2) I'm not sure there is such a difference between the
intensional and extensional approaches. Here, I would point to the ontology
design algorithm I developed in my thesis. It tries (i think pretty
successfully) to bridge the gap between the two approaches, starting first with
concrete examples, and "learning" through falsification hypotheses to
refine an intensional definition that captures the semantics contained in sets
of accepted and rejected concrete (empirical / extensional / examples) models.
[MW] Well the way this normally plays out is that those who take
an intensional approach do not necessarily think they have something different
when the membership of a set changes. So If I ask “How many cars are
there”. They will give a certain answer, and if I ask the same question a
year later, they will give a different number, and will be quite happy that the
membership of the set has changed. An extensionalist, on the other hand, will
insist that these are actually two different sets: Cars-at-time-1 and
Cars-at-time-2, and a 4D extensionalist will say that the set of all cars, is
all the cars that have existed and will exist.
From where I stand - extensions correspond to fragments of
models (Tarski sense).
[MW] I think you are talking about the ones you know about,
rather than the ones that exist. Extensionalism does not require that you know
all the members, only that the membership is actually unchanging (including
the ones you do not know).
Any set of axioms A has associated with it a set of models MA.
The beauty / difficulty of ontologies is finding the right match between
the two. Limiting ourselves by defining what exists only to things we have
concretely encountered seems too restrictive;
we would like to conjecture as to what would count as well. Yet as many have
noticed, if the set of acceptable models is too expansive / restrictive, the
quality of the resultant ontology suffers.
To me, this makes a strong case for developing a set of
referent ontologies sooner than later, (ideally unified under some umbrella).
If our goal is to move towards ontology interoperability,
instead of focusing on whether Extensional or Intensional approaches are
[MW] The question is not one of superiority, but of recognising
the differences, rather than trying to pretend that they are the same “really”.
Once you recognise the differences, you can start to relate them to each other,
and that I think is a worthwhile exercise.
or whether one particular ontic category hierarchy is
appropriate for all, I think efforts would be more fruitful in explicating /
generating mappings between what various peoples find useful. I.E. take
the IDEAS hierarchy and compare it to DOLCE or SUMO -- what's being reused?
[MW] Wrong question. More important is how do you map from one
to the other.
what are people disagreeing on?
[MW] That is nearly always the commitments of the different
what are the implications of the different choices?
[MW] That is a good question.
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But perhaps I digress here :P.
On Sun, Feb 15, 2009 at 2:20 PM, John F. Sowa <sowa@xxxxxxxxxxx> wrote:
Mike and Mitch,
I would like to comment on the following point:
MB>> According to that definition the Okavango is not a river.
MH> The Okavango surely is a strange kind of river.
> Do you really expect to hold natural language to the same
> strictness standards as formal ones?
This question has nothing to do with the differences between
natural languages and formal languages. It is the result
of trying to map a continuously variable world to a discrete
set of labels (i.e., words, terms, symbols, concepts, signs).
As a continuous fluid (at least to a degree far below human
perception), there is a continuous range of ways that water
can flow across a surface. For various purposes, people label
those ways of flowing that happen to be significant for their
interests. The way they group them and label the groupings
depends on what they consider important in their environment.
The kind of language, natural or artificial, is irrelevant.
This is a commonly discussed issue in philosophy:
"Since the synthesis of empirical concepts is not arbitrary
but based on experience, and as such can never be complete
(for in experience ever new characteristics of the concept
can be discovered), empirical concepts cannot be defined.
"Thus only arbitrarily made concepts can be defined
Such definitions... could also be called declarations, since in
them one declares one's thoughts or renders account of what one
understands by a word. This is the case with mathematicians."
Wittgenstein's *family resemblances* :
Empirical concepts cannot be defined by a fixed set of necessary
and sufficient conditions. Instead, they can only be taught by
giving a series of examples and saying "These things and
that resembles them are instances of the concept."
Waismann's *open texture* :
For any proposed definition of empirical concepts, new instances
will arise that "obviously" belong to the category but
excluded by the definition.
As Kant observed, precision depends on the kind of concept, not
on the kind the language used to define the concept.
As Waismann observed, if you state a precise definition for an
empirical concept (such as 'river'), you will simply exclude
many reasonable examples, such as the Okavango River.
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