RE: SUO: RE: Conformance
Matthew,
That is a point I have been trying to explain by means
of the following diagram:
http://www.jfsowa.com/figs/mthworld.gif
>2. I am beginning to think that how terms in FOL
>relate to the domain (life the universe and
>everything) is about the model theory, from what I
>have been able to grasp of Chris M's recommended
>reading on model theory recently. However, it is
>no clearer to me how the link is made.
Following are two paragraphs from Section 7 of my article
"Signs, Processes, and Language Games" that describe the
diagram mentioned above. If you want to read them in context,
see the full paper:
http://www.jfsowa.com/pubs/signproc.htm
Or see Ch. 6 of my KR book, which goes into more detail.
John Sowa
______________________________________________________________
Theories, Models, and the World
The problems of knowledge soup result from the difficulty
of matching abstract theories to the physical world. The
techniques of fuzziness, probability, defaults, revisions,
and relevance are different ways of measuring, evaluating,
or accommodating the inevitable mismatch. Each technique is
a metalevel approach to the task of finding or constructing
a theory and determining how well it approximates reality.
To bridge the gap between theories and the world, Figure 5
shows models as Janus-like structures, with an engineering
side facing the world and an abstract side facing the theories.
On the left is a picture of the physical world, which contains
more detail and complexity than any humanly conceivable model
or theory can represent. In the middle is a mathematical model
that represents a domain of individuals D and a set of
relations R over D. If the world had a unique decomposition
into discrete objects and relations, the world itself would be
a universal model, of which all accurate models would be
subsets. But as the examples in this book have shown, the
selection of a domain and its decomposition into objects
depends on the intentions of some agent and the limitations
of the agent's measuring instruments. Even the best models are
approximations to a limited aspect of the world for a specific
purpose. Engineers express that point in a pithy slogan:
All models are wrong, but some are useful.