-pages of the dialogue, you can just check

How do you think I concluded they are somewhat wooden? By not reading them?

The CHORUS was sung. The rest of the plays are not sung at all...

So, no dialogue then.

No one here claimed that the dialogues are how it all happened. In fact their form (most of them are recollections of old events) (...)

The Parmenides, as noted, is supposedly a recollection of a discussion happening 20 years before, and by a person who claims (Antiphon) to have lost interest in philosophy by then (blame Parmenides ). So Plato himself rather clearly did not aim to present the dialogues as recording of actual discussion. This has nothing to do with whether Socrates had met Zeno and/or Parmenides and talked to them, which is rather the hugely likelier event. Even his student Diogenes of Sinope was noted to have met Zeno, etc.

You seem to contradict yourself. It this particular dialogue is not a representation of actual events, caution should be taken to things depicted in them. It may be your personal opinion that there actually was a meeting between Socrates and Zeno (which is immaterial to the dialogue), but this is not the opinion shared by most scholars. Seeing as I'm not familiar with your personal scholarship on this, I think it safe to go with general opinion - among scholars, that is.

 

[Kyriakos]

How do you think I concluded they are somewhat wooden? By not reading them?



So, no dialogue then.



You seem to contradict yourself. It this particular dialogue is not a representation of actual events, caution should be taken to things depicted in them. It may be your personal opinion that there actually was a meeting between Socrates and Zeno (which is immaterial to the dialogue), but this is not the opinion shared by most scholars. Seeing as I'm not familiar with your personal scholarship on this, I think it safe to go with general opinion - among scholars, that is.

Ok. Should i do the same, given you now claimed that in your view the ancient plays only had dialogue in the Chorus parts?

..
.
But don't tell me: you would not have concluded this either if you hadn't read them..

 

[gay_Aleks]

There was also a Greek philosopher named Polonophile, who was known for his love of Poland. It is however likely that his tale was a fabrication by Polish nationalists.

That doesn't sound like canon.

 

[Agent327]

It sounds selfcontradictory, actually.

Ok. Should i do the same, given you now claimed that in your view the ancient plays only had dialogue in the Chorus parts?

You can claim what you please, but I didn't claim this.

But don't tell me: you would not have concluded this either if you hadn't read them..

Yes, I would not have concluded if I had not read.

Perhaps we should get back to the actual topic of Parmenides?

 

[Kyriakos]

Ok

Although indeed there was little talk about the actual meaning of the work by Zeno, despite that i mentioned it already in the OP and then a few times in the thread. Namely that it tried to showcase how the view hostile to Parmenides, ie the view that in reality there are Many things and not just One, is also creating paradoxes.

Btw, in the library programs Zeno is always the most difficult part for the people there, although some show keen interest on it. It always ties to math, of course, since it started from it, and then there is a minor presentation of calculus (in reality just the diverging or converging infinite series, along with infinity being not defined by that either cause it is out of the set- it is the bounded indistinct part of the limit- in the first place).

In the same period (likely just a couple of decades later, or even less) Anaxagoras presented his own take on the Eleatic philosophy, creating a model where infinity was not the edge of the system but already in ALL particles of the system. Eg in his model any object X is at the same time all other objects, but not in the same way which still grants it the notable element of X. In this way too, though, infinity is not bounded. It is just inferred as bounded outside of the field of the presented model.
Anaxagoras also very notably posed "NOUS" (usually translated as 'intelligence' or 'mind' or 'thinking' etc) as the sole element of the world of phenomena which is distinct from them, ie the observer always is a different type of effect onto the phenomena through observation.

 

[Agent327]

So, basically this revolves around the quest for the essential element started by the early philosophers.

Zeno certainly uses mathematics, but in doing so actually takes this unsolvable quest to a different level (since mathematics isn't actually part of reality - or the world), if you will). And consequently Plato takes it to an entirely new level by declaring the world 'immaterial', so to speak. To him the ideal Ideas are the essential thing, not any specific element to be found in reality. By doing this he solves the oppostion 'one' and 'many' by saying that it is not the many that are important but the One they refer to. So with Plato we see philosphy no longer obsessed with the physical world, but rather with the metaphysical. Yet at the same time he stays within the tradition of explaining the physical world.

In the process, of course, early Greek philosophy left us with such essential terms as element and atom. Quite interesting, really.

Sorry, I've been meaning to ask: I appreciate your enthusiasm about the topic, but why Parmenides specifically? Is it a subject in classes currently?

 

[Kyriakos]

So, basically this revolves around the quest for the essential element started by the early philosophers.

Zeno certainly uses mathematics, but in doing so actually takes this unsolvable quest to a different level (since mathematics isn't actually part of reality - or the world), if you will). And consequently Plato takes it to an entirely new level by declaring the world 'immaterial', so to speak. To him the ideal Ideas are the essential thing, not any specific element to be found in reality. By doing this he solves the oppostion 'one' and 'many' by saying that it is not the many that are important but the One they refer to. So with Plato we see philosphy no longer obsessed with the physical world, but rather with the metaphysical. Yet at the same time he stays within the tradition of explaining the physical world.

