> Dear Chris M and Chris P,
> Can I suggest we take this to the Ontolog Forum, I don't think it is really
> of interest for this year's ontology summit, and I will respond there.
> Matthew West
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>> -----Original Message-----
>> From: ontology-summit-bounces@xxxxxxxxxxxxxxxx
] On Behalf Of Chris Partridge
>> Sent: 16 December 2010 22:37
>> To: 'Ontology Summit 2011 discussion'
>> Subject: Re: [ontology-summit] FW: [ontolog-invitation] Invitation to a
>> brainstorming call for the 2011 Ontology Summit
>> Not every logician agrees with Chris (which I am sure is no surprise to
>> anyone - including Chris).
>> For example,
>> Vicious Circles: On the Mathematics of Non-Wellfounded Phenomena - Jon
>> Barwise (Author), Lawrence Moss (Author)
>> Product Description
>> Circular analyses of philosophical, linguistic, or computational phenomena
>> have been attacked on the assumption that they conflict with mathematical
>> rigour. Barwise and Moss have undertaken to prove this assumption false.
>> This volume is concerned with extending the modelling capabilities of set
>> theory to provide a uniform treatment of circular phenomena.
>> Jon Barwise (http://en.wikipedia.org/wiki/Jon_Barwise
) argues that the
>> circularity found in non-well-foundedness is common in the real world -
>> it is a common requirement. As such it would make sense to include it on
>> your foundation.
>> While personally not finding all his examples persuasive, I think the
>> general point that it is a requirement is well made.
>> Another interesting recent (technical) book on a similar the same topic is
>> Generality - Agustín Rayo (Editor), Gabriel Uzquiano (Editor).
>> I believe the introduction can be found somewhere on the net.
>> > -----Original Message-----
>> > From: ontology-summit-bounces@xxxxxxxxxxxxxxxx
>> > summit-bounces@xxxxxxxxxxxxxxxx
] On Behalf Of Christopher Menzel
>> > Sent: 16 December 2010 20:53
>> > To: Ontology Summit 2011 discussion
>> > Subject: Re: [ontology-summit] FW: [ontolog-invitation] Invitation to a
>> > brainstorming call for the 2011 Ontology Summit
>> > On Dec 16, 2010, at 2:24 PM, Matthew West wrote:
>> > >> -1 for 15926, with arguments:
>> > >> http://ontology.buffalo.edu/bfo/west.pdf
>> > >
>> > > Which are answered in:
>> > > http://www.matthew-
>> > west.org.uk/documents/Reponse%20to%20Barry%20Smith%20Comments%2
>> > 0on%20ISO%2015926.htm
>> > Barry's criticisms of the use of a non-well-founded set theory like
>> Aczel's AFA
>> > are on the money. He notes that it is a greatly overpowered for the
>> > the document; it entails, among other things, the entire massively
>> > hierarchy of transfinite numbers. (How massive? So massive that there
>> > no transfinite number big enough to number them.) 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
>> > well, everything. The existence of such a class (understood as a non-wf
>> > is flatly inconsistent with non-wf ZF spinoffs like AFA.
>> > Bottom line (as John Sowa likes to say): The underlying class theory of
>> > document needs to be thrown out and rethought completely.
>> > Chris Menzel
>> > ________________________________________________________________
>> > _
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