🚀 go-pugleaf

In article <1992Oct9.203658.25387@tamsun.tamu.edu> e343mh@tamuts.tamu.edu (Michael Hand) writes:
>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.

But this approach applies to anything being itself rather than
something else.

>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"]
>_______________________________________________________________________
>-----------------------------------------------------------------------
>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.
  
Au contraire, it is obvious which set the cardinal number 3 is.  It is
the set of all sets with three elements (this _can_ be defined in a
non-circular manner, by the way).  The technical problem is that this
set is not a first-class citizen in the usual set theory ZFC.  It is
in the set theory NFU of Quine and Jensen, however.

But there are some other objects closely related to 3, too.












-- 
The opinions expressed		|     --Sincerely,
above are not the "official"	|     M. Randall Holmes
opinions of any person		|     Math. Dept., Boise State Univ.
or institution.			|     holmes@opal.idbsu.edu