Dear Avril, (01)
It seems you have an example that does not need non-well founded sets. Indeed
most cases do not need non-well founded sets. All of which is fine until you
come across a case that does need them. (02)
Regards (03)
Matthew West
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> -----Original Message-----
> From: Avril Styrman [mailto:Avril.Styrman@xxxxxxxxxxx]
> Sent: 18 December 2010 11:28
> To: [ontolog-forum] ; Matthew West
> Cc: mail@xxxxxxxxxxxxxxxxxx; 'Ontology Summit 2011 discussion'; '[ontolog-
> forum] '
> Subject: Re: [ontolog-forum] Non-Well Founded Sets
>
> Dear all,
>
> I'm not aware of anything that requires to be modeled by non-well
> founded sets.
>
>
> In some computer applications, self-reference appears to work without
> difficulties. We can have e.g. a picture of Earth taken from space. We
> zoom into some continent, country, city, house, through the window of
> the house, and in the room we have a picture of Earth taken from
> space. We zoom into that image, and we get to the start of the process
> again: we have a picture of
> Earth taken from space. We can zoom boundlessly many times. Now, is
> this a case of self-reference? —no, it was only a computer system that
> connected together a variety of photos, a system that only appeared to
> implement self-reference, but it did not.
>
> http://www.ted.com/talks/blaise_aguera_y_arcas_demos_photosynth.html
>
> Non-well founded sets can be used to model this. Imagine that there
> are three zoom-levels: A) a picture of Earth taken from space; B) a
> picture of a country; C) a picture of a room where is the picture A
> among other things. Now, we have the sets A={B}, B={C}, and C={A},
> that can be used to model the situation. We can zoom from A to B, from
> B to C, and from C back to A. But why should we use non-well founded
> sets to model this? It would be simpler just to say that there is a
> link from C to A; when you klick C, the link takes you to A. This is
> what is done in practice; there is no need for a non-well founded
> foundation for a thing that does not require it.
>
>
> -Avril
>
> Lainaus "Matthew West" <dr.matthew.west@xxxxxxxxx>:
>
> > 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.
> >
> > Regards
> >
> > Matthew West
> > Information Junction
> > Tel: +44 560 302 3685
> > Mobile: +44 750 3385279
> > matthew.west@xxxxxxxxxxxxxxxxxxxxxxxxx
> > http://www.informationjunction.co.uk/
> > http://www.matthew-west.org.uk/
> >
> > This email originates from Information Junction Ltd. Registered in England
> > and Wales No. 6632177.
> > Registered office: 2 Brookside, Meadow Way, Letchworth Garden City,
> > Hertfordshire, SG6 3JE.
> >
> >
> >
> >> -----Original Message-----
> >> From: ontology-summit-bounces@xxxxxxxxxxxxxxxx [mailto: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,
> >> 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)
> >>
> >> 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 -
> > 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.
> >>
> >> 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.
> >>
> >> Chris
> >>
> >> > -----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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> --
> Always forward towards the supreme maxim of scientific philosophizing (06)
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