Oops. Thanks for clarifying, I was confusing senses of
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.
I think those questions (reuse) are part of the process of
understanding and developing such mappings.
[MW] Yes, but it turns out that real reuse (identity) is minimal
between 3D and 4D, as you have noted below. What you do have is different
meanings attached to the same terms, and the risk is that you think they
really refer to exactly the same thing.
[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.
So each ontology interprets the notion of set differently,
which affects the notion of a definition.
Forgive me if what I say is obvious, but for posterity, in
the above we have a statement, "set of all cars" which corresponds to
three distinct sets, depending on what framework one employs.
[MW] Indeed. But it is surprising how many people leap to the
conclusion that because the same term is used, the same meaning must follow.
So in an intensional framework, depending on when a query is
executed (a question is asked), Sint= Sext@Tquery.
In a 4D extensional framework, set S4Dex =
U (forall i) Sext@Ti
[MW] Well it is worse than that of course, because a 4D car has
a temporal extension , and a 3D car does not, so there is no common base of
objects that are members of the different sets.
where @Tx is the unique name of each set in the extensional perspective
at time x.
Seemingly, the above suggests that if we want mappings to
work, while each group may choose their own framework, if they intend to
interoperate, we need to know what pieces of information we need to track
(though perhaps not ontologically commit to), to enable such mappings. Thus if
using an intensional framework, with an eye on translating to an extensional
one, we'd need to track when extensions are generated, etc.
[MW] That sounds about right.
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On Mon, Feb 16, 2009 at 2:19 AM, John F. Sowa <sowa@xxxxxxxxxxx> wrote:
Ali, Mitch, and Frank,
AH> If you've given a definition of River, and it is inadequate
> when you encounter something as the Okavango
River, ought it
> not indicate that you only need to update your definition of
> river? Isn't the whole point of defining something trying to
> abstract the generalizable qualities / properties of the
> object/entity under consideration? You can still have a
> monotonic logic, you just need smart revision
It's always possible to legislate a definition and to revise
the definition whenever you encounter an exception. But the
point of Waismann's notion of 'open texture' is that there is
no stopping point. If you arbitrarily choose a stopping point,
you will inevitably exclude unanticipated cases that are just
as reasonable as the ones you do include.
That is a serious problem for any legal system. Any system
of laws has inevitable exceptions and borderline cases that
require a judge and jury to decide.