Is that supposed to mean that you wont get across the room because you would have to reach other points first? That is pretty weak.

"Half" is not a number, it is something relative and only a principle. It means something in concept but has no numeric value in itself. 50 is a number as in 50ft. 50 has one half, that is 25, 25 has one half that is 12.5.

If there are not an infinite number of feet in 50 feet there can be only one half.

An archer sees his target as the goal, he understands that given its distance, and the current envirnmental conditions (wind direction and force etc) that he will have to aim the arrow at such an angle, and given the distance the bow will need a certain amount of tension to reach that distance from that position. He knows it is 5o ft away.

Within the active principle (the cause of the event) the factors are set into action- as the arrow crosses the trajectory it could be said to have travelled half that trajectory at 25 feet, but this is only half in relation to the 50feet considered in the action that began the motion. When it hits another 12.5feet it will have traveled .75 of the trajectory, only because 50ft had previouslly measured out. You could not say that it travelled another half of its actual trajectory until it hit its trajectory. You could say that it traveled 0.5 of 25 feet but 25ft is not in relation to the trajectory, its sounds more like whoever is doing the measuring got carried away with the concept of "half way point" and started going backward at some point forgetting that a straight line, if it has two points has one half way point with an infinite numbeer of PERCIEVED points.

And then there is also like I said above, that if the trajectory is not intended until it is reached, then the half way concept is never perceived until the wanderer reaches what the observer would call the other side. There would be no such half way point until the event had a beginning and an end.

Half is a reference to a number relative to itself, so I do agree with you on that note. But for the purposes of the explanation? half of fifty feet is 25 feet. I am not sure I agree with your assertion that half has no numerical value. Instead of saying 2.5, we can say 2 and- a-half because we equate half with that particular numerical value? heck, we could even say 5 1/2, a numerical value incorporating your said concept. But aren't even numbers concepts unto themselves? Zero doesn't exist, yet in concept we use it. What about percentages?

As to the supposition "If there are not an infinite number of feet in 50 feet there can be only one half," I don't find this overly correct.




This is part of the paradox? hence it is a paradox. The arrow will obviously travel that 50 feet given all things go according to plan (conditions, etc.) I'm sure the archer does know that the target is fifty feet away, however the logical implications do not equate to the physical implications of shooting the arrow.




Though the factors that sent the arrow flying towards its target may be in motion, this does not mean they logically equate? that is the paradox. And for all intensive purposes, we could say that the arrow traveled 94.73745845% instead of 50%, which would be 47.368729225% instead of 25 feet.., heck we could even say the arrow traveled 25 bushels of corn, this doesn't matter as that's not the point of the paradox. I think you are getting hung up on the units of measure more than the philosophical implications of the paradox. This may be an issue of mixing deductive and inductive reasoning.



A trajectory can be determined on any two points in a given line, etc. Does a missile need to hit its target before its trajectory can be calculated? No. Take the asteroid Apophis that's going to fly within a few miles of earth in 2029. Scientists know that, based on its trajectory, it will fly by earth in 2029. They also know that if its trajectory is within a certain influential factor, in 7 years that asteroid will hit the California coastline. It can be done, and also that the paradox relies on all thing being equal ceteris parabus to remain constant, leaving us the room to digest the paradox. Apophis does not equate to that CP principle, but zenos arrow does.

So the trajectory is always intended. The micro-second that arrow is let fly, a trajectory is intended? even before. Going half way does not even mean going the full distance in ordered to be applied. Take again the idea of the missile, we can calculate the trajectory of the missile before it lands anywhere, and from any moment in our calculations while that missile is in flight, calculate half that distance.

So when you conclude that "There would be no such half way point until the event had a beginning and an end," I completely disagree in both abstract philosophical principles and scientific doctrine.

Also, there is a hugely problematic issue with the observer/wanderer inclusion. This is a problem for Berkeley rather than Zeno.

Zeno's paradox is basically this.

