🚀 go-pugleaf

In article <1992Oct13.213159.23649@tamsun.tamu.edu> cmenzel@tamsun.tamu.edu (Chris Menzel) writes:
>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.

Real objects are eternal (including the ones which appear to change).
Parmenides was one smart guy.  Think about chunks of 4-space...

>
>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...
>

Which is exactly the same thing, if one identifies properties with
their extensions, as I do...

>>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


-- 
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