Re: SUO: Mass vs Count distinction
This seems like a good place to jump into this. I'm still about a day
behind in catching up with the list, so forgive me if this point has been
made within the last 24 hours!
This discussion of mass vs. count provides a good opportunity to mention
_intent_. Or, as I've mentioned before, _pragmatics_.
The five rods may become ten, then 20, then 40. From some pragmatic point
of view, the count may continue to be important. From some point of view
it may be actually be important to identify each individual rod. It's
likely more common to just care that there are 38, because two have been
sold, or consumed in some sub-assembly. At some point the number of rods
transforms into something else, say "rodlettes", which will be used for
some purpose (where the original rods were more in the nature of raw
material - more like mass than the larger number of processed and countable
components).
Or, take one of the canonical mass terms: sand. Sand, for most purposes,
is measured by weight or volume, even though it is universally known that
it is composed of individual grains. Yet we can surely imagine that there
must be purposes for which the characteristics of individual grains becomes
important. I don't know anything about silicon wafer fabrication, except
that material purity is critical. But take the case of sandpaper. Grain
size is important, and so during the manufacturing process a mass of sand
of one grain size may need to be rendered into a mass of sand with a
smaller grain size. Then, at another manufacturing step, the grit level of
a certain grade of some sandpaper product will need to be known in terms of
the actual count of grains of a certain size in one square inch. At an
extreme, placement of a particular specially-marked grain of sand may need
to be tracked for quality control purposes.
Whether we're talking about sand or sawn wooden rodlettes, there are
several key points here:
One point is that there are at least _three_ levels of concern about such
physical objects: mass, countable, and individually identifiable.
Another point is that the relevance of such distinctions is not intrinsic
to the objects themselves, but is influenced, or determined by intent,
purpose or pragmatics.
I hope I'm saying this in a meaningful way, but it seems that Peirce/Sowa
thirdness may be nearly ubiquitous in our ontological considerations.
This has some implications for the SUO, driven by the expectations that
people will have for the SUO itself. Can we make statements in the SUO
that are true for all imaginable purposes?
This has even more implications for the relationship between the SUO and
any related ontology. Can we define compliance to, or derivation from, the
SUO to be meaningful for any community and/or application regardless of
purpose, independent of purpose, or inclusive of all possible purposes?
Doug McDavid
Certified Executive Consultant
Business Innovation Services - IBM, US
Member of IBM Academy of Technology
mcdavid@us.ibm.com -- 916-549-4600
David Whitten <whitten@lynx.eaze.net>@ieee.org on 09/21/2000 11:28:57 AM
Sent by: owner-standard-upper-ontology@ieee.org
To: standard-upper-ontology@ieee.org
cc:
Subject: Re: SUO: Mass vs Count distinction
John Sowa asked:
> But what about a wooden rod?
>
Michael Uschold had said:
> >Distinction: Mass-Count
> >Proposer: Adam Pease / Mike Uschold
> >Options:
> > X: something that cannot be divided into parts, each of which
> > is the same type/class of thing as the whole was.
> > E.g. A person, a car.
> >
> > Y: something that can be divided into parts, each of which
> > is the same type/class of thing as the whole was.
> > E.g. a quantity of sand, an amount of water
> >
> >Proposed name for Y: Mass-Thing
> >Proposed name for X: Countable-Thing
>
John Sowa continued:
> Suppose I have 5 wooden rods. Then I cut each one in half,
> and I get 10 wooden rods. I can count wooden rods, but when
> I divide them, I get more wooden rods than I started with.
This is one the reasons I enjoy participating in the SUO mailing
list. We have some very capable people who are willing to ask hard
questions about what other very capable persons have presented.
Incidentally, Mike's original statement above has been altered
by me to match my understanding (and John Sowa's pg 98 of KR)
of what a Mass-Noun and a Count-Noun refer to. (I swapped X & Y).
In my opinion, being countable is saying that you can count
the elements in a collection, not that you necessarily want to.
Count-Things can be represented by sets, since you can discern
individual elements. Mass-Things require a collection that
tracks quantity, not identity of the individual elements.
Perhaps we need to expand this format of Mike's to include
this distinction as well as boundary conditions.
One boundary seems to be on the division into parts operation
mentioned. I can imagine dividing each wooden rod into parts,
each of which would be a wooden coin.
In this case, the operation would be taking something I thought
of as a Mass-Thing (a specific group of wooden rods)
and producing another Mass-Thing (a specific group of wooden
coins) but these two groups are not of the same type/class.
Another related boundary is interepreting the division into
parts operation as a division of the group of wooden rods into
two or more subgroups. Clearly, one wooden rod does not make a
group. So this division into parts operation, when applied
to the group as as whole, must produce subgroups, each of which
are the same type/class. Thus this looks like the group of
wooden rods is a Mass-Thing which has parts that are Count-Things.
Another boundary is the fact that any object made of wood,
when separated into two or more parts, will produce objects made
of wood. This seems to require the group of wooden
rods to be composed of parts, each of which are a Mass-Thing.
Does this match anyone else's analysis ?
David (whitten@lynx.eaze.net) (713) 791-1414 ext 6116