Achilles and the Tortoise.

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Reply Thu 6 Nov, 2008 02:28 pm
from
Zeno's Paradox of the Tortoise and Achilles (PRIME)

Quote:

The Tortoise challenged Achilles to a race, claiming that he would win as long as Achilles gave him a small head start. Achilles laughed at this, for of course he was a mighty warrior and swift of foot, whereas the Tortoise was heavy and slow.
"How big a head start do you need?" he asked the Tortoise with a smile.
"Ten meters," the latter replied.
Achilles laughed louder than ever. "You will surely lose, my friend, in that case," he told the Tortoise, "but let us race, if you wish it."
"On the contrary," said the Tortoise, "I will win, and I can prove it to you by a simple argument."
"Go on then," Achilles replied, with less confidence than he felt before. He knew he was the superior athlete, but he also knew the Tortoise had the sharper wits, and he had lost many a bewildering argument with him before this.
"Suppose," began the Tortoise, "that you give me a 10-meter head start. Would you say that you could cover that 10 meters between us very quickly?"
"Very quickly," Achilles affirmed.
"And in that time, how far should I have gone, do you think?"
"Perhaps a meter - no more," said Achilles after a moment's thought.
"Very well," replied the Tortoise, "so now there is a meter between us. And you would catch up that distance very quickly?"
"Very quickly indeed!"
"And yet, in that time I shall have gone a little way farther, so that now you must catch that distance up, yes?"

"Ye-es," said Achilles slowly.
"And while you are doing so, I shall have gone a little way farther, so that you must then catch up the new distance," the Tortoise continued smoothly.
Achilles said nothing.
"And so you see, in each moment you must be catching up the distance between us, and yet I - at the same time - will be adding a new distance, however small, for you to catch up again."
"Indeed, it must be so," said Achilles wearily.
"And so you can never catch up," the Tortoise concluded sympathetically.
"You are right, as always," said Achilles sadly - and conceded the race.



Can you see that this proves that the Soul exists?
 
Didymos Thomas
 
Reply Thu 6 Nov, 2008 08:48 pm
@Poseidon,
No, I can't. This paradox is interesting, but it ultimately collapses. All one has to do is ask: How long does it take Achilles to go one meter? How long does it take the tortoise to go one meter? If Achilles can cover a meter faster than the tortoise, Achilles can eventually overtake the tortoise.
 
Khethil
 
Reply Fri 7 Nov, 2008 05:21 am
@Didymos Thomas,
Yea, I'd like to echo DT's comments here.

I read this, and it struck me as so absurd that I concluded I must be missing something obvious. Glad to see I wasn't alone.

Thanks
 
jgweed
 
Reply Fri 7 Nov, 2008 05:37 am
@Poseidon,
No. I do not, and would appreciate knowing how animals have Souls; although I could understand someone concluding from Zeno's paradox of the arrow that bows exist.
 
manored
 
Reply Fri 7 Nov, 2008 09:18 am
@jgweed,
That doesnt really makes sense, the idea of a race is to reach the end before the oposition, not to stop in the exact same spot the oposition is... and I cant see how it proves the soul exists.

The universe is likely to extend itself infinitely in bigger and smaller forms than we know, and that means it is impossible to explain, so its probally also pointless to bother with such paradoxes Smile
 
Poseidon
 
Reply Fri 7 Nov, 2008 01:28 pm
@Poseidon,
It is no use saying that Achilles is faster than a tortoise.
We know this!

What you need to do is try and explain why the argument causes a paradox.

This thread gives you a clue:
http://www.philosophyforum.com/forum/lounge/general-discussion/2630-thought.html
 
manored
 
Reply Sat 8 Nov, 2008 11:37 am
@Poseidon,
Well it causes a paradox because you cannot tranverse infinite distance, but any distance can be divided in infinitely small pieces, so anything that moves is tranversing infinite distance. But if you think about it, then you measure the distance, no matter how small the pieces, it becomes finite... quantum mechanics? Smile
 
Poseidon
 
Reply Fri 14 Nov, 2008 08:46 pm
@Poseidon,
Quote:

any distance can be divided in infinitely small pieces


now here we have the problem.
If any distance could be divided by infinity then a tortoise is faster than Achilles.

Seeing as though Achilles is faster than a toroise, and x/~ is not computable, we thus know that space cannot be divided infinitely. (time as well)

So the concept of infinity is purely a property of mind, and not the world.
So we must accept that this aspect of mind (infinity) is an a priori concept of mind.
Thus the mind is not born a 'blank slate', as nowhere in the world can we learn about infinity, because it does not exist in the world, because if it did then a tortoise would never be overtaken by Achilles.

So the soul exists.

The soul, in terms of this definition, is the ability to conceive of an a priori feature without observing it in the world.

So the soul is (at the least) the ability to conceptualize the infinite.
 
manored
 
Reply Sat 15 Nov, 2008 08:27 am
@Poseidon,
However if we cannot see the end of something it would seen logical for us to interpretate it as having no end, having no proof of that it has a end.
 
Poseidon
 
Reply Sat 15 Nov, 2008 06:27 pm
@Poseidon,
for us to make that interpretation we would have to first be able to conceptualize what it means for something to have no end,

otherwise we would logically just assume that the end of that thing is exactly where it appears to end
 
manored
 
Reply Sun 16 Nov, 2008 02:41 pm
@Poseidon,
We would need to know then the concepts of finite and infinite are formed to be sure of that... I wouldnt see it as impossible to learn about infinite in our world, with for example noticing that things can be divided into any amount of pieces, but I can not know because I can not imagine the working of a mind that knows only finite.
 
