Re: SUO: RE: Axiom and Intentionality vs Extentionality
At 12:40 PM 03/11/01 +0100, Jean-Marc Orliaguet wrote:
Pierre Grenon wrote:
Dear David, dear Ian,
Pardon my confusion, maybe I'm too unfamiliar with the SUMO, but I find
puzzling your interpretations of this axiom.
To be consistent with the claim that "collections have position in
time"
(assuming I'm not mistaken in understanding that it means that at
different time, members may not be the same) shouldn't an axiom stating
the necessary non emptiness of a collection be alike the following:
(=>
(and
(instance ?COLL Collection)
(instance ?TIME TimePosition))
(exists
(?OBJ)
(holdsDuring ?TIME (member ?OBJ ?COLL))))?
That is, at any time a collection has at least one member?
But, one way or another, I confess that it seems odd to me to require of
a collection that it be non empty. If a collection really preserves its
identity under alteration of membership, i.e., "members can be added
and
subtracted without thereby changing the identity of the
&%Collection".
Does that mean that collections are intermittent
beings?
A collection is not an "intermittent being", it is an
abstraction, and a collection that has no member is called
"nothing"
Peirce in 4.650 "[...] two apparent and highly interesting
ornithological collections, the one of whatever phoenixes there ever were
or will be, the other of whatever cockatrixes there are at this moment,
are one and the same collection, having one and the same essential
character. It is that quite unique collection that goes by the name of
Nothing.
Some writers whose logical conceptions would seem to be in a state of
disintegration have supposed the collection whose sole member is Gaius
Julius Caesar to be identical with Gaius Julius Caesar himself -- a
strange confusion considering that the latter was a man of immense force
of intellect who was brought into the world by a grossly unskillful
operation of surgery, while the other is nothing but an ens rationis
brought into being by the idea of that man being chosen without any
surgery at all and utterly deprived of any force of intellect or
life."
Is this the same sense of 'Collection' as that being defined in the SUMO,
i.e., in the definition of &%Collection? &%Collection seems
to be something very pedestrian, I'm understanding it to mean something
like "group of physical objects" or maybe "identifiable
group of physical objects." (Are all groups of physical
objects instances of &%Collection, e.g., is any subgroup of a given
flock of sheep an instance of &%Collection?) A group of
physical objects doesn't seem to be "brought into being by the
idea" of its constituent member(s). Also, it
doesn't seem that a &%Collection is an "abstraction"; a
flock of sheep (example from the definition of &%Collection) isn't an
abstraction is it?
But even with this earthy defintion of &%Collection, I share Pierre's
concerns here. Given that a &%Collection can survive
membership changes, it seems rather arbitrary to declare that a
&%Collection can't survive a time period in which it has no
members.
Consider an example given in the definition, a football team.
If all the members of a football team die in a bus crash and the team is
replenished the next day in an emergency draft, would we declare that the
team had to start with a new 0-0 record and that the members couldn't
pursue old club records? Or would we see this simply as a radical
personnel change that the organization survived? If we
maintain that &%Organization is a subclass of &%Collection, then
it is not clear that no &%Collection can survive a loss of all of its
members.
3.638 "The collection A is not the letter
A, but it contains A and nothing else. If it be said that there is no
such thing, the reply is that every collection, every system may be said
to be an ens rationis. To this point we shall return. Even Nothing may be
said to be a collection. For when we say that Nothing is less than 1, we
do not mean that a self-subsisting individual is so, but that an ens
rationis whose mode of being consists in the absence of everything is
less than 1."
PS: I searched for "nothing" in the Knowledge Base Browser
(
http://128.136.11.33:8080/rsigma/SKB.jsp?req=SC&name=nothing&skb=Merge
)
The result was:
Nothing would appear here
If SUMO does not consider "nothing" as a collection, is it because it does not consider a collection as an abstraction?
JM
--
Jean-Marc Orliaguet ( jmo@medialab.chalmers.se )
- http://www.medialab.chalmers.se/people/jmo/
- Tel: +46 31 772 8581
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