Refuting the counters to Zeno's paradox

[SpeedOfSound]

I think ZP is a silly mind game but...

Doesn't it only work for an infinitesimally small point? If a rigid body is moving and two arbitrary points on the body are following the Zeno descent into hell, if the point farthest from the destination is infinitely falling into the halving space then the point closer has to have arrived.

Has this been handled? Haven't read the thread.

Does this silly idea only work for bodies that have no width? Hence no body at all?

Edit. Ahh shit. I've embarrassed myself here while waiting for the coffee.

...but, can rigid bodies ever start moving?

[Animavore]

Sorry XP but I'm getting you to explain this to me in Nottingham whether you like it or not.

EDIT: That's what tying to fix a PC for hours does to you.
I meant XC.

[jamest]

However, does all this math really answer Zeno's paradox in reality?

It's not because of any certainty that mathematics is inadequate to model "reality". It's because Zeno's paradox is an ill-posed question about "reality" intended to treat the empirical with worse than mere skepticism. This is the work of the metaphysicians, and is the reason this unfortunate thread is happening at all.

Fundamentally, Zeno questions the reality of objects that are somehow distanced from one another. Now, essentially, it doesn't really matter which parameters we use to explain this separation - the bottom-line is that whichever parameters correctly describe the separation between objects must be quantifiable. Therefore, those parameters must be subject to the kind of reasoning that Zeno utilised.

Sure, Zeno's understanding of space & time might appear relatively simple, compared to how we describe spacetime, now. But what we have to consider, is that Zeno is essentially questioning the reality of separation. It doesn't matter, then, how he or we [now] describe this separation - that's missing the point entirely. Ultimately, the fundamental point of Zeno's reasoning has to be taken seriously and we have to explain how quantifiable measures of separation can exist between objects in reality.

Of course, since it is questionable that what is being observed cannot be 'real', then anything that physics says cannot really be employed to counter Zeno's argument, as observation is the basis for whatever physics might say. So it seems to me as though this discussion has taken a turn for the worse, with several people trying to refute Zeno via current physics.

[SpeedOfSound]

Fundamentally, Zeno questions the reality of objects that are somehow distanced from one another.

Did Zeno write to you about this or are you guessing? Got a reference or a quote?

[jamest]

I'd like to add that it was never my initial intention to focus upon mathematical proofs that claim to have countered Zeno's reasoning - I just became aware of rational flaws inherent within the premises of the math that XC has employed and decided to deal with this first. Therefore, my post from last night (UK time), still has relevance... and nobody has addressed that at all.

With my last post in mind - which attempted to check the divergence from this original theme - I shall now bump the contents of last night's post, in the hope that somebody will address it:

I was very careful never to perform a single operation on the 'sum' as a whole. Every step involved actions on individual terms. That was the whole point in rewriting the proof (at great length, I might add.)

Firstly, I sincerely thank you for the effort and time that you have given to this thread.
Secondly, if I - as is apparent - misunderstood the basis of the second proof, then I apologise.
Thirdly, please read my last post to Jerome - any attempted counter here, by me, is reducible to a philosophical consideration of any math that have been forthcoming. I am not attempting to 'correct your math' per se.
Finally, I now actually do understand the basis of your 2nd proof and will proceed from that...

My counter to your 2nd proof will still be upon your initial foundation, though. So, you start with:

[pre]1/2 + 1/4 + 1/8 + 1/16 + .... = 1/2 + 1/4 + 1/8 + 1/16 + ....[/pre]

There is still a problem here, even if we are not considering 'the sum' of anything. The problem now has to focus upon the ellipsis (... ), as SD mentioned.

... Here, you are equating one series with another. But, the problem is this: if the series of numbers (1/2 + 1/4 + 1/8 + 1/16 + ....) has no end (is infinite), then any purported equivalences of that set must be finite, by logical default. That is, there can be no equivalences of anything unless it is in a definite/finite state. This is the my rational conclusion as per why you cannot state that:

1/2 + 1/4 + 1/8 + 1/16 + .... = 1/2 + 1/4 + 1/8 + 1/16 + ....

Thus, I am trying to argue that nothing is equivalent to anything else (including itself), unless that thing is in a finite state of being. Of course, I recognise that this requires further explanation, so I shall proceed:

Is the equivalence of a line without-end, just a line without-end? No, since both lines could be running through different places, at different times.
Such unending lines cannot be equivalent, then. So, what basis is there for equating unending lines? Not in their unendingness - as has been explained - but in their 'endedness'. That is, no unending line can be equivalent to another except in finite/definite terms. That is, the equivalence of one thing to another, demands the utilisation of definite/finite facts to facilitate that equivalence. Therefore, there is no equivalence of an unending line - even with itself - unless definite/finite claims impose an equivalence on such an unending line.