Fairbanks
 
Reply Mon 17 Nov, 2008 01:05 pm
@Poseidon,
Poseidon wrote:

Can you see that this proves that the Soul exists?

Smile
Not really, but it points out the epoche wherein time is not illusory.
 
Poseidon
 
Reply Mon 17 Nov, 2008 04:48 pm
@manored,
manored wrote:
We would need to know then the concepts of finite and infinite are formed to be sure of that... I wouldnt see it as impossible to learn about infinite in our world, with for example noticing that things can be divided into any amount of pieces, but I can not know because I can not imagine the working of a mind that knows only finite.

Well, we can observe an apple chopped into halves and quarters, or even miniscule crumbs. But we have to use our imagination, and the idea that it can be chopped infinitely, to go beyond what we have observed.

I suppose, what I am saying is that imagination itself, is this infinite concept.

We cannot observe imagination in others, unless we already have imagination with which to picture this, in our minds.

Quote:

Smile
Not really, but it points out the epoche wherein time is not illusory.

Please elaborate.
 
Fairbanks
 
Reply Mon 17 Nov, 2008 05:23 pm
@Poseidon,
Poseidon wrote:


Please elaborate.

Smile
Time is the original dimension, the dimension of thought. The division is time, that is dimension. Time as in physics, as in Newtonian or Einsteinian physics is a measure not a dimension. Time has no spatial extent although in physics it as measure can be converted into space, which is also a measure not a dimension. Time is also form, although we confusedly think of form as shape. So long as we stay within the parentheses, the epoche, time has meaning. If we jump from one philosopher to another we jump epoche and the meaning changes, but if we stay within one, roughly Kantian, we can approach some degree of coherence.
 
Didymos Thomas
 
Reply Mon 17 Nov, 2008 10:21 pm
@Fairbanks,
So, evidence of imagination is evidence of the soul?
 
Solipsistic Cat
 
Reply Tue 18 Nov, 2008 12:31 am
@Poseidon,
Hey, forgive me if im making some glaring error, but wasnt:

[quote]any distance can be divided in infinitely small pieces [/quote]

The point of this exercise, and wasnt this argued to show the proposition time and thus motion is an illusion?
Because before i can get a meter away, i must get halfway there, and so on ad nauseum, thus beginning something is imposible, so completing it is certainly so.

But to me it simply suggests that there are no
(Cannot for the life of me think of the word. Means higher, existing outside human definition) units, and that the universe is not arbitarily divisible, into distance or time, that analogue processes continue beneath our ability to visualise them.

So it seems this serves to illistrate, as Fairbanks says:
Quote:
Not really, but it points out the epoche wherein time is not illusory.
 
withawhy
 
Reply Mon 29 Dec, 2008 10:40 pm
@Poseidon,
Poseidon wrote:
Can you see that this proves that the Soul exists?


This concept illustrates the concept of infinity. The closer you come to grasping the concept of infinity, the closer you understand the concept of the soul.

Based on the facts the Tortoise gave, he would always be winning as he constantly is setting the end goal. What he's essentially saying is "I will win the race as long as I am winning the race". What Achilles failed to ask was "How far are we racing?"

More interesting is to imagine the race continuing. The tortoise continues to always be ahead, but after a while you have to step quite close to notice who's winning. Then you've got to get a magnifying glass out to see whos toenails are winning. Then a microscope to see whose cells of their toenails are winning. The tortoises, of course. Keep going, electrons, quarks, "strings?", "matter?". Once you get down to the things that make up everything we know, you will eventually have to reach something that cannot be cut in half or split. This in itself is impossible. Or possibly by cutting it in half, it remains a whole before it is ever cut. Youd have to figure out if these things work outside of time as we know it. If this is the case, neither the tortoise nor achilles can win this race without entering some sort of tunnel through time, at which point we would stop caring about the race and start admiring the beauty of the universe. Smile
 
ogden
 
Reply Tue 30 Dec, 2008 10:58 am
@manored,
manored wrote:
However if we cannot see the end of something it would seen logical for us to interpretate it as having no end, having no proof of that it has a end.


The surface of a sphere has no end but it is not infinate.
 
manored
 
Reply Wed 31 Dec, 2008 04:53 pm
@ogden,
ogden wrote:
The surface of a sphere has no end but it is not infinate.
It has a end, wich is located in the same place than the beggining. The fact the end is not marked doesnt means its not there Smile

Its different from an infinite line. If it is infinite, you could mark a spot wich would be the beggining, and divide the line in 2, but it would not be the end of either.
 
ogden
 
Reply Wed 31 Dec, 2008 08:18 pm
@manored,
manored wrote:
It has a end, wich is located in the same place than the beggining. The fact the end is not marked doesnt means its not there Smile


Yes I understand that, I was just using it as an example of sorts. Just because we cannot see the begining or the end of time doesnt mean they are not posible. Would we be able to realize it if we were in a giant time loop?

Quote:
Its different from an infinite line. If it is infinite, you could mark a spot wich would be the beggining, and divide the line in 2, but it would not be the end of either.


The idea of infinity is not gained by empirical means. Finding the end of it is its distruction, just as the end of the race spoils the totoises argument! :shifty:
 
 

 
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