Zeno was rumored by Plato to be a lover of Parmenides (A philosopher and Zeno's teacher); and wrote these paradoxes to defend his teachings. Parmenides was against pluralism;" a belief in the existence of many things rather than only one" and Zeno set out to show that absurd conclusions can come out of this belief. (Talk about checking your sources)
PARADOXES OF PLURALITY---
1. The Argument from Denseness:
"If there are many, they must be as many as they are and neither more nor less than that. But if they are as many as they are, they would be limited. If there are many, things that are are unlimited. For there are always others between the things that are, and again others between those, and so the things that are are unlimited. (Simplicius(a) On Aristotle's Physics, 140.29)"
this can be summarized as follows: If you have a finite number of objects, then there is an infinite amount of "stuff" between these objects. Therefore the "limited collection is also unlimited." I keep thinking of the Reals when I hear this argument.
2. The Argument from Finite Size:
"… if it should be added to something else that exists, it would not make it any bigger. For if it were of no size and was added, it cannot increase in size. And so it follows immediately that what is added is nothing. But if when it is subtracted, the other thing is no smaller, nor is it increased when it is added, clearly the thing being added or subtracted is nothing. (Simplicius(a) On Aristotle's Physics,139.9)
But if it exists, each thing must have some size and thickness, and part of it must be apart from the rest. And the same reasoning holds concerning the part that is in front. For that too will have size and part of it will be in front. Now it is the same thing to say this once and to keep saying it forever. For no such part of it will be last, nor will there be one part not related to another. Therefore, if there are many things, they must be both small and large; so small as not to have size, but so large as to be unlimited. (Simplicius(a) On Aristotle's Physics, 141.2)"
There is a third argument (that I won't go into) but these two can be summarized as follows: If you join or remove a size-less object...then it was nothing joined or removed to begin with. A "size-less object" seems like an oxymoron in terms to me and shows fallibility in the paradox because of this. Is he setting himself up for failure here?
3. The Argument from Complete Divisibility:
"… whenever a body is by nature divisible through and through, whether by bisection, or generally by any method whatever, nothing impossible will have resulted if it has actually been divided … though perhaps nobody in fact could so divide it."
This is a tough one...I think what he was trying to ask the question: can a finite object be divided infinitely and still have magnitude?
4-7 are the paradoxes of motion as described in class.
8. The Paradox of Place:
"Zeno's difficulty demands an explanation; for if everything that exists has a place, place too will have a place, and so on ad infinitum. (Aristotle Physics, 209a23)"
Can we be in many places at once? I think so: I am at my desk, in my house, in Montgomery Village, on Earth, in the Solar System, etc. all at the same time. Beyond this concept I got a bit lost on how every "place has a place." Any clarification on this would be grand.
9. (My personal favorite) The Grain of Millet:
"… Zeno's reasoning is false when he argues that there is no part of the millet that does not make a sound; for there is no reason why any part should not in any length of time fail to move the air that the whole bushel moves in falling. (Aristotle Physics, 250a19)"
So you drop a huge sack of grain on the floor and it makes a loud "thud." Logically it is to follow that if you drop a 1/2 of a grain on the floor it should also make a sound. I wonder if the old saying "if a tree falls in the middle of the woods and no one is around does it still make a sound?" came from this? I like this one because it teaches us that our own senses can deceive us. Being a person with the highest regard to science but also a person of faith; I find this comforting somehow.
Apologies for the length.
Hi Catherine,
ReplyDeleteI do appreciate your work. I'm happy you were able to find out he was having an affair with a professor who taught him these philosophies. No wonder his ideas where just imaginary things that was difficult for people to understand. I was wondering how they were able to use some of his ideas and it was the reason why I was asking in class if some of the mathematicians were able to create something from what he was deriving. He was just defending his lover's beliefs and no wonder he had so many enemies.
"I'm trying to answer your question about if a place too has a place". In our computer World because of internet access, you can be conferencing in so many places which we assume you are present. If you have to be paid for all of them you will get a lot of money. Your picture image on that screen shows your present, it’s not physical but it’s a place through a medium.
I agree with that part of his concept because everything on this earth has a place so every place should have a place, that's why we have names to identify each place. If a place does not have a “place”, nothing would have existed because there is no place.
I hope it was helpful and good job on your research.
Yaa
Catherine,
ReplyDeleteYou pretty much just knocked it out of the park with your post. I've been looking at it all week and trying to come up with something worthy to post and sadly, I don't have much. I've been thinking about these paradoxes and have lots of thoughts regarding the planet (and it's orbit/rotations) and how it relates to the reading. Many, many more questions and ideas on that but I won't go in to it. I DO have a perspective on infinity and the paradoxes that might spark conversation or might just get me a room full of stink-eye looks. Here goes: So I was thinking about movement and how it pretty much defines everything (even on a cellular level) and how our planet and the universe is moving. It seems to me that we are strategically put right smack dab in the middle of infinity/paradoxes in sort of a state of equillibrium. I say this because it seems like we can divide things infinitely and expand things infinitely and we seem to coexist right in the middle as sort of a point of origin. With everything in constant movement it would seem like the "origin" is never in the same spot. Just when I think I grasp this concept, it's gone again. Then it comes back to me and it's gone...so I thought I would get in down on "paper" and see what you guys think.
ok so for #8 what I got out of it is that what exists has a place. So for infinity to exist, it too has a place. that is a paradox because how can something that goes on infinately be bound? but then to say infinity doesn't exist when we've seen its proved existence in ways like one-to-one correspondence, it makes the statement false.
ReplyDeletealthough we did learn that there are infinities within infinities, the mere of existance of infinties requires that it occupies some place or space. How can something that can be continously reduced occupy some infinte space? And hence, the paradox. If it has no place, than infinity doesn't exist, but we know that it does.
Thank you for clearing #8 up and all of your ideas ladies :)
ReplyDeletecan a finite object be divided infinitely and still have magnitude? I think the universe is a good example, if it is finite. I follow what you're saying, Tracy. We're able to divide things in our universe infinitely, with all that it contains, including us. This could also be answered by the Achilles paradox, maybe, because distance is divded infinitely, although I don't know that the race has magnitude because at some point the race ends, I think.
ReplyDeleteA "size-less" object is totally an oxymoron! That paradox drives me crazy! If it is size-less and "nothing" then why analyze how it must be added or subtracted. sounds like he just shot himself in the foot!
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