FOM: Hersh's fingers

[steel@math.berkeley.edu]

On Sat, 28 Feb 1998, Reuben Hersh wrote:

 
> Why don't you respond to the serious point I was making?
> Some people say that five is an empirical, physical entity, because
> it applies to *the set of your toes*  and *the set of my fingers.*  Some 
> say, with equal or greater force, that five is an abstraction, part of an 
> abstract theory.  I claim to resolve this contradiction by showing that  
> "five" has two distinct but related meanings, one empirical, and
> one in the so-called "abstract theory" (which is  real and
> resides in our collective thinking.)


    It is debatable whether this is a "serious point". I personally just
find it muddled. For example, the assertion "five is an abstraction, part
of an abstract theory" confuses the word "five" with the number five. 
Theories are linguistic entities; it is the word "five", not the number
five to which it refers, which is part of a theory. This sort of confusion
is probably the fundamental one underlying Hersh's views, and I and many
others have pointed it out before. For example, I wrote on 1/4/98:

 Mathematics IS a human institution ( as is Physics, Chemistry, Music,
...), but it is not ABOUT human institutions. Sociology, Politics,
History, etc., are sciences which are ABOUT human institutions, but
mathematics is not of this nature. Martin Gardiner made this point several
times in his exchanges with Hersh...

Just recently, Soren Riis made the same point:

Notice the "existence" here is used on two different levels. The
existence of comic strips / mathematics is not to be confused with
the question of the existence of Mickey Mouse / non-abelean groups.


    To my knowledge, Hersh has not yet made any response to this
objection.


John Steel