FOM: Arithmetic vs Geometry : Categoricity
pollack at dcs.gla.ac.uk
Fri Oct 9 09:06:05 EDT 1998
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
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
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