FOM: Hersh's fingers

[steel@math.berkeley.edu]

Reuben Hersh writes:

  So the natural numbers as describing physical objects
are not the same as the natural numbers in pure mathematics. 

The fact that I have five fingers on my left hand is an empirical
observation.  "Five" in that usage is an adjective.  There is no
conceptual difficulty there, any more than in saying my fingers are long
or short.



       "Five" is indeed an adjective here, but it does not express a
property of fingers, as does "short". It expresses a property of a certain
SET of fingers . Frege discusses this very clearly in "Grundlagen
der Arithmetik". Perhaps one reason logicians and foundations specialists
are shocked by Hersh's views (as I confess I am) is that they are so well-
publicized despite the fact that they are shot through with such
elementary blunders.


John Steel