🚀 go-pugleaf

Randall Holmes and Chris Menzel write:

Holmes> I also maintain that the physical world is a "mathematical object".

Menzel> I take it you don't think the physical world is *literally* a 
      > mathematical object, if only for the fact that, as you yourself 
      > hint, any number of other mathematical objects would have served 
      > just as well.

Holmes> Indeed many other objects would have served as well (do in
      > fact serve as well?); our position makes it impossible to discover
      > which one has in fact served :-)

Recall Benacerraf on a similar skepticism + absurd ontological 
identification (namely, identifying numbers with certain sets 
instead of certain others, much as Holmes identifies the world
with a certain mathematical object instead of another that would
serve as well); the application to Holmes's view is obvious.
I also recommend that anyone interested in attacking Benacerraf
on this issue read his paper instead of reacting just to these
suggestive quotes.

  If the numbers constitute one particular set of sets, and not another, 
  then there must be arguments to indicate which...

  In awaiting enlightment on the true identity of 3 we are not awaiting a 
  proof of some deep theorem.  Having gotten as far as we have without 
  settling the identity of 3, we can go no further.  We do not know what a 
  proof of that *could* look like.  The notion of "correct account" is 
  breaking loose from its moorings if we admit of the possible existence 
  of unjustifiable but correct answers to questions such as this...

  ...[T]here is little to conclude except that any feature of an account
  that identifies 3 with a set is a superfluous one -- and that therefore
  3, and its fellow numbers, could not be sets at all.

  [from "What Numbers Could Not Be"]
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Michael Hand                     phone (409)845-5660, fax (409)845-0458
Dept of Philosophy, Texas A&M Univ, College Station TX 77843-4237 U.S.A.