Ali and Mike, (01)
The point I was trying to make (which Kant, Wittgenstein, Waismann,
and many others have state over and over again in different ways)
is about the origin of vagueness and its relationship to language: (02)
1. Any classification that captures aspects of nature in a
discrete set of predicates is nearly always an approximation
intended for a particular purpose. (03)
2. It is irrelevant whether those predicates are labeled by
words in a natural language or by artificial symbols.
The source of vagueness is in the subject matter, not
in the choice of language. (04)
3. The only predicates that can be absolutely precise are ones
that are stipulated or legislated to have exact boundaries.
The typical examples are geometrical and mathematical
concepts. The definition of a cube, for example, is just
as precise whether it is stated in English or predicate
calculus. However, there are no precise cubes in nature. (05)
AH> I appreciate Waismann's point. I don't think what I said is
> in opposition to it, as far as i can tell, it embraces it.
> Though I like to get at his insight by thinking that once
> specified, any system begins to decay. Suggesting then simply
> that maintenance / upkeep / revision is a necessary part of
> any specification framework. (06)
But you can have specifications of mathematical systems and
structures that do not need maintenance. The definition of
a circle or a cube never changes. The definitions of anything
in nature (which includes the human body) are never complete. (07)
MB> This means that when setting out to define anything formally,
> one has to be aware of when one is modelling some discrete thing
> such as a pump or an elephant, and when one is modelling human
> perceptions of things. (08)
The question of human perception is not the issue. It's the
nature of the thing itself. (09)
Elephants are naturally occurring entities, whose detailed
specifications are just as difficult to formulate precisely
as a complete specification of the human body. Fortunately,
we don't need a very precise specification to recognize an
elephant simply because there is nothing on earth that looks
remotely like an elephant except another elephant. (010)
But it is impossible to for anybody to state necessary and
sufficient conditions that are sufficiently precise for
reconstructing an elephant. Even if somebody sequenced the
complete genome of a particular elephant, we still could not
say how much variation in that genome would be permitted
before it determined something that was not an elephant. (011)
As for pumps, a person who invented a new model P782 pump
could write a precise specification for that particular
type of pump. But the number of types of pumps that have
been invented over the many centuries is enormous, and it is
very difficult to specify necessary and sufficient conditions
for recognizing every type of pump that anyone has built or
will ever build. And for that matter, there are naturally
occurring pumps (such as hearts), which raise all the issues
of any kind of natural object. (012)
MB> In practical terms, if you are building an ontology for
> some genuine business purpose then I imagine the appropriate
> legally-grounded definitions will suggest themselves. (013)
Yes, but legal definitions that involve natural systems get
bogged down in exactly the same issues of vagueness. You
might find a law that outlaws elephants as pets. But suppose
somebody genetically engineered something that looked like
a tiny elephant, but had a completely different genome.
Would the law apply to it? (014)
Any decent lawyer would instantly recognize a lawsuit that
could be argued either way -- depending on who had more money. (015)
John (016)
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