Mike, (01)
I think ChrisM explained this all in a mail to this list a few weeks ago. (02)
I believe the terms are well-understood and defined - and google will reveal
many excellent sources that explain them. (03)
At its (rough) simplest, if a definition is a definition and it is a list,
it is extensional - otherwise it is intensional. (04)
The choice of type of definition and type of identity criteria have an
effect on one another - but, I believe, only in so far as intensional
definitions are needed for intensional identity criteria are they dependent. (05)
Other specific comments below. (06)
One general point. I believe many of the terms you use below have a
well-established meaning (which you can easily establish with a little
googling) - please let me know if I am mistaken - and have quite an
important role in discussions of ontology. So it is important that if we are
going to use them in a non-standard way, we say this clearly. (07)
Regards,
Chris Partridge
Chief Ontologist (08)
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> -----Original Message-----
> From: uom-ontology-std-bounces@xxxxxxxxxxxxxxxx [mailto:uom-ontology-
> std-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Mike Bennett
> Sent: 07 August 2009 18:32
> To: uom-ontology-std
> Subject: Re: [uom-ontology-std] uom-ontology-std - strawman UML
>
> John and Chris,
>
> > God rarely testifies on the witness stand.
>
>
> I think the insurance companies are still looking for him.
>
> 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? (012)
CP> I am not sure where you got this idea from. (013)
>
> 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. (014)
CP> No, just wiki 'definition' to see this is not how the terms are used -
http://en.wikipedia.org/wiki/Definition (015)
Intension and extension (016)
Main articles: Intension and Extension (semantics)
An intensional definition, also called a connotative definition, specifies
the necessary and sufficient conditions for a thing being a member of a
specific set. Any definition that attempts to set out the essence of
something, such as that by genus and differentia, is an intensional
definition.
An extensional definition, also called a denotative definition, of a concept
or term specifies its extension. It is a list naming every object that is a
member of a specific set.
So, for example, an intensional definition of 'Prime Minister' might be the
most senior minister of a cabinet in the executive branch of government in a
parliamentary system. An extensional definition would be a list of all past,
present and future prime ministers.
One important form of the extensional definition is ostensive definition.
This gives the meaning of a term by pointing, in the case of an individual,
to the thing itself, or in the case of a class, to examples of the right
kind. So you can explain who Alice (an individual) is by pointing her out to
me; or what a rabbit (a class) is by pointing at several and expecting me to
'catch on'. The process of ostensive definition itself was critically
appraised by Ludwig Wittgenstein.[3]
An enumerative definition of a concept or term is an extensional definition
that gives an explicit and exhaustive listing of all the objects that fall
under the concept or term in question. Enumerative definitions are only
possible for finite sets and only practical for relatively small sets. (017)
If an extensional
> definition is of the form "all the States in the USA", (018)
CP> No, to be extensional, it needs to be the actual list of the states. (019)
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?
>
> 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. (020)
CP> Not if you are a 3-D-ist. (021)
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. (022)
CP> Spot on. But do not expect everyone to agree with you. (023)
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.
>
> 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, (024)
CP> This distinction relies to a large extent on having a 3-D-ist viewpoint,
and so is incompatible with you earlier 4-D-ist statement above. (025)
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.
>
> 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. (026)
CP> This is an unusual interpretation. Usually people use the term
continuants for things that do not exist in time, whereas occurents do. This
distinction is enshrined in, for example, Barry's BFO where occurents are 4d
(and continuants 3d).
Again, as far as I am aware there is a very well-established usage and if
you are recommending a revision, you should make this clear. (027)
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.
>
> 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.
>
> 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.
>
> 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.
>
> 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. (028)
Mike, as I made clear in the subsequent emails, it would be rather difficult
to have an extensional definition of most UoMs - as they have a very large
extension. It would be odd (but very interesting) if someone actually could
produce an extensional example (excluding things such as a list of the SI
units). However, this has nothing whatever to do with extensional criteria
of identity. (029)
>
> 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? (030)
CP> This point has been made a lot of times. My guess is that if it was
easy, someone would have done it by now. (031)
>
> Mike
>
> 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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> >
> >
>
>
> --
> Mike Bennett
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