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In article <1992Oct13.191930.17813@guinness.idbsu.edu> holmes@opal.idbsu.edu (Randall Holmes) writes:
>Michael Hand writes:
>>  ...[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).  

Surely it is obvious that this set is *not* the cardinal number 3,
since otherwise, by extensionality, we get a different number 3
whenever something begins or ceases to exist--unless you want to say
that only pure sets (or at least sets of eternal objects) are elements
of the number 3, but that would introduce just the sort of
arbitrariness that gives Benacerraf's argument its bite.

Nonetheless, there *is* something very natural about the set you
identify with 3; maybe because it is the *extension* of a much more
plausible candidate (at least for the friends of intensionality),
viz., the *property* that all 3-membered sets have in common...

>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

--Chris Menzel
  Department of Philosophy
  Texas A&M University