Path: utzoo!utgpu!news-server.csri.toronto.edu!rpi!uupsi!sunic!news.funet.fi!hydra!klaava!kruuna!sinkkone From: sinkkone@kruuna.Helsinki.FI (Janne Sinkkonen) Newsgroups: comp.ai.philosophy Subject: Re: continuous vs discrete Message-ID: Date: 18 Apr 91 15:37:31 GMT References: <381@sein.enst-bretagne.fr> Sender: news@klaava.Helsinki.FI (Uutis Ankka) Organization: University of Helsinki (Finland) Lines: 43 In-Reply-To: beugnard@sein.enst-bretagne.fr's message of 9 Apr 91 13: 32:21 GMT Originator: sinkkone@kruuna In article <381@sein.enst-bretagne.fr> beugnard@sein.enst-bretagne.fr (Antoine Beugnard) writes: > The paradox... Achilles and a turtle are about to run a race. > Obviously as Achilles can run faster than the turtle, he decides > to let her start N meters ahead. They start running at the same > time, but Achilles never reaches the turtle... > When Achilles reaches the previous Turtle location, she has gone > forward. d(n) denotes the distance she has covered while Achilles > was reaching her previous location. So, > > A(0) = 0 and A(n) = T(n-1) defines A(n). > T(0) = N and T(n) = T(n-1) + d(n) defines T(n). > According to Zenon, d(n) is positive then Achilles never reaches > the Turtle. "Never" here means "not for any value of N", and this is quite true. However, with these formulas you can only describe the system during the timepoints defined by some event A(n) or T(n) happening. (Timepoint is here referring to the time we are experiencing.) If you compute the timepoints when A(n) or T(n) happens, you find that all these times are _before_ the time (t0) Achilles really reaches the Turtle. So, "not for any value of N" really means "not before t0". Zenon's use of the word "never", or whatever he used, is misleading. It is only referring to the timepoints defined by A(n) or T(n), and misses the future after all these. > But in every day life, we can notice that Achilles overtakes her. > We do not call into question the mathematical modelling. So where is > the problem? Most people would say our model is wrong since it > does not describe the real world. We do ask why it is wrong!! It matches the real world perfectly, but describes only a part of it. ;) > Therefore the world is discontinuous !! No ?? Yes, I believe so! janne