indivisible. Either way the key to understanding this
　　   Paradox  lies in understanding  that Zeno is not here
　　   assuming the atomicity  of empty space or empty time;
　　   these concepts  were foreign  to the ancient  Greeks,
　　   who thought

　　　　　　　　　　　　  p.285

　　   instead　　　　 in　　   terms　　　　 of　　   the
　　   space-which-something-occupies,　　   or　　　　 the
　　   time-in-which-something-occurs. What is assumed  here
　　   is,   for　　 example.　　 the　　 atomicity　　 of   the
　　   space-which-something-occupies.   and  therefore  the
　　   atomicity of that which occupies the space, as well.
　　　　  The interpretation  of this Paradox  turns on the
　　   phrase, "half  a given time is equal  to double  that
　　   time."  It should  be borne  in mind that the wording
　　   here  is Aristotle's, not Zeno's, and that  Aristotle
　　   clearly misunderstands  this Paradox.  He thinks that
　　   Zeno  reasons   fallaciously   that  a  given  object
　　   traveling  at a given  speed  will pass two identical
　　   objects, one stationary  and one itself in motion, in
　　   the same amount  of time.  Modern  exponents  of this
　　   same  interpretation  express  it  differently: Zeno,
　　   they say, is misled  by his ignorance  of the concept
　　   of  relative  velocity.  Whichever  way  the  alleged
　　   fallacy is stated, Zeno is not foolish enough to have
　　   committed it. He is not saying that (B) will pass (A)
　　   (stationary) and (C) (moving at the same speed as (B)
　　   but in the opposite  direction) in the same amount of
　　   time;  instead  he is  pointing  out  that, if (B) is
　　   traveling  at, for example, a speed  of one minim  of
　　   space  per minim  of time, it will pass one minim  of
　　   (A) in one minim  of time, but it will pass one minim
　　   of (C) in half  a minim  of time, thus  dividing  the
　　   indivisible minim, which is impossible.  The issue of
　　   relative velocity is irrelevant and anachronous.
　　　　  Not  one  of  these  Paradoxes  is, by  itself, a
　　   convincing  argument  against  motion, but each, when
　　   taken  to include  its proper  assumptions  about the
　　   nature  of space  and  time, neatly  disposes  of one
　　   possible  account  of the  universe  in which  motion
　　   occurs.  (Of course, some  of these  arguments  would
　　   serve for more than one case, but it is reasonable to
　　   assume  that  four  were  included  for  the sake  of