Also, many people understand zeno's paradox by different examples, whether it be an arrow, a hare and a tortoise, or even a man and a room. The arrow is the best example I know of so I am using that one.

Picture yourself shooting an arrow at a target 50 feet away from you. Logically, if you shoot that arrow at the target 50 feet away from you, that arrow will have to travel half that distance (i.e. 25ft) to reach its target. But in order for that arrow to go 25 ft, it will have to go half that distance (i.e. 12.5 ft) to get there. But in order for it to reach that distance, it has to go half that disctance, etc, etc, etc. Ultimately, the paradox is that though the arrow is moving towards the target, the logical process is actually reversing, that is, halving its distance as the arrow goes further. There is actually a finite mathematical principle in this, which is that in between two points there are an infinite amount of points.

Nothing to do with perception really? unless you are Berkeley. This is a thorough mire in empirical thinking with rational concepts. John Locke would reach the other side of the room, but logically, he would never be able to make it there in the first place. Hence the paradox.

Do you understand? If a straight line is the whole, how can we assign infinite halves when by definition half is very specificly in relation to the whole? if we are talking about an infinite distance, which we arent, then the concept of half is meaningless. Again-I dont understand why we would measure the halves because they do not become new wholes, they are still fractions progressively changing based on the whole which is definite.

Well I did say that "half" would have a numeric value, but it would be inrelation to the entire trajectory, so in the case of a 50ft straight line course half would be 25ft. And yes 12.5 is half of 25-but I dont understand why the halves are being measured, why if the arrow has completed 50% of its trajectory are we seeing the last half, as a new whole with a new half.

Do you understand? If a straight line is the whole, how can we assign infinite halves when by definition half is very specificly in relation to the whole? if we are talking about an infinite distance, which we arent, then the concept of half is meaningless. Again-I dont understand why we would measure the halves because they do not become new wholes, they are still fractions progressively changing based on the whole which is definite.

I don't know who berkeley is but I used the illustration of a man wandering where no one knows the trajectory and only the observer knows the goal because I think its a valid argument to such an explanation of something that seems contradictory. I understand that it is a paradox, but a paradox should be able to be explained as to why it is a paradox. If

I agree with you in spirit, yet the fact that someone crosses the room is not what I'm tripping on. I know what a paradox is, its when two things are true and because of what they are true about they both say different things regaurding that subject which would lead someone to think that one has to be false.

I've offered up some pretty valid, even philosophical arguements to the information presented, yet neither one of you has been able to represent the info as tho it is part of your own understanding. To explain it away as incommunicable because it is a paradox means its not understood well enough by whoever is representing the idea. Because the paradox itself should be definable.

I understand what was said, my counter argument was partialy avoided and partially misunderstood, so because I see it a certain way I'm not going to swallow it just because some guy said that some guy said so when they don't understand it themselves. As a child I refused to believe in Santa Clause, I just wouldn't believe it because I could tell that none of the adults believed it. My dad said when I was 4 and 5 and someone started talking about santa I would look to my dad and smirk. I get the feeling that alot of people swallow these ideas because they've been convinced or they just agree, yet they never construct the idea in their own minds and thus the understanding is never established, it gets learned and remains unknown.

My arguement isn't necessarilly that the guy crossed the room so the information regaurding zeno's idea is false, it had more to do with the reasoning used to explain why he couldnt because of the halves. At this point it sounds more like pretentious intellectualism then philosophy.

Can you explain to me how this is a paradox based on my arguement?

Yes. If we allow the first half to be travelled as a whole, it is inconsistent not to allow this for the second half also. The division of the journey into smaller and smaller fractions is completely arbitrary. But in any case, the paradox can be resolved as follows.

The 'infinite division' refers to an ongoing but never completed process. So at any given time, however far in the future, there will be a last intermediate point, from which the traveller can reach his destination in one go.

