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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."
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