RE: SUO: RE: Re^n: Collections - Aggregation or Set
Pat,
You wrote:
No, they aren't, at least in the way these collection-words are
usually used. They have associated sets (which can change with time
in a 3d ontology, or which might contain history-episodes rather than
complete histories, in a 4d ontology), but they cannot be identified
with the sets of their members, because for example shoals have fish
as members, not episodes of fish-histories
This is a tricky point. It is unclear whether when we talk about fishes (or
whatever) we commit to a standard fish history. It has been suggested that
being a fish may be a 'spatial' characteristic that applies to many
different types of life history; including standard birth-death as well as
pack-episodes. This is something that needs to be clarified in an ontology.
It may be things like wheels are easier to consider. Consider my car's front
right wheel (also, for the sake of argument, consider it as a physical
object rather than a role) consider also wheel #10, currently 'installed' as
my car's front right wheel. We naturally think of them both as wheels - so
wheelness is a spatial property - which applies to different life histories.
Regards
Chris
-----Original Message-----
From: owner-standard-upper-ontology@ieee.org
[mailto:owner-standard-upper-ontology@ieee.org]On Behalf Of pat hayes
Sent: 27 February 2001 20:08
To: standard-upper-ontology@ieee.org
Subject: Re: SUO: RE: Re^n: Collections - Aggregation or Set
"West, Matthew MR SSI-GREA-UK" <Matthew.R.West@is.shell.com>:
>Dear Chris,
>
> >
> > Chris P wrote:
> > > Max Black's essay (referred to in an earlier email) starts with a
> > > quote from a working mathematician's book on set theory -
> > which claims
> > > that packs of wolves etc. are standard examples of sets.
> >
> > A claim that is pretty obviously false. A pack can change its members
> > (if, for example, a pup is born) and remain the same pack. Not so the
> > set corresponding to the pack at any given time.
>
>MW: Not so obviously in fact. You have assumed a 3D ontology, Chris and I
>would assume a 4D ontology (I don't know about Max Black). In this case the
>set of members of the flock is the spatio-temporal extent of all members of
>the flock, past, present and future. This doesn't change over time.
No, you are missing the point, which can be described just as well in
4d as in 3d. Consider a wolf pack where one wolf gets left behind,
gets lost and is then no longer part of the pack. In 4d this is a
lone history that projects out'sideways' from the pack history, like
a loose thread hanging off a unravelling cardigan. The point being
that it is NOT part of the pack, so one cannot identify the (history
of the) pack with the mereological union of the (histories of the)
animals in the pack. Packs, like most collections, have their own
special criteria both necessary for membership (being a wolf) and
sufficient for membership (a complex kind of social acquaintance and
mutual recognition, probably fully known only to wolves.) Wolves can
also be absorbed into packs, by the way, so it works both ways round.
BTW, what you say here is almost certainly wrong in any case, apart
from lone-wolf examples. A spatiotemporal extent is not a set of
members. You can have the pack be a spatiotemporal extent, if you
want, though I think that would be severely inadequate for actual
reasoning; or you could have it be a set, if you want, though again
that has problems; but you definitely can't consistently have it be
both at once.
> >
> > > If I had the time, I am sure I could come up with other examples.
> >
> > There are lots of similar examples that go wrong for similar
> > reasons --
> > flocks of geese, schools of fish, citizens of a country, sets
> > of dishes,
> > etc. All of these collective entities can change their membership, at
> > least to some extent, and remain the same collective entity.
> > Not so the
> > corresponding sets at any given time.
>
>MW: These are sets too of course.
No, they aren't, at least in the way these collection-words are
usually used. They have associated sets (which can change with time
in a 3d ontology, or which might contain history-episodes rather than
complete histories, in a 4d ontology), but they cannot be identified
with the sets of their members, because for example shoals have fish
as members, not episodes of fish-histories.
Pat
---------------------------------------------------------------------
IHMC (850)434 8903 home
40 South Alcaniz St. (850)202 4416 office
Pensacola, FL 32501 (850)202 4440 fax
phayes@ai.uwf.edu
http://www.coginst.uwf.edu/~phayes