That is: (1/2 + 1/4 + 1/8 + 1/16 + .... = 1/2 + 1/4 + 1/8 + 1/16 +....) is only true for definite/finite points of this series. The point being that since 'infinity' is an unknown quantity - and is neither definite nor finite - that the utilisation of the ellipsis (... ) means that there is no equivalence to anything beyond that which is definite or finite. I.e., one cannot equate anything with an ellipsis with anything else with an ellipsis, including 'itself'.

I.e.: 1/2 + 1/4 + 1/8 + 1/16 + .... ≠ 1/2 + 1/4 + 1/8 + 1/16 +.... [except at definite/finite points of the series].

Of course, if correct, this counter renders any subsequent math as null & void.

Perhaps this is difficult to understand... I dunno. But, just ask and I will try to elucidate further. It beats responding with posts of near-infinite boobs, anyway. (edited to add that this is a generalised statement).

Again, with my previous post in mind, what I said here does still have relevance, and therefore requires attention.
Cheers.

[jamest]

Fundamentally, Zeno questions the reality of objects that are somehow distanced from one another.

Did Zeno write to you about this or are you guessing? Got a reference or a quote?

Are you joking?

If Zeno has presented reasoning that questions the reality of motion/space, then what's your problem with my statement?

[SpeedOfSound]

Fundamentally, Zeno questions the reality of objects that are somehow distanced from one another.

Did Zeno write to you about this or are you guessing? Got a reference or a quote?

Are you joking?

If Zeno has presented reasoning that questions the reality of motion/space, then what's your problem with my statement?

I'm just sensing an arguments from the authority of the Old Wiser Ones coming on here and wondering if you have references to any direct writings about what Zeno's intentions were.

[jamest]

Fundamentally, Zeno questions the reality of objects that are somehow distanced from one another.

Did Zeno write to you about this or are you guessing? Got a reference or a quote?

Are you joking?

If Zeno has presented reasoning that questions the reality of motion/space, then what's your problem with my statement?

I'm just sensing an arguments from the authority of the Old Wiser Ones coming on here and wondering if you have references to any direct writings about what Zeno's intentions were.

As I said, the proof is in the pudding. Nobody (even Zeno) can question the reality of space or motion without questioning the reality of objects that are somehow distanced from one another. Therefore, I don't need references to say this.

[SpeedOfSound]

Fundamentally, Zeno questions the reality of objects that are somehow distanced from one another.

Did Zeno write to you about this or are you guessing? Got a reference or a quote?

Are you joking?

If Zeno has presented reasoning that questions the reality of motion/space, then what's your problem with my statement?

I'm just sensing an arguments from the authority of the Old Wiser Ones coming on here and wondering if you have references to any direct writings about what Zeno's intentions were.

As I said, the proof is in the pudding. Nobody (even Zeno) can question the reality of space or motion without questioning the reality of objects that are somehow distanced from one another. Therefore, I don't need references to say this.

Well the story I heard was that the only thing that Zeno wanted to do was win the debate and take the hot chick in the audience home.

[jamest]

Well the story I heard was that the only thing that Zeno wanted to do was win the debate and take the hot chick in the audience home.

That's my plan too. Are you a hot chick?

[SpeedOfSound]

Well the story I heard was that the only thing that Zeno wanted to do was win the debate and take the hot chick in the audience home.

That's my plan too. Are you a hot chick?

I can be if you have the right kind of money.

[SpeedOfSound]

See, this is why I usually refrain from posting when sober. I always manage do something wrong. More ad more absurd? What happen?

I need to stop posting before my Turkish coffee is done settling. Or find the delete button on this damned forum.

[jamest]

Well the story I heard was that the only thing that Zeno wanted to do was win the debate and take the hot chick in the audience home.

That's my plan too. Are you a hot chick?

I can be if you have the right kind of money.

For the plastic surgery? Don't bother - I like 'natural'.

I know - from something that you said earlier - that you haven't given much attention to this thread. That's a shame, I think, since I know that you believe in the reality of 'separation'.
Ultimately, the 'reality of separation' is what all of our discussions have been about. And, of course, the whole point of everything that idealists discuss, is that such a reality makes no sense... and that, therefore, reality is as One. So, perhaps you should give more time to this thread.

[SpeedOfSound]

I would argue that quantized parts of space-time makes no sense, ...

You just figured something out here. You should stop now.

[SpeedOfSound]

That's a shame, I think, since I know that you believe in the reality of 'separation'.

What ever gave you that idea?