Re: SUO: 4-D representations in relativity and cubism
Peirre,
I'll start my reply by clarifying the point I made at the end
of my note:
JS>> Bottom line: As I have said many times before, the ontology must
>> be based on an open-ended framework that can accommodate any and
>> all representations that might be invented. That is the fundamental
>> rationale for organizing the ontology as a lattice of all possible
>> theories with systematic ways for navigating from one to another.
The lattice of all possible theories is a useful mathematical way
of making Whitehead's slogan explicit: "We must be systematic,
but we must keep our systems open." Since the lattice is infinite,
it can never be fully represented. In that sense, it is like the
integers: no computer can ever store all of them, but the fact that
they are unbounded means that we will never run out of integers
whenever we need another one.
The completeness of the lattice is important: given any two theories
A and B, there is always a common generalization that includes only
those propositions that are true in both. If A and B are contradictory,
then they have no common specialization other than the absurd theory
at the bottom of the lattice. But if they are not contradictory, there
is always a common specialization that includes everything provable in
either one.
> I don't really understand what you meant with this posting, esp. your
> bottom line. Sorry, I won't try to discuss the subject matter of the
> book, I'm a little leery about that sort of analogies between
> theoretical physics and art....
So am I -- especially since most of them have been written by people
who do not understand physics. But that book was written by a historian
of science who had a solid background in physics. What he was doing is
pointing out the intellectual sources that inspired both Einstein and
Picasso. This is not after-dinner speculation over brandy, but a
solid study of the publications in the late 19th and early 20th
centuries that inspired those two individuals and their colleagues.
> Did you mean to make a case that a theory based on and serving
> "commensensical representations" (or call it whatever) should include a
> fragment treating of special relativity?
I have never been happy with the term "common sense" as it has been
used in AI because that term is a constantly moving target. Every
culture, every time period, and every subculture within every culture
has a very different notion of what is common sense. I think that
it is wrong or at least misleading for Cyc or SUO or any other group
to aim at representing "common sense", since that is incurably vague.
And as a matter of fact, Cyc (or SUO) isn't really restricted to
common sense, since they include quite a large amount of work on
specialized topics that even most college-educated people are not
familiar with. So I would maintain that it is much more appropriate
for any system of ontology, whether Cyc, SUMO, or whatever to aim for
an open-ended structure that can accommodate all possible theories,
whatever their source.
> Maybe the question should be: did you mean that a formalization adequate
> for the purpose of building a theory of reality based on and serving
> "commensensical representations" should also include ressources fitting
> the purpose of contemporary fundamental physics?
Not quite. What I intended was that any satifactory formalization
for ontology should be able to accommodate any theory whatever.
> The only suggestive reason I found to date for considering a 4-d
> framework seem to be based on Einstein's conception of spacetime (I
> should mention also some unimpressive antirationalist new-agy
> orientalish lucubration.) I still can't really grasp what's so curcial
> about the alternative. In particular, I fail to see clearly how to
> distribute the merit between formalisms. But you seem to mean that
> appeal to Einstein stuffs provides additional evidence. My understanding
> is that appeal to relativity theory is dispensable for most purposes
> having to do with "common sense". I guess I just fail to see the
> evidence.
There has been a prolonged discussion on this list by many people who
advocate a 4-D representation for much more than just representing
Einstein's relativity. Pat Hayes, Chris Partridge, Matthew West, etc.,
have been arguing very strongly for that viewpoint, completely
independentl of any applicatoin to Einstein's relativity.
My point is even simpler than their point: I claim that any framework
that is adequate for ontology should be completely agnostic about the
merits of one representation or another -- i.e., it should make room
for *all* of them. And that is what the lattice of all theories does.
> To be fair, I cherish the idea of leaving some room for the upcoming
> novelties. I'm just afraid of utterly painful contorsion for the sake of
> doxtrinal completude or mere manierism.
On the contrary, the lattice of all possible theories is the simplest
structure that can accommodate anything and everything. It doesn't
require any contortion at all. It just allows every possible theory
to be included. All of the current contents of Cyc could fit into
such a framework very nicely -- as well as all the current contents
of SUMO or any other ontology. The lattice simply shows how any two
theories are related to one another.
> I think you'll have to provide another of those pointers to articles of
> yours (I apologize for not keeping track of this.) I'm confused by what
> you actually claim should be done with the lattice of all possible
> theories. But anyway, I'm more puzzled by trying to imaging what would
> be an non-open-ended framework. If you have an ontology at time t and
> want to account for novelties overflowing your intitial setting, can't
> you just extend your ontology, your language, your theory? Can you do
> otherwise anyway?
Essentially, the infinite lattice is a proposal for how theories
should be indexed and related to one another. It doesn't require all
possible theories to be explicitly represented anymore than Peano's
axioms require anyone to store all the integers.
The lattice is nothing more nor less than a systematic guideline
for how a collection of microtheories can be extended to accommodate
novel contributions,
The most detailed discussions are at the end of Ch. 2 and Ch. 6 of
my KR book. I'm also writing another paper on the topic that I'll post
to the WWW shortly.
John Sowa