Not every logician agrees with Chris (which I am sure is no surprise to
anyone - including Chris). (01)
For example,
http://www.amazon.co.uk/gp/product/1575860082/ref=wms_ohs_product
Vicious Circles: On the Mathematics of Non-Wellfounded Phenomena - Jon
Barwise (Author), Lawrence Moss (Author) (02)
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. (03)
Jon Barwise (http://en.wikipedia.org/wiki/Jon_Barwise ) argues that the
circularity found in non-well-foundedness is common in the real world - i.e.
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. (04)
Another interesting recent (technical) book on a similar the same topic is
http://www.amazon.co.uk/gp/product/0199276439/ref=wms_ohs_product - Absolute
Generality - Agustín Rayo (Editor), Gabriel Uzquiano (Editor).
I believe the introduction can be found somewhere on the net. (05)
Chris (06)
> -----Original Message-----
> From: ontology-summit-bounces@xxxxxxxxxxxxxxxx [mailto:ontology-
> 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 needs
of
> the document; it entails, among other things, the entire massively
infinite
> hierarchy of transfinite numbers. (How massive? So massive that there
is
> 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
contains,
> well, everything. The existence of such a class (understood as a non-wf
set)
> is flatly inconsistent with non-wf ZF spinoffs like AFA.
>
> Bottom line (as John Sowa likes to say): The underlying class theory of
the
> document needs to be thrown out and rethought completely.
>
> Chris Menzel
>
>
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