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From: mikew@cutthroat.cs.washington.edu (Mike Williamson)
Newsgroups: comp.ai.philosophy
Subject: Re: Continuous vs discrete
Message-ID: <1991Apr10.182036.29916@beaver.cs.washington.edu>
Date: 10 Apr 91 18:20:36 GMT
References: <382@batz.enst-bretagne.fr>
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Reply-To: mikew@cs.washington.edu (Mike Williamson)
Organization: Computer Science & Engineering, U. of Washington, Seattle
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In article <382@batz.enst-bretagne.fr> beugnard@batz.enst-bretagne.fr (Antoine Beugnard) writes:
>
>Is the model wrong, or are the hypotheses of continuity false?
>Why the classical model works (matches our experience) while Zeno's one don't?
>
>Our interpretation is that the world is by essence discontinuous.
>

The problem with Zeno's paradox is that it makes makes use of the
concept of infinity, while ignoring the concept of the infintessimal.

A quick precis of Zeno's paradox is:  "Assume space is continuous.
Then there are an infinite number of points between any two points A
and B.  To travel from A to B, you must first travel to each of these
infinite number of points.  This could not be done in finite time.
Therefore, if you are able to travel from A to B, space must not be
continuous."

What this ignores, of course, is the fact that some infinite series
have a finite sum.  Zeno's "paradox" may have baffled an ancient
Greek, but it shouldn't fool anyone who knows calculus.  The proper
conclusion to draw in the Achilles and Turtle scenario is:  "Achilles
never reaches the Turtle, until he does."

-Mike