[FOM] Liu Fengsui's infinite paradox

A.P. Hazen a.hazen at philosophy.unimelb.edu.au
Thu Nov 21 21:36:10 EST 2002

  Liu Fengsui presented a paradoxical scenario, involving the movement of
infinitely many balls in and out of urns, with plausible arguments to show
that one urn both would and would not be empty at the end of the process,
and asks what is known about it.
  I believe the scenario he presents is known in the literature as "Ross's
Paradox."  It is one of the family of puzzles known generically as
"supertasks": processes (like that of Zeno's runner running through the
infinitely many subintervals of an interval) consisting of infinitely many
successive parts.
  A good reference on this family of paradoxes is
	John Earman and John D. Norton, "Infinite pains: the trouble with
supertasks," in Adam Morton & Stephen P. Stich, eds., "Benacerraf and his
Critics" (Oxford: Blackwell, 1996; ISBN0-631-19268-9),
which discusses Ross's Paradox among others.
  The usual resolution is to is to say that the description of the scenario
only implies that the the urn contains a positive number of balls after
each finite number of transfers, and so allows it to be empty at the end of
infinitely many.  It is thus analogous to "The Thompson Lamp," another
standard supertask.  The lamp is turned on after 30 seconds, off afte 15
seconds more, back on after another 7.5, and sdo on, infinitely many times.
Paradoxical conclusion: at the end of the minute is both on (because it was
turned back on after every time at which it was turned off) and off
(because it was turned back off after every time at which it was turned
on).  Resolution: the initial description determines the state of the lamp
at each instant during the minute, but doesn't imply anything about whether
it is on or off when the minute is over.
Allen Hazen
Philosophy Department
University of Melbourne

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