RESPONSE TO POST #11

That?is...the?paradox. When a half becomes half of its half of its half of its half ad infinitum. Does the arrow actually move even though it does not logically travel half its distance.


Think of two points on a line. They dissect an infinite so-called "whole" which I am assuming is the geometric plain in which we can half it. Seriously, I don't think this is too difficult to understand. Two points on a plain discern something finite. But it is a good thing we are not talking about an infinite distance? in fact quite the opposite. That you do not get why we are measuring halves is because we are not. We are defining halves from something twice its size. Again, OMG, this is the substance of the paradox.



LOL! Thats the nature of a paradox... otherwise it wouldn't be one.



RESPONSE TO POST #13

Etymologically, paradox derives from the latin paradoxum meaning "statement seemingly absurd yet really true." The deeper meaning paradoxos means "contrary to expectation, incredible," from para- "contrary to" + doxa "opinion." (OED) There is no implication of truth or falsity in a paradox? hence the title of para-dox. It is contrary to logical supposition.




Have you? Is your criticism only that the notion of zeno's paradox is explained through the actually academic interpretation of it? It is not explained away as incommunicable because it is a padox in itself, it is to say that the issues the paradox raises underlines the problematic account of it being a paradox in the first place. That you say "the paradox itself should be definable" is? well? horribly, horribly wrong. Otherwise it would not be a paradox? would it?


I don't think you do. And nothing was avoided. On Santa Claus? how do you know that he does not exist? Think about it like this. Have you ever been to India? Chances are no. So how do you know that India exists? Pictures and videos show images of India, Indian people you meet are from India and tell you want a beautiful country it is, but how do you know it really exists. It's the classic Cartesian argument, How do I know something exists? Santa exists in much the same way India exists. You are to some extent relying on abstract notions of India to affirm its existence.

Also, and this is important, this is first and foremost a philosophy site. We are dedicated to abstract thinking both empirically and rationally. Think farther outside the box.





Zeno's paradox incorporates the fact that the guy crossed the room? but in a logical sense, could never reach half his distance because he had to travel half that distance and half that distance and so on. The halves that you are hung up on are in so many words redundant.
But seriously, "? it seems more like pretentious intellectualism than philosophy?" Dude? seriously. It's a paradox!!! LOL! I seriously cannot believe this. Intellectualism is a prime tenent of philosophy? especially when you are dealing with paradoxes. Good god man.


LOL!

Quick reply- You've been misunderstanding me from the begining and keep repeating yourself without answering anything. Youre just not getting it and it is probably my fault.

A paradox can to be explained. Example

LBW paradox.

Babies born with a low birth rate have a higher mortality rate.

Babies born to mothers who smoke have a high mortality rate.

here is the paradox-Low birth weight babies born to mothers who smoke seem to be otherwise healthy and have a normal survival rate. I understand that this is a paradox and I understand why.

I think ABC is finding it easier to follow me and I appreciate abc taking the time to explain without trying to insinuate that I am incapable of understanding.

I think if you dont question to gain a thorough understanding then you're not really getting it and will fail to establish the info/phenomenon in your mind as something you are cognitive of, and it is merely something you've m,emorised which you clearly havn't.

here is an example of a type of paradox.

I have a bag of coffee. This particular strain of coffee has a very high alkaloid content lets say 3% by weight (but I dont know if that is really alot of caffine)

Someone gives me another bag of coffee, twice as much, however this new coffee is 1.5% caffine by weight so I now have more.

I put them togeather and by weight I have less cafine then I started with, even tho I have more.

I'm capable of understanding things far more complicated then these examples if anyone is capable of explaining it a complicated enough manner.

Aristotle remarked that as the distance decreases, the time needed to cover those distances also decreases, so that the time needed also becomes increasingly small.[11] Aristotle solves the paradoxes by distinguishing "things infinite in respect of divisibility" (such as a unit of space that can be mentally divided into ever smaller units while remaining spatially the same) from things (or distances) that are infinite in extension ("with respect to their extremities")