Barry,
Re: Leaving aside administrative domains (e.g. tax collection), types,
like instances, are discovered. They are out there in reality. They
form the subject-matter of scientific inquiry. (01)
As stated earlier - this is simply not the general case, at least not in my
world. We can accept the existence of such "natural types" and provide a
prominent place for them in our ontology, but MOST of the types we and our
customers deal with represent concepts made up by man. Some are
"discovered" in watching what man does but many are simply made up as a
means of specifying a future system or interpreting an existing systems.
Even those that are discovered are an abstraction and interpretation of this
"real world" - essentially an opinion. Instances, likewise, are then
created based on this constructed world - such as an electronic payment.
Every organization, business process and information structure was an idea
before it existed and a specification (formally or informally) before it was
realized. These architectures are represented, largely, as type systems.
These type system intersect the real world as
aspects/facets/views/abstractions/roles [pick your favorite context word] of
the things you like to talk about - like people, rocks and rabbits.
There are clearly two concepts here - lets label them as different concepts
and move on. I would suggest terms like; "type" (the general case) and
"natural category" - discovered categories of objects in the real world. (02)
Examples of types;
Accountant
Invoice
Price
Form-671
Customer
Customer Record
Project manager
Post invoice
Process claim
U.S. Dollars
Asset
Person
Rabbit (03)
-Cory (04)
-----Original Message-----
From: ontac-dev-bounces@xxxxxxxxxxxxxx
[mailto:ontac-dev-bounces@xxxxxxxxxxxxxx] On Behalf Of Smith, Barry
Sent: Wednesday, January 25, 2006 3:27 AM
To: ONTAC Taxonomy-Ontology Development Discussion
Subject: RE: [ontac-dev] Representation of attributes (05)
> >
> > membership
> >
> > 1. the number 4 is a member of the set {4, the moon, Napoleon}
> > 2. there is no corresponding type
>
>MW: Why? Surely a trivial type listing the members can be constructed. (06)
Leaving aside administrative domains (e.g. tax collection), types,
like instances, are discovered. They are out there in reality. They
form the subject-matter of scientific inquiry. (07)
> >
> > 3. Harvey is a member of the set of rabbits
> > 4. Harvey is also an instance of the type rabbit.
> > It is in virtue of 4. that 3. is true.
> >
> > We see that there are cases of set-membership where there is no
> > counterpart to 4. Hence set membership is at least a wider notion.
>
>MW: Yet membership would not be time indexed whilst instance_of could
>be (for you at least). Sounds to me as if each is narrower than some
>common core. Can I assume (correctly) you consider that they have the
>same properties in terms of transitivity and the like? (08)
I offered my two pennies' worth on this here:
http://ontology.buffalo.edu/bio/logic_of_classes.pdf
esp. pp. 6ff. (09)
> >
> > Sets are abstract entities, with wonderful mathematical properties,
> > but they are not what, e.g., biologists study.
>
>MW: Interesting how often it is people don't recognise what they are
>looking at. (010)
So you really haven't heard of Charles Darwin! You have some
interesting reading ahead of you. I suggest you start with a book
called 'The Origin of Species'. (011)
> >
> > > > Types have instances.
> > > > We represent these instances using various means, e.g.
> > English words
> > > > ('red', 'bright red') or hexadecimal numbers, or what you will.
> > > > Sometimes our representations are more precise, sometimes
> > less. They
> > > > may still all be correct (as it may be equally correct to say:
> > > > 'animal over there', or 'cat at fifty paces').
> > >
> > >MW: I think I have mostly grasped what you mean by a type, surprising
> > >as it has been to me. Just one last clarification here. I presume you
> > >agree there are some types whose membership does not change,
> > i.e. your
> > >type and set have the same members, e.g. integers and real numbers.
> >
> > If integer is a type, then the set of its instances is indeed always
> > identical to the set of its instances. And ditto for 'real number'.
>
>MW: So one possibility here might be for me to settle for types whose
>instances didn't change over time, and just forget about the "sets"
>as uninteresting. (012)
Quine used to talk about desert landscapes. You, it seems, are pining
for desert landscapes from which all traces of the biological have
been eliminated (even, I suppose, the oil and gas underneath). (013)
>MW: My problem now is that I understand that you want types to be
>restricted to things like rabbits, not "people with 376 hairs on their
>arms" or "4, the moon, and me". Now, whilst I am sympathetic
>to the idea of natural kinds, it seems to me that these three examples
>actually sit in a spectrum and there is no clear divide between them
>(though these three being prototypical can be easily distinguished). (014)
There are many terms for which we have clear examples of entities
which fall under them, clear examples of entities which do not fall
under them, and then a penumbra of problematic cases in between.
Responses to this problem for 'type' might be: (015)
1. it is hard work to find out which types exist (this work is called
'science') (BS)
2. we should refrain from formulating axioms about what is a type (JS)
3. 'type' is redundant; we should talk of sets instead, keeping our
heads under the desert sand to avoid all sight e.g. of anything biological
(MW) (016)
BS (017)
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