elegance.)  Once   the  Paradoxes   are  seen   as  a
　　   destructive  tetralemna, they then form an impressive
　　   demonstration  that  any additive  conception  of the
　　   universe  renders  an intelligible  account of motion
　　   impossible.
　　　　  Furthermore, these  puzzles  then  can be seen as
　　   part of a comprehensive  Eleatic argument against the
　　   possibility   of  motion.   Fundamental   to  Eleatic
　　   philosophy is the premise that what is unintelligible
　　   cannot exist.  Therefore, in order to demonstrate the
　　   impossibility  of motion, one need  only show that no
　　   matter   what  kind  of  universe   one  assumes,  no
　　   intelligible account of motion can be given.  It will
　　   then follow that motion cannot  occur in any possible
　　   universe.
　　　　  We begin  with the assumption  that  the universe
　　   must be either  additive  (that is, made up of parts)
　　   or continuous (that is, made up, not of parts, but of
　　   a continuous, unbroken substance). If it is additive,
　　   then  there  are  three  possibilities: (I) that  the
　　   universe is composed  of bodies separated  by a void;
　　   or, (2) that the universe is composed  of minims;  or
　　   (3) that  the universe  is composed  of dimensionless
　　   points  and  instants.  Case  (1) is disposed  of  by
　　   Parmenides  himself;  he argues that the void is unin
　　   telligible,  and   therefore   cannot   exist,   thus
　　   rendering  (1) impossible.  All possible permutations
　　   of (2) and (3) are refuted  by Zeno's  Paradoxes;  no
　　   conceivable assortment of minims and

　　　　　　　　　　　　  p.286

　　   dimensionless  points and instants makes possible  an
　　   intelligible  account  of  motion.  Thus, on  Eleatic
　　   terms, the universe cannot be additive.
　　　　  On the other hand, if the universe is continuous,
　　   then  motion  can  only  be  explained  in  terms  of
　　   compression  and  rarifaction.  However.   these  are
　　   clearly species of change, and Parmenides argues that
　　   change  of any kind is impossible, since  it involves
　　   coming-to-be  (that  is, arising  from nothing, which
　　   "nothing," since it is unintelligible, cannot  exist)
　　   and   passing-out-of-being   (which   requires   that
　　   something  which exists commence  to not-exist, which
　　   is likewise unintelligible and therefore impossible).
　　   These  arguments, it should be noted, all turn on the
　　   confusion  of not-being  (for example, being not-red)