John and Chris, (01)
> God rarely testifies on the witness stand. (02)
I think the insurance companies are still looking for him. (03)
Seriously though, I've been trying to get to the bottom of this business
about 3D/4D incompatibility assertions, and the apparently related issue
of extensional versus intensional definitions and why they go together,
and I'm picking up clues in this exchange but would like to know if I've
understood it right. Is it about the ability to define a state of being
intensionally, versus having to go back in time to an event in order to
define that state of being extensionally? (04)
I've always assumed that a definition is (by definition!) intensional,
whether that definition is a written one or a set of logical statements
about what it is to be a member of that class. If an extensional
definition is of the form "all the States in the USA", then surely you
are describing an extent, not defining a thing (the definition would be
framed in terms of what it /means/ to be a State). In any case I wonder
if that sort of extensional description can be framed for every kind of
Thing? Similarly if a role type has an extensional definition like "all
the people who are customers of X", then the state of "being a
customer" would require an intensional definition - does that put the
concept of "being a customer" outside the scope of what can be defined
in an extensional ontology? Unless, perhaps, you go back in time and
observe them /becoming/ customers? Is that the issue here? (05)
I'm trying to work out if this is where the perceived need for a 4D
ontology comes in. I've yet to see a 3D ontology. The world as we know
it has things which have an extent in space and time, and have mass,
charge, temperature and so on - the basic dimensions of the "good
enough" Newtonian physics we all learnt at school. So that's what I'd
expect to model in an ontology. If a given application is only
interested in things at the current point in time, then the implied
ontology of that individual application will clearly be a 3 dimensional
(or less) ontology. But as soon as we start to define an ontology that
can work across a whole business unit or supply chain, one would want to
start asserting facts in different dimensions, especially time, in order
to disambiguate terms. For example, a bond has an interest rate, and as
far as one application is concerned, that interest rate is "obviously"
(i.e. contextually) the interest rate right now, while to another
application it's just as "obviously" the interest rate defined when the
bond was issued. For a bond with a variable interest rate, one of those
is a number and the other is a formula for determining that number.
Creating an ontology that goes beyond one part of the business workflow
obliges us to take account of the time dimension in order to
disambiguate terms that were meaningful only in the implied 3D
ontologies of individual systems. (06)
If you set out to define a comprehensive model of "how things are" then
I would argue that you need some kind of lattice of basic types of thing
that partition the model - continuant v occurrent, independent v
relative and so on - and I accept that these need not be the same
partitions or that any one partitioning is "right", though the above two
are pretty fundamental even if they are not explicitly stated in a
particular ontology. (07)
There is a question of terminology as to whether these top level
distinction are framed as "things" (Continuant Thing and so on) or
"partititions" in the UML sense (Continuant v Occurrent maps neatly to
the UML Structural versus Behavioural partitions), or as something else,
representing a kind of ontological commitment or a theory, and I think
people sometimes talk at cross purposes about what sits at this top
level of most ontologies. In defining an ontology with a Continuant
partition, one is making an ontological commitment to the existence of
classes of "Thing" which exist at some period in time and therefore
necessarily have a beginning and an end - and therefore of course a
commitment to the 4th dimension. Like people, roles, states (in the
USA), states (in state diagrams) etc. There are things outside that
partition, that do not continue to be, but simply happen - events, state
transitions and so on. Then you have one, mutually exclusive and
completely exhaustive pair of partitions. Continuant things continue to
be, even if they change over time, as surely they must. (08)
All of which is both 4 dimensional and intensional. By using a lattice
of theories, one can define the partitions of a model in terms of the
ontological commitments made towards the "God's eye view" as novelists
call it, of what are the intensional definitions we are going to give to
things. This would cover as many things as are of interest to the
application or business, in as many dimensions are are relevant. I don't
see any reason to deny that to the ontology modeller. (09)
Then for example the concept of ownership is a concept which can exist
within such an ontology, and can be given an intensional meaning -
written and/or with properties, e.g. ownership must always have an
autonomous, self-directing being that does the owning, and a thing which
is owned. You might also model the temporal event of coming into
possession of something, but the state can be defined intensionally
without that, surely. (010)
In other words I don't see why there is any need, practically or
conceptually, to go back in time to some event which brought about the
state so described, in order to be able to define the state as a state.
