Steve, Frank, Duane, and Mike, (01)
Some comments. (02)
JFS>> The source of vagueness is in the subject matter, not
>> in the choice of language. (03)
SN> That formulation confuses things, because it blurs the
> crucial distinction between the kind of existence that
> a thing has, and the kind of existence that a subject
> of conversation has. (04)
I agree that your distinction is important, but I was addressing
a different question: Given a particular kind of existence (say
mathematical systems or natural phenomena), how does the nature
of the subject matter affect the way any language (natural or
artificial) can be used to describe it? (05)
If the subject is precise, such as mathematics, statements
in natural languages can be just as precise as statements
in logic. (06)
But if the subject is continuously variable, such as most
natural phenomena, predicates with sharp boundary conditions
cannot be precisely mapped to the phenomena. It is irrelevant
whether those predicates are expressed by NL words or by
symbols in some version of logic. (07)
SN> *All* subjects of conversation are vague, because every
> human consciousness is very much a world unto itself, whose
> isolation is relieved only by the signs it interprets and emits. (08)
The first line is false, and the condition following "because"
is so complex that it's more distracting than helpful. (09)
Two mathematicians can talk on the telephone about mathematics
and understand each other just as precisely as if they were
filling a blackboard full of symbols. They would prefer to have
a blackboard because it makes it easier for them to keep a large
pattern of relationships in mind. But even without a blackboard
their NL sentences are precise. (010)
FK> Most of these issues are not issues in real life, as people
> introduce conventions and artificial measures. (011)
Every issue I discussed in the previous notes in this thread
is *critical* to real life. In the legal system, for example,
the obvious cases are settled out of court, because the guilty
party knows very well that there is no chance of acquittal. (012)
So the overwhelming number of cases that go to trial by judge
and jury are the borderline cases where those problems arise. (013)
It is true that people do agree on large numbers of artificial
standards, conventions, and measures. But the research on
knowledge representation (for example, the Cyc system, which
has defined over 600,000 concept types) shows that the number
of exceptions grows faster than the number of rules. (014)
DN> I would argue that the context in which the question posed...
> would be crucial. (015)
Indeed. That point is not only crucial, it is key to addressing
the problem of dealing with the overwhelming number of exceptions. (016)
DN> This list could go on and on to infinity, thus supporting
> John's argument in another thread that capturing all possible
> detail in a formally documented ontology is probably an
> impossible task. (017)
Yes. In developing Cyc, Lenat & Co. learned an important lesson:
low-level "microtheories" devoted to specific kinds of problems in
narrow contexts are more important than the upper-level categories. (018)
The upper level is useful, but not for detailed reasoning. It is
more important for providing guidelines about the kinds of things
to represent and how to represent them. For detailed reasoning,
the low-level, context-dependent microtheories are "where the
action is". (019)
MB> I think the problem is not one of having too much to capture.
> Rather, it is a matter of trying not to capture too much. I think
> it takes imagination and constraint to know when to stop, and
> the Protege example given at the root of this thread was a good
> example of what happens when you don't. The scenarios you
> describe relate to realistic reasons to make the appropriate
> ontological commitments for specific business purposes. (020)
Yes. That is what the Cyc project showed. They discovered that
most of the detail should be removed from the upper levels and
put in the domain or context dependent lower levels. (021)
John (022)
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