Xeno's Paradoxes (was Re: [UA] The End of the World, and so on.)

[Cassady Toles]

On 11 Jun 2001 12:19:16 -0000, ua at lists.uchicago.edu wrote:

  But Aristotle pointed out that moving an infinitely small distance takes
an infinitely small amount of time.  That is, motion is a ratio between
distance and time and what Zeno did was divide one side (distance) by
infinity while not dividing the other by the same, a mathematical fallacy. 
The two infinities cancel out, leaving the ratio the same.  

Either way, math, before the advent of calculus had no way of dealing with
an infinite series of numbers.  Xeno didn't believe that you could never
touch anything.  But what he was pointing out was the flaw in greek
mathematical logic.  He was noting that every fixed number is by definition
an infinite series of smaller numbers, and thus, an infinite series of
numbers may in fact be a fixed number.  He knew that it didn't work that
way, but was pointing to a danger sign in math.
  
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