Sometimes it is of practical use and relevance to the target
application(s) that you connect events in the past with states in the
present or at some other point in time, for example to model the
relationship between a legal event or ceremony and a legal state.
However, I don't see any reason why this should be a necessary
pre-condition of being able to model the thing at all, if indeed that is
what is being suggested. Just as an event has a cause whether we know it
or not, so a continuant thing has a beginning whether we know it or not. (011)
Chris: Does the need for a (specifically extensional) 4D approach follow
from the extensional approach, and if so how does it differ from the 4+D
approach implicit in most intensional ontologies? For instance the Units
of Measure work is proceeding just fine in creating intensional
definitions in all the dimensions in which we can measure things. (012)
On a more practical note, is there some fundamental dichotomy of
theories that would sit /above/ the lattice of theories of a
multi-dimensional intensional ontology, to distinguish if from a
BORO-style extensional ontology? Can this theoretical dichotomy be
dissected in such a way that two ontologies, one in each of these
styles, can be related to one another, or are terms in extensional
ontologies not reusable? I'm thinking in terms of what sort of meta-data
can be defined about an ontology or its terms or partitions, that can
help people in different domains identify and reuse ontology material
that has definitions for terms that are of interest to them. If we can
formalise the relationship between these approaches, perhaps we can
formalise the required meta-terms? (013)
Mike (014)
John F. Sowa wrote:
> Chris,
>
> The term 'Cambridge property' was introduced by Peter Geach in the
> derisive phrase "mere Cambridge property" without giving a definition.
> Barry Miller (in the Stanford page you cited) gave a definition:
>
> A Cambridge property is the referent either of a relational
> predicate or of a purely formal predicate.
>
> That's fairly clear, but it's at the level of Quine's dictum:
> "To be is to be the value of a quantified variable."
>
> I use the term 'role type' for a very widely used type of word
> or concept that everybody uses daily:
>
> Author, Player, Spouse, Buyer, Seller, Pet, Employee, Manager,
> Contractor, Pilot, Driver, Mathematician, Brother, Sister,
> Student, Weed, Nuisance, Tool, Prize, Reward, Favor, Example...
>
> CP> However, I can easily give an extensional definition of them
> > - if the role of the definition is to capture the extension...
>
> The primary role of a definition is to tell people how to use
> the term in a way other people will understand. None of those
> words can be defined by observable properties of the individual.
> The same plant, for example, could be a weed or a delicacy,
> depending on somebody's intention.
>
> Brother and Sister are two of the easiest to define, but note
> that there may be only one person in the world who actually
> observed the relevant conditions, and you have to take her word
> for it. The 4-D proponents usually reply "Yes, but somewhere
> in that vast infinity of space and time, the relevant events
> really do exist."
>
> CP> "For example, if I buy a car, the car does not change in any
> > observable way." One can, of course, observe the process of
> > buying.
>
> How do you observe it? By watching someone go to a car dealer
> and negotiate? By watching the buyer go to an auction and
> raise a hand at the appropriate moment? By seeing somebody
> typing away at a browser connected to the Internet? Even
> if you saw those events, how would you know that the buyer
> didn't sell the car or the repo man didn't tow it away?
>
> Since car ownership is registered by the government, there are
> more reliable methods than observing the act of buying. But
> very few things anybody owns are ever registered in that way.
>
> For things other than cars and houses, it would be far more honest
> to use the traditional way of stating the criterion: "God knows."
> Unfortunately, when you need proof of ownership, God rarely
> testifies on the witness stand.
>
> John
>
>
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> (015)
--
Mike Bennett
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