Zeno paradox, part II - the problematic nature of infinity and movement

This article is the second and final part of a two-part series on Zeno of ELEA. In the first article, we consider the first five paradox to Zeno, in addition to some interpretive grey areas. Again should I note that scientists discuss the best interpretation of Zeno, particularly in light of our limited primary sources. For reasons this article I the traditional interpretation of Zeno, keep further by Plato, in the paradoxes of Zeno build up and support the work of this teacher Parmenides. Finally I briefly considering the tremendous impact that has made the Zeno on Western philosophy.


Large and small paradox. Zeno argues that a plurality is present, then a plurality parts at the same time as small, have no size and be as large, infinitely great. Is coming Zeno such as to this conclusion?


To get started, Zeno shows how parts of plurality, not a size have can be so small. We must first adopted, parts of the plurality because we can divide pluralities parts in parts but not be can all further divided not pluralities. Parts must have no size, since all can everything broken down into parts with size and parts will not be further divided. Therefore, parts are so small that they have no size at all.


On the other hand, all parts of a plurality must be infinitely large. A plurality must be divided into parts a size. However, if the parts have no size then the plurality as a whole will not size and stop a plurality. Therefore any part of a plurality must be greater than 0 (zero) a size. And each sub-part of each part has a size greater than 0 (zero), and each sub sub part must be a size greater than 0 (zero) as well as the sizes of the parts of a plurality all equal infinity make ad infinitum, because they are infinitely divisible and infinity can be grouped together.


We see in this paradox, the Zeno intends the problems of a metaphysics of plurality. As a result, he adds more credibility, Parmenides monistic metaphysics.


Infinite divisibility paradox. Again we see Zeno attack metaphysics of plurality. You look at, you will be an object that you divide half, then further divided the halves in half and the subdivision of the remains in half, and so on, and so on, ad infinitum. If we ever this operation, Zeno proposes, that we would in the end the metaphysical "elements", and we could three conclusions from these elements.


First, the elements are Nothing(s), and the elements "add", to make the original object, and you can not add a number of nothing is to make something. Therefore, not the elements can be anything. Secondly, the elements are something (s) still have no size. Again, adding elements that have no size an object is any size, and have an object no size not divisible. Thirdly and finally, the elements are something (s) and closer as well. If the elements of flats have, then the elements can be further subdivided and be no more elements, and we are left with the original problem.


Therefore, Zeno does that infinite divisibility is no operation, because you requires a metaphysics of plurality. Rather the world would reasonable be, unified whole, which can be divided as Parmenides argued.


The grain/bushel wheat paradox. Imagine a bushel wheat from a table at the bottom fall. We all agree that the bushel a noise when hitting the ground. However, hundreds, even thousands of parts make the individual grains that make up the bushel. We but not hear a sound when a - thousandths grain hits the ground. As these parts do sounds when they are deleted, but the whole bushel a noise makes? Zeno points here that a monastic metaphysics is more than a metaphysics of the plurality of plausible.


The paradox of locations. We can assume that all corresponds to his own place. So, everything has existed what a place, as a place is a thing that exists, it have an own and which place their own place, ad infinitum. So, we conclude that there is an unlimited number of places for everything that is contrary to our original premise. Although this paradox of Parmenides does not directly support philosophy, it discredit a general faith in his time, the proposed all people must have their own places.


Zeno, highlighted in its brilliance, very important concepts, namely infinity, and plurality to show, to strengthen philosophy their shortcomings and his teacher. Mathematician perplexed his works on indefinitely, and it was not until the introduction of the calculus that mathematician could solve some of the paradoxes of Zeno, according to. Even now, still search the most fundamental particles or the "God particle," physicist and chemist with Zeno condition that infinity is no practical way.


He was not only brilliant, but he was innovative. Instead of his philosophy in poetic writing forms as the pre-socratics before him, he wrote extensively in prose, which is still in the commonly used genre in philosophy and science. Aristotle sang Zeno praise for its innovation, but not for his writing. Indeed, Aristotle on Zeno leads the invention of the "dialectic".


The dialectic was enormously important, later philosophers, most notable Hegel. Zeno leave, even its inherently justified Hegel contradictory metaphysics. Bertrand Russell found to Zeno importance the Academy in General when he said: "Zeno's arguments, in any form, ground for almost all theories of space and time, and infinity granted that from his time, our own were built."



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