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- From: holmes@opal.idbsu.edu (Randall Holmes)
- Newsgroups: sci.logic
- Subject: Re: The Mathematical Universe
- Message-ID: <1992Oct15.193338.20463@guinness.idbsu.edu>
- Date: 15 Oct 92 19:33:38 GMT
- References: <1992Oct9.203658.25387@tamsun.tamu.edu> <1992Oct13.191930.17813@guinness.idbsu.edu> <1992Oct13.213159.23649@tamsun.tamu.edu>
- Sender: usenet@guinness.idbsu.edu (Usenet News mail)
- Organization: Boise State University
- Lines: 52
- Nntp-Posting-Host: opal
-
- 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
-