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Re: [ontolog-forum] [ontology-summit] FW: [ontolog-invitation] Invitatio

To: "'[ontolog-forum] '" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "Matthew West" <dr.matthew.west@xxxxxxxxx>
Date: Fri, 17 Dec 2010 15:03:17 -0000
Message-id: <4d0b7b9b.e4e8d80a.31e0.1780@xxxxxxxxxxxxx>
Dear Chris,    (01)

Well let's start by confusing the situation with a few facts.    (02)

> Barry's criticisms of the use of a non-well-founded set theory like
> AFA are on the money.     (03)

MW: ISO 15926 does say that a class can be a member of itself for reasons
Chris P has alluded to, but it is not committed to a particular form of
non-well foundedness. Aczel is mentioned in an informative note, and there
is an informative annex that gives a lay explanation of some different sorts
of structures sets might have, including well-founded and non-well founded
sets.    (04)

> He notes that it is a greatly overpowered for the needs
> of the document; it entails, among other things, the entire massively
> hierarchy of  transfinite numbers.  (How massive?  So massive that there
is no
> transfinite number big enough to number them.)      (05)

MW: I don't know why this should be a problem, since there is no commitment
to record them all.    (06)

> Moreover, ironically, AFA and
> its like are in a sense underpowered as well for the given task. Notably,
as I
> understand the document, THING is itself a class that contains, well,
> everything.      (07)

MW: Yes. Every upper ontology has such an class, so ISO15926 is not the only
one with this problem.    (08)

> The existence of such a class (understood as a non-wf set) is
> flatly inconsistent with non-wf ZF spinoffs like AFA.    (09)

MW: I had missed that. Could you give me a section reference (I have Aczel's
> Bottom line (as John Sowa likes to say): The underlying class theory of
> document needs to be thrown out and rethought completely.    (010)

MW: What would you suggest? Not much point kicking up a storm unless you
have a better alternative.    (011)

Regards    (012)

Matthew West                            
Information  Junction
Tel: +44 560 302 3685
Mobile: +44 750 3385279
http://www.matthew-west.org.uk/    (013)

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