FOM: Jurassic pebbles (more on Davis/Hersh)

[Lincoln Wallen]

   Comments: ( Received on motgate.mot.com from client pobox.mot.com, sender 
	     peter at galois.geg.mot.com )
   Date: Tue, 17 Mar 1998 09:07:55 -0700
   From: peter at galois.geg.mot.com (Peter White)

   > Now, coming to the temporal arguments concerning the Jurassic beach.
   > Isn't it clear that in drawing the conclusion that the rearrangement
   > and counting can be done *in principle* on a Jurassic beach, Davis is
   > making a claim about the relationship between the practices of
   > formulating and proving mathematical theorems and some very particular
   > human practices of rearrangement and counting, and their relationship
   **^^^^^***
   > with the situation as we understand it pertaining in Jurassic times.

   Suppose the human process is replaced with a "natural" one. For example,
   what if there is a crystaline structure that prefers deposition of new
   atoms in a square arrangement of atoms, thus given a positive integer
   number of new atoms, the new atoms are *more likely* to be arranged in
   four squares as given by Lagrange's theorem, and *less likely* to be
   arranged in some other way. Now there is no human component to the
   argument. The question is: Does the lack of a requirement for a
   human (or otherwise competent) observer affect your arguments
   concerning the objective/subjective nature of mathematics?

   ...

   Peter White, Motorola

I don't believe it does.  Arguments like the one I advanced are often
wrongly caricatured as *requiring* human observers.  Notions such as
"crystalline", "square", "atom", "positive integer" etc. are
meaningful against a background of language and practical action.  To
talk about Jurassic times (or astrophysics) we simply argue that all
factors that might effect our use of language today, and our ability
to conduct ourselves in particular practical ways are unchanged.  So
it is our present practices that make such hypothetical judgements
possible.  [Note I am not saying such notions are indeterminate; but
that making them determinate rests on adopting certain attitudes
toward them and their uses.]

What it is about our current practices that allows this is the central
question, rather than denying that it is meaningful to reason this
way.

Lincoln Wallen
Reader in Computing Science
Oxford