FOM: Arithmetic vs Geometry : Categoricity

[Randy Pollack]

V.Kanovei (Fri, 9 Oct 98 08:29:16 +0200), commenting on NT:

  .....
  2) Counting objects, we always have an exact result 
  which does not depend on the type of objects, their, say, 
  colour or shape, do we use computer or, say, fingers 
  to count, et cetera. 
  In other words, physical counting is claimed to be 
  in 1-1 precise correspondence with mathematical 
  counting, in opposite to 1) above (on geometry).

  However is 2) that true ? 
  Let's count a collection C of enough many objects 
  using a counting device D. By Quantum Mechanics, 
  objects in C will necessarily appear or disappear 
  with some non-0 probability, and D will have 
  similar problems, so, basically, is it at all 
  physically sound to claim that a big enough C 
  has a certain number of objects ? 
  If it is not then 2) becomes questionable. 

While the imprecision of continuous measurement is clearly different
than the possibilities for error in discrete counting, it is the case
that we humans do make errors in counting sets, even sets of feasible
size.

-- 
Randy Pollack                      <http://www.dcs.gla.ac.uk/~pollack/>
Computing Science Dept.                         <pollack at dcs.gla.ac.uk>
University of Glasgow, G12 8QQ, SCOTLAND          Tel: +44 141 330-6055