Zeno of Elea :: essays research papers

Zeno of EleaZeno of Elea was born in Elea, Italy, in 490 B.C. He died there in 430B.C., in an attempt to oust the citys tyrant. He was a noted pupil ofParmenides, from whom he learned most of his doctrines and political ideas. Hebelieved that what exists is one, permanent, and unchanging. Zeno arguedagainst multiplicity and motion. He did so by showing the contradictions thatresult from assuming that they were real. His argument against multiplicitystated that if the numerous exists, it must be both unnumberedly large and infinitelysmall, and it must be both limited and unlimited in number. His argumentagainst motion is characterized by two famous illustrations the flying arrow,and the runner in the race. It is the illustration with the runner that isassociated the first part of the assignment. In this illustration, Zeno arguedthat a runner can never flip the end of a race course. He stated that therunner first completes half of the race course, and then half of the remainingdist ance, and will continue to do so for infinity. In this way, the runner cannever reach the end of the course, as it would be infinitely spacious, much as thesemester would be infinitely long if we completed half, and then half theremainder, ad infinitum. This interval will shrink infinitely, but never quitedisappear. This type of argument may be called the antinonomy of infinitedivisibilty, and was part of the dialectic which Zeno invented.These are only a small part of Zenos arguments, however. He is believedto have devised at least forty arguments, eight of which have survived until thepresent. spell these arguments seems simple, they have managed to raise anumber of profound philosophical and scientific questions about space, time, andinfinity, throughout history. These issues still interest philosophers andscientists today.The problem with both Zenos argument and yours is that neither of you dealwith adding the infinite. Your argument suggests that if one adds the infinite,the sum will be infinity, which is not the case.