Re: lattice of ontology
I moved this discussion to SUO list.
AA> As a matter of fact, there are several levels
> of the conceptual representations: a framework, or
> generic theory modeling the properties and relationships
> of all things of a given domain (as Maxwell equations);
> a specific theory or theoretical model representing
> some features of some things of a given domain (like
> the accounts of specific physical effects); a diagram
> or graph sketching the composition and structure of
> a thing of a given domain; and a schema just listing
> the specific properties of a thing in a given domain.
The number of levels and ways of conceiving things are
open-ended. And the lattice of theories is just one tiny
piece of a very, very big puzzle. (And when I say that
an infinite lattice is a tiny piece, you must realize
that the whole puzzle must be very big indeed.)
In a previous note, I compared it to the integers, but that
led to too many confusing associations. Therefore, I'll
give another analogy: the coordinates of latitude and
longitude on the earth.
1. Some places, such as the clock in Grand Central Terminal,
are very busy with lots of people coming and going all
the time.
2. Other places, such as the North Pole and South Pole are
important reference points, but almost nobody ever goes
there.
3. And the great majority of the places are in open ocean,
where people occasionally pass through, but nobody ever
builds a home there.
4. Like the geographical coordinates, the lattice makes no
value judgments. It doesn't say that one place is better
or worse than any other. The only thing it does is to show
how one place is related to its neighbors and to other
places that are far away.
5. The four theory revision operators are like directions:
move N, move S, move E, move W. And the analogy operator
is like an airplane flight that suddenly picks you up in
one place and deposits you in another place far, far away.
But like an airplane schedule, the lattice doesn't tell you
why or whether you should go one place rather than another.
6. Furthermore, having a system of coordinates does not magically
give you a way of determining the coordinates of any given
point. After the modern system of latitude and longitude was
invented, it took many years before even a rough approximation
to latitude could be computed, and it took centuries before
the modern GPS system became available. Yet some people such
as the Polynesian islanders were able to navigate thousands
of miles of open ocean without any such system and without
any instruments.
7. But like any analogy, you can't push it too far. Especially
because the earth is finite, but the lattice is infinite.
Please remember point #6: people have discovered many brilliant
theories without any coordinate system whatever, but having a GPS-
like method for specifying the position of theories could be useful,
but it's not magic.
For further information, please reread the tutorial on theories,
especially Section 1, which explains the difference between a
theory, a model, and the world:
http://www.jfsowa.com/logic/theories.htm
Also remember that the lattice is only a small piece of a much
bigger puzzle. A GPS device might tell you that you're close
to Mt. Everest, but it won't help you climb it.
John Sowa