Re: SUO: "Abstract" and "dimensionality" - Re: SUMO axiomatization
Dear Graham:
See comment below.
best,
Mike Pool
At 06:18 PM 02/01/02 +1100, Horn, Graham wrote:
>
> John et al,
> . I have had considerable problems with trying to tie
> down the nature of pure structure, theory, etc. I tried to apply the term
> "concept" to this, but was ruled out of order on the basis that a concept
had
> to have been conceived by someone, and by implication, at a given point in
> time. The latest draft of ISO/IEC 111793 accordingly defines "Concept" as
>
> · "a unit of thought constituted through abstraction based on
> characteristics common to a set of objects".
>
> . I fear the same attitude may be taken to "Abstract", since
> someone had to perform the (mental) task of "drawing away" the pattern or
> structure from the original observation or thought.
Others have already made helpful responses but I thought I'd point out that
there is a nice discussion of the notion of an "abstract object", and some of
the difficulties in drawing a distinction between these and concrete objects,
in the online Stanford Encyclopedia of Philosophy:
<http://plato.stanford.edu/entries/abstract-objects>http://plato.stanford.e
du/entries/abstract-objects/
The phrase 'abstract object' is often used to denote much more than just the
set of objects that have resulted from the mental process of abstraction, a
distinction Frege tooks pains to elaborate. I wouldn't hesitate to use it to
denote the entire set of (possibly mind-independent) non-concrete entities.
As noted, the term is frustratingly vague but that doesn't mean that it's
illegitimate or inaccurate to use it in the context(s) you describe.
>
> . Personally, I feel there is something in the nature of pure
> structure or pattern that can exist independently of whether it exists in
> physical reality, and also independently of whether any intelligent being
has
> conceived of or observed it.
>
> . By way of explanation, I would suggest that both Newton's
law
> of gravity and Kepler's laws of planetary motion are not precisely accurate,
> and so do not exist in physical reality, but are rather mere
approximations of
> physical reality. Yet, I would suggest that they are both timeless and
> without location or mass ("zerodimensional" in the physical sense), and
> hence existed infinitely before either Newton or Kepler were born, and will
> continue to do so after all records and other traces of them have been
> obliterated.
>
> . The problem is I don't know what term I can use to apply to
> such pure structures or patterns that one can abstract or conceive.
>
> . Neither does "information" cover this. One can observe and
> document the spread of information, whether be it physical, such as through
> the spread of genes, etc., or purely conceptual, such as with nemes, by
means
> of, say, semaphore communication.
>
> . The reason I ask this question is that there are times
when I
> wish to consider these "zerodimensional" patterns / structures.
>
>
> . Incidentally, t have a related problem about the nature of
> "dimensionality". I wish to apply the term beyond the traditional physics
> scope of mass, length and time, into far more abstract areas. This is
because
> it can be extremely useful in information management and information based
> sciences to apply to a far broader range of concepts. Statisticians
> psychologists and pharmacists do this when they are looking to ascertain
> which factors are relevant, and which irrelevant, for particular avenues of
> research and endeavour. The concept of "dimensionality", along with others
> like "mutual exclusivity" or "orthogonality" also come into play here, and
> can greatly facilitate conceptual design and analysis.
>
> . Can anyone suggest a rigorous definition that covers this
> broader scope?
>
>
> Cheers Graham Horn
> National Data Standards Unit
> Australian Institute of Health and Welfare
> ================================================
> Phone: 02.6244.1094
> Fax: 02.6244.1199
> Email:
> <mailto:graham.horn@aihw.gov.au>Graham.Horn@aihw.gov.au
> Knowledgebase: www.aihw.gov.au/knowledgebase/
>
> -----Original Message-----
> From: John F. Sowa [<mailto:sowa@bestweb.net>mailto:sowa@bestweb.net]
> Sent: Wednesday, 2 January 2002 14:28
> To: kif@philebus.tamu.edu
> Cc: standard-upper-ontology@ieee.org
> Subject: SUO: Re: KIF: Re: SUMO axiomatization
>
> Chris,
>
> I would include all mathematical structures under the category Abstract
> in my ontology. In fact, everything under that category is of the
> same nature as Abstract; i.e., it is the category of every kind of
> form that can be defined without contradiction.
>
> The subtype Schema includes all the "static" structures, and the
> subtype Script includes all the "dynamic" structures -- i.e., all
> those that have a time-like succession of forms. As Nicola keeps
> insisting, the category of abstractions is outside of space & time.
> That is true, but you can have mathematical theories that include
> a dimension labeled t, which just happens to be very time-like.
>
> "Christopher A. Welty" wrote:
>
> CW> Thanks for pointing this out, John. It brings up an interesting
> > point for me - (sorry if this was discussed already during my
> > SUO-absence) - do people find this to be "upper level"? Certainly if
> > graphs is considered upper level, then this library demonstrates that
> > there are over a hundred other things at the same "level".
>
> At 1:55 PM -0500 12/22/01, John F. Sowa wrote:
>
> JFS>There is a collection of over a hundred mathematical theories
> > >(fully axiomatized) that were developed to run under IMPS
> > >(Interactive Mathematical Proof System). The theorem-proving
> > >programs that use these axioms run on most versions of LISP and
> > >are available from Mitre as software that has been made freely
> > >available. Following is the home page:
> > >
> > > <http://imps.mcmaster.ca/>http://imps.mcmaster.ca/
> > >
> > >The theories include graphs, groups, fields, automata,
> > >and several versions of geometry, arithmetic, etc.
>
> The category of all abstractions has forms for everything that exists
> and everything that might exist without contradiction in any kind of
> universe. So it is even richer than the category Physical, which only
> includes those kinds of things that are physically possible in our
> universe.
>
> All those theories can be organized in a lattice, according to
> the partial ordering defined by implication; i.e., if every axiom
> of theory A is a theorem of theory B, then A is more general than B.
>
> But not all mathematical theories are in the upper level. Chess,
> for example, is a mathematical theory, but it would be farther down
> the hierarchy.
>
> And I would also include the mathematical forms of virtual reality
> under the category of abstractions. For examples, see the following
> web site, which has a couple of frames from a recent movie. It took
> 90 minutes of time on a supercomputer to do all the computations for
> each frame:
>
>
>
> <http://a330.g.akamai.net/7/330/2540/e15dfb847b2b87/www.e-insite.net/ednma
>
> g/contents/images/185947f6.pdf>http://a330.g.akamai.net/7/330/2540/e15dfb8
> 47b2b87/www.e-insite.net/ednmag/contents/images/185947f6.pdf
>
> All the computer is doing is generating lots of colored polygons.
> Those polygons would be fairly far down the hierarchy, but they're
> still abstract.
>
> John
________________________________
Mike Pool
Information Extraction & Transport, Inc.
(703) 841-3500 x632
(703) 841-3501 Fax