W3C home > Mailing lists > Public > semantic-web@w3.org > August 2008

Re: singleton sets

From: Elisa F. Kendall <ekendall@sandsoft.com>
Date: Tue, 12 Aug 2008 14:51:54 -0700
Message-ID: <48A205FA.60909@sandsoft.com>
To: "Richard H. McCullough" <rhm@pioneerca.com>
CC: Pat Hayes <phayes@ihmc.us>, KR-language <KR-language@YahooGroups.com>, Semantic Web at W3C <semantic-web@w3.org>, Adam Pease <adampease@earthlink.net>

Having studied under both John Barwise and John Etchemendy just prior to 
publication of this book, I would have said that they wanted to ensure 
that their students were clear about the distinctions, not that they did 
not believe singleton sets were useful at times, as long as one was 
careful in crafting the logic.


Richard H. McCullough wrote:

> Here's someone else who doesn't like singleton sets,
> and hence doesn't like classes which are individuals.
> John Barwise & John Etchemendy (1992), "The Language of First-Order 
> Logic",
> Third Edition, Revised & Expanded, Center for the Study of Language 
> and Information, Stanford, Page 212
>    Suppose there is one and only one object x satisfying P(x).  
> According to the
> Axiom of Comprehension, there is a set, call it a, whose only member 
> is x. That is,
> a = {x}.  Some students are tempted to think that a = x..  But in that 
> direction lies,
> if not madness, at least dreadful confusion.  After all, a is a set 
> (an abstract object)
> and x might have been any object at all, say Stanford's Hoover Tower. 
> Hoover is
> a physical object, not a set.  So we must not confuse an object x with 
> the set {x},
> called the singleton set containing x.  Even if x is a set, we must 
> not confuse it with
> its own singleton.  For example, x might have any number of elements 
> in it, but {x}
> has exactly one element: x.
> Dick McCullough
> Ayn Rand do speak od mKR done;
> mKE do enhance od Real Intelligence done;
> knowledge := man do identify od existent done;
> knowledge haspart proposition list;
> http://mKRmKE.org/
Received on Tuesday, 12 August 2008 21:52:36 UTC

This archive was generated by hypermail 2.4.0 : Tuesday, 5 July 2022 08:45:08 UTC