Sean, Pat, et al., (01)
There are some deadlines I have to meet, and I can't discuss
the recent flurry of notes. (02)
But I strongly agree with the approach that Sean mentioned in
his last two notes. I won't get into the details, since they
can be analyzed endlessly. (03)
SB> Actually, circles, lines and points are all the same primitive
> - half-spaces of the plane: lines have zero curvature, points
> zero radius, and circles have finite radius and finite curvature.
> An ellipse is a circle after linear transformation.
>
> A triangle is the intersection of three linear halfspaces. (04)
That's an excellent example of the fact that there can be many
different choices of "primitives" for axiomatizing the same
"subject". As a related example, I often cite Tarski's
axiomatization of solid geometry with spheres as the only
primitive. That axiomatization, by the way, is physically
more realistic than assuming infinitely sharp lines and edges. (05)
These examples show that the choice of primitives is arbitrary.
They also illustrate the principle that the choice of primitives
has almost *nothing* to do with interoperability. You can work
with your primitives while Duane works with his. But when you
interchange data, your systems can interoperate, even though
your underlying primitives are totally different. (06)
From the thread "Context in a sentence", (07)
SB> You [Pat C] seem to be in the position of a man in a field
> of duck-rabbits and saying they are all ducks, where I want
> to say that some are ducks, some are rabbits. (08)
I agree, but I'd use more than two options. (09)
SB> Firstly, what I am trying to say is there are two fundamentally
> different views of ontology, which I usually characterise as the
> language-as-picturing the world and language-as-talking about
> the world.... (010)
That's a good discussion of some important issues. There's a lot
to say about the details, but there are two points that I believe
are very important: (011)
1. For a "newbie", who is just getting started in ontology, it
is helpful to have some examples to work from. A set of
primitives and guidelines may be useful. But concrete,
implemented examples are even more important. (012)
2. A fixed, frozen set of primitives edicted for everybody
would be a far greater *obstacle* than a foundation for
ontology, knowledge representation, and system design. (013)
SB> Experience suggests that one cannot get down to semantics
> until one has deconstructed the semiotics. (014)
I agree, but there are many volumes that could be and have been
written on that subject. And more work needs to be done to
systematize the ideas into a methodology. But I believe that
kind of work is far more important in the long run than selecting
2000+ so-called primitives. (015)
John Sowa (016)
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