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My paper for phil-201 re: Zenos paradox of motion

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My paper for phil-201 re: Zenos paradox of motion

bevans15
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Posted 05/21/09 - 01:40 AM: Subject: My paper for phil-201 re: Zenos paradox of motion	#1
Brad Evans EVANS 1 Philosophy 201-01 Marcel Daguerre Disproving Zeno’s Paradox I am going to be attempting to bring to light some of the flaws in Zeno’s paradox that seem to be apparent to me, a college freshman who is still taking GE classes. The battle of the vaunted Pre-Socratic thinker and the college freshman is about to commence. The point of Zeno's paradox was the hare has to cross an infinite number of points in order to catch up to the turtle and that, Zeno claimed, must require an infinite amount of time. In order to attempt to disprove this, I would like to ask you to think about the fact that the infinite sum: 1/2+ 1/4+ 1/8+ 1/16+ ... +1/2n+... has the finite sum, 1. I consider this to be a fairly damning piece of evidence right from the start. I consulted a math major to help me come up with another way to prove it is a finite sum by noting that: If S= 1/2+ 1/4+ ... then S- 1/2= 1/4+ 1/8+ ...= (1/2)(1/2+ 1/4+ ...)= (1/2)S. Now solve for S Better would be to look at the finite sums: if S= 1/2+ 1/4+ ...+ 1/n2 then S- 1/2= 1/4+ 1/8+ ...+ 1/2n= (1/2)(1/2+ 1/4+ ...+ 1/2n-1) Now, unfortunately, that last sum is not the same as S. But we can make it the same EVANS 2 by adding and subtracting 1/2n: S- 1/2= (1/2)(1/2+ 1/4+ ...+ 1/2n-1+ 1/2n- 1/2n S- 1/2= (1/2)(1/2+ 1/4+ ...+ 1/2n-1+ 1/2n)- 1/2n+1 S- 1/2= (1/2)S- 1/2n+1. Now solve for S and then see what happens to that as n goes to infinity (it will inevitably get closer and closer to and finally become equal to 1. Zeno's assertion that no movement is possible has been hotly contested throughout the ages, most notably by people in motion. While no definitive proof has been developed to counter Zeno's theory, there are several philosophical objections to Zeno's work: Denial is a common method of disproving everything. All one must do is refuse to accept something, and they have effectively disproved it. This is the least acceptable method of disproving something, and most people deny it any credibility and it seems to me that Zeno, at times, seems to lean on this concept rather heavily. I have dubbed the next objection “Zeno's Paradox Paradox Objection.” If we consider Zeno's Paradox to be true, then we must accept that life is impossible because if we cannot trust one of the most ‘basic’ aspects of our life because our senses fool us, how can we trust them when they tell us that we actually are alive? This is a very philosophically dangerous thing to consider, so we shall not dwell on the personal implications this holds. Instead we shall look at Zeno's life. If life is indeed impossible, then it is impossible for Zeno to actually have existed. If it is impossible for Zeno to have existed, then it is impossible for Zeno to have theorized about movement. If it is impossible for Zeno to have theorized about movement, then it is impossible for Zeno to have created his Paradox Theory. If it is impossible for Zeno to have created his Paradox Theory, it is impossible for EVANS 3 the Paradox Theory to exist. If it is impossible for Zeno's Paradox Theory to exist, then we must consider the possibility that life is possible. If we consider that life could be possible, we must consider that Zeno's life may have been possible. So now, in the true Socratic Method, we have reached a logical contradiction in our assertions (Zeno cannot both be alive and not alive at the same time). Unfortunately, if we must consider that Zeno's life may have been possible, we must consider that he may have created his Paradox Theory. This creates the Zeno's Paradox Paradox. It is both possible and impossible for Zeno's Paradox to exist. Therefore, although things such as movement, life, and wars are impossible, they are also extremely possible. This claim was logically and thoughtfully derived from Zeno’s own claims. Now it is time for me to be rather snide and cynical for a moment. Although during his lifetime, which surprisingly didn't end until 45 years after he proved its impossibility, Zeno never realized the predicament in which he had placed everyone. When the Nobel Prizes were created it was recognized that Zeno had already been awarded four of these prizes: Nobel Peace Prize: Having proved that movement was completely impossible, Zeno had effectively proved it impossible to engage in wars of any kind. Zeno effectively ended every war which ever had, or would, happen. For this, he was awarded the Nobel Peace Prize for having brought the world to peace. Nobel War Prize: Seeing as movement was impossible, so too was life itself proved impossible. For having killed every known living thing, by proving that what they were doing was impossible, Zeno was awarded the Nobel War Prize. EVANS 4 Nobel Mathematics Prize: For having applied mathematics to a real-world, real-life situation in order to end all wars, all life, and all movement, Zeno was awarded the Nobel Mathematics Prize. In all seriousness however, I believe that I have effectively disproved Zeno’s paradox both mathematically and logically. I do think that, while false, they should continue to be used in order to provoke the proverbial ‘deep-thoughts’ and intellectual enticing conversations that I consider myself lucky to have been a part of this semester.

