FOM: social construction?

[Lincoln Wallen]

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   From: martind at cs.berkeley.edu (Martin Davis)
   Cc: Lincoln.Wallen at comlab, csilver at sophia.smith.edu, fom-digest at math.psu.edu
   Date: Sun, 22 Mar 1998 12:12:43 -0800

   At 08:03 PM 3/22/98 GMT, Lincoln Wallen wrote:
   >

   >Can you elaborate on what you see to be problematic in looking into
   >mathematical activity this way?
   >

   I take this relativistic point of view as moving to deny the possibility of
   establishing objective truth.

   Martin

I see nothing relativistic in the view whatsoever!  We must be
thinking about different ideas.  Are you sure you are not thinking
about social constructivism?  

Let's accept that there is objective truth from the outset.  The
question is how we gain access to it and investigate it.  You would
have no objection I suppose to my saying that the particular conduct
of the natural scientist in designing and carrying out experiments,
the practical methods of holding parameters fixed, accountably so, and
the practices involved in determining experimental error from
interesting phenomenon are part of his/her ability to discern
objective truth (to the best of our knowledge), and part of the skill
of designing repeatable experiments.

It is a reasonable activity to seek to articulate how to achieve this.
It goes by the name of experimental design and is bound up in the
education and practice of science.  Courses are taught on it!  When
faced with a new phenomenon this body of practice changes to
accomodate the peculiarities of that phenomenon.  This is not to say
that the phenomenon is not real, or that we are unable to gain access
to it.  Just that our account of it is bound up with and partly
reflective of our practices for investigating it.  This is surely how
we are able to countenance changing our view of nature all the time
without necessarily feeling that our ability to "know it" is in a
sense independent of our currnet state of knowledge and the terms we
use to discuss it.

As with science, so with mathematics.  Whatever we might mean by
objective truth in science, one account of it can surely be obtained
by reference to these practices, rather than by speculation about god,
mind, the universe etc.  In fact this is an incredibly ordinary
statement; blindingly obvious it seems to me.

One way of articulating what is eternal about the truths mathematical
practice gives us access to is to seek to understand this word
"eternal" through the structure of our practice.  Is this saying
anything more than logicians have said in trying to isolate the
elements of logical consequence?  I don't think so.  But there is more
to understand.  That is all.

Lincoln Wallen