In the process, of course, early Greek philosophy left us with such essential terms as element and atom. Quite interesting, really.

Sorry, I've been meaning to ask: I appreciate your enthusiasm about the topic, but why Parmenides specifically? Is it a subject in classes currently?

Parmenides is likely the most interesting of the dialogues, insofar as the notion of 'infinity' goes (it is also one of the very few moments where Socrates actually does shut up ).

As for Plato to Parmenides:

It seems that mostly the other way around is closer to the motif here, cause while Plato at least argues (through Socrates, eg in the Republic) that the Eide/Archetypes (which btw are hugely misleadingly translated as 'ideas', cause part of the work is the negation of the Eide being in the realm of human ideas) that humans have some minor border with a world of immortal Eide, Parmenides either claims that this is highly unlikely (in the eponymous dialogue by Plato) or that it is downright not true (in his own surviving part of work, titled "On Nature").

While your comment is entirely correct in light of Anaxagorian so-called 'pluralism' (basically Anaxagoras was in between Parmenides and Democritos, so focused both on notions and physical world), it is not correct in regards to Parmenides or Zeno, given they could not care less about the physical world since they viewed it as a complete illusion.
One of the most core lines in On Nature by Parmenides is that every human sense or thought is an illusion

So Parmenides was the most hardcore in that way. More than Plato. Aristotle moved focus drastically to the physical, and the previous focus on notions was later termed as 'metaphysical', cause Aristotle's own treatises on that came after his books on Physics.

 

[warpus]

 

[Kyriakos]

^Yeah. "Infinitely many mathematicians walk into a bar. The first one says: I'll have a beer. The second says I'll have half a beer. The third 'one fourth of a beer', and so on. The bartender sends two beers to their direction, and comments: 'guys... know your limits'"

(math jokes are bad :\ ).

 

[Borachio]

sum = 1 + 1/2 + 1/4 + 1/8 + ...

2*sum = 2 + 1 + 1/2 + 1/4 + ...

sum = 2*sum - sum = 2 + 1 + 1/2 + 1/4 +... - 1 - 1/2 - 1/4 - 1/8 - ... = 2

 

[Kyriakos]

^Can't add infinite sums, exactly due to the infinite sum not ever having a last part, and not reaching (in this case 2) the limit it is to anyway (ie the limit it is to is not part of the progression).

For similar reason you cannot detract a limit from another one, in an arithmetic way. Eg the fibonacci spiral is not the golden spiral, despite the former having an absolute limit (which it approximates very fast) of the progression between its parts to phi, phi being the progression in all parts of the latter.

 

[Borachio]

I don't see why not. I think my proof is good, if not totally rigorously expressed.

 

[Kyriakos]

I don't see why not. I think my proof is good, if not totally rigorously expressed.

+1
(+1/2+1/4+...)

Well yes, why not. I mean we are friends here anyway.

 

[Borachio]

Link to video.

 

[Kyriakos]

^I know of Hilbert via the debate on Cantor and his take on the sets, but i doubt the above is his claim? (that in a place with infinite parts you can move each part to double its position). Cause in an infinity already all positions are taken, they just are not accounted for. A progression to a limit is not "running"; it is already done, but the positions are not always distinct as to what they have in them.

 

[Kyriakos]

Yeah, but what exactly does that mean?

"Everything is one." .. What do you mean by this statement? Let's say I have a notebook and a pen in front of me. "They are one" - what does this mean? How are they one? Can you explain like I'm 5?

I'm not disputing that they are or aren't, I just don't understand what you mean. Do you mean that the universe is some sort of a blob that's uniformly the same throughout? Because that seems to be clearly not true.

To get back to this, and since i aswered in the program today on the same thing more or less, it is likely better to refer to Democritos proposing a model where an 'atom' does exist (ie that at some point matter reaches a final, smallest particle). If there is no such atom, matter inevitably (well, to be brief) will always keep on dividing or interlinking to everything else in the world. But if there is no final point/particle then how can one claim that our human senses are not 'illusion-creating' when we obviously always see things moving from one position to another one? Ie if really there is no atom, then the distance between the two positions is literally a collection of infinite interim positions, so if that is true and we still sense movement this seems to lead to the conclusion that our senses transform (alter/falsify) a "really" infinite relocation into a trivial phenomenon we pick up as evidently true.

Aristotle suggested an easy way out (but it is a cope-out), in that "logic/thinking does not always work in direct relation to external reality". But that is not the issue, cause that seems correct anyway. The issue is that our senses show full progressions as something trivial, while this may be more likely a hint that they are not just particular/human (evident again) but moreover against a supposed 'reality' which would be different.

But not all philosophers of that era argue for such a reality. Most seem to argue that 'reality' is either a term to use for practical purpose in very bounded systems or observations (eg a human being has a head, or if you drink poison you risk dieing, or in axiomatically set systems with 1+1=2 etc) or a term which is not an observation on some object, but a tie between that object as a particular phenomenon to a particular species (eg human) or a particular human.