Yahadreas
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Posted 05/21/09 - 05:18 AM:	#2
I think the best objection to Zeno's paradox is that there are not actually an infinite number of points between X and Y. Mathematics does not equate exactly with reality. There are a finite number of points between X and Y. Which would be (Y-X)/1.616252(81)×10⁻³⁵. Edited by Yahadreas on 05/21/09 - 11:38 PM
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Yahadreas
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Posted 05/21/09 - 05:31 AM:	#3
And in addition: I'm not sure what a Phil-201 class is, but if it's anything other than fun and games, I wouldn't submit that paper.
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Posted 05/22/09 - 04:18 AM:	#4
bevans15 wrote: Now solve for S and then see what happens to that as n goes to infinity (it will inevitably get closer and closer to and finally become equal to 1. Better as in... what? Much, much more convoluted and mathematically less correct? bevans15 wrote: If it is impossible for Zeno to have created his Paradox Theory, it is impossible for the Paradox Theory to exist. Not true. That's like saying if Newton or Einstein had never existed there would be no gravity.

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Posted 05/22/09 - 07:00 AM:	#5
Zeno's paradexes are actually criticism of the mainstream view in Greek philosophy about divisibility. The whole problem is that we do not know well what Zeno's philosophy really was and the texts on Zeno are done by those who opposed the Eleatic School. So no wonder people now say that the Eleatic School thought movement "was impossible". After all, wasn't it a Greek philosopher (whos name I forget from Plato's book) that simply walked away after hearing Zeno's arguments? But that indeed was the point for Zeno: obviously there is something wrong in the should one say "Aristotelean" divisibility. We counter actually the same problems Zeno was talking with the infinitesimals in the 17th Century, which Berkeley put into words.

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Posted 05/22/09 - 02:52 PM:	#6
In a block universe, Zeno's paradox disappears, also infinite divisibility is a myth as stated. I think there isn't anything smaller than a plank length. If the universe is complete as in a block universe and time is merely emergent for some reason, then there is no problem. As in, In Universe X, A goes to B, then goes to C. A does pass through many other points between AB and BC, but it is established that A goes to B and B goes to C.

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Posted 05/22/09 - 04:48 PM:	#7
Well...to deny something is not to disprove. You didn't cite where in some text Zeno 'relies heavily' on this notion...and I personally find it hard to believe that Zeno does, considering he was a fairly formidable logician and metaphysician for his time. -- To deny something and give REASONS may be to disprove. Other than demonstrating that there is a formal logical mistake at hand...it is notoriously difficult to disprove any claim. That is a philosophical topic in itself. My main issue with the paper, if I was grading it, is that you seem to go out on a tangent rather early, a tangent that is irrelevant to analyzing Zeno's position. That 'life' is impossible under Zeno's paradoxes is not a real problem for Zeno. Of course life is not possible if motion is not possible. Zeno very likely (given that presumably his paradoxes were meant to substantiate Parmenides' metaphysics) would have held that there does appear to be living things...and there appears to be motion. What is so dangerous here? And even if it is dangerous...what does that have to do with whether Zeno is correct or not? This being a 200 level class...you were not required to do any research?

Aetixintro
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Posted 05/22/09 - 05:23 PM:	#8
To turn the argument around, it should be quite clear that no-one who aims to get somewhere never begins their journey with such an incredibly small step. Let's imagine this person has a walk over to the neighbour.
Efficacy of "for since it is at present manifest to me that even bodies are not properly known by the senses nor by the faculty of imagination, but by the understanding alone" - Descartes, Meditation II I'm always wanting more, Anything I haven't got, Everything, I want it all, I just can't stop - The Cure, Want

treysuttle
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Posted 05/22/09 - 09:26 PM:	#9
Anytime someone says 'quite clear'...it should be quite clear to you that it is not clear at all. Explain?

Aetixintro
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Posted 05/23/09 - 09:59 AM:	#10
treysuttle If you view it from Zeno, you first cover the first half of the distance and then the next half of that half distance remaining and so on until there is an incredibly small half remaining of the total distance. If you begin covering the distance on the opposite end of the argument, you begin with the smallest half first and it seems to me it's almost impossible to make such a small step of a relatively short distance. Is it good?
Efficacy of "for since it is at present manifest to me that even bodies are not properly known by the senses nor by the faculty of imagination, but by the understanding alone" - Descartes, Meditation II I'm always wanting more, Anything I haven't got, Everything, I want it all, I just can't stop - The Cure, Want

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