Hans, Doug, William, Pat, et al., (01)
I'd like to make a few observations about logic, set theory, and
mereology, which I hope will end this thread once and for all.
But I realize this is a forlorn hope for any topic in Ontolog Forum. (02)
HP
> Remember that the conceptual flight object also has a life cycle,
> not just the individual flight instances... (03)
DF
> Just because something has properties, it doesn't mean that
> that thing is an individual... (04)
WF
> As Hans and Mathew emphasize, the sine-qua-non of an *individual*
> is that it has a life cycle... (05)
The basic terms of ontology should not depend on anything as complex,
undefined, and undefinable as "life". Even the word 'cycle' requires
some kind of ontology. And the basic terms should be independent of
3D or 4D or even any notion of space and time. (06)
I agree with Pat: (07)
PH
> Member of is the classical name for the (inverse of the) relation
> between a set and something in that set... AFAIK, the part/whole
> relationship described by mereology is never referred to using
> "member" or any grammatical variation. Also, "member" is virtually
> synonymous with "instance", if one identifies classes as sets
> (which is commonly, though not universally, done.) (08)
The word 'ontology' comes from the Greek 'on' (being). The Latin
translation of 'on' is 'ens' (being). In Latin, the participle 'ens'
was nominalized as the noun 'entitas', which was borrowed as the
English noun 'entity' in the 16th century. (09)
To be as neutral as possible, I recommend the word 'entity' for
anything that exists in any way. Since any formal ontology must,
by definition, be stated in some logic language L, we can use
Quine's criterion for existence: (010)
"To be is to be the value of a quantified variable." (011)
But there are logics that do not have variables. However, they
do have ways of using some kind of names. In Common Logic, there
are names bound by quantifiers and names not bound by any quantifier.
So I'll use 'name' as the more general term that includes variables
as a special case: (012)
Definition: For any logic L and ontology O stated in L, an *entity*
is whatever can be indicated, selected, or referred to by a name
or variable of L in any proposition P of the ontology O. (013)
As Pat said, defining an individual as an entity that does not have
members requires an ontology of sets (or other collections) for which
a dyadic relation memberOf(x,y) or elementOf(x,y) has been defined: (014)
Definition: For any logic L and ontology O stated in L, if O makes
a distinction between entities called sets and entities that are not
sets, then an *individual* is any entity that is not a set. (015)
Mereology is a theory that uses the partOf relation instead of memberOf
or elementOf. In mereology, the sum of two or more entities is another
entity. Therefore, the term 'individual' is not defined. (016)
However, the term 'individual' literally means something that cannot
be divided. So you could define an individual in mereology as an
entity that does not have parts. But that's your choice. (017)
Summary: If you want to use the term 'individual' in an ontology
that does not include sets, then adopt the Humpty-Dumpty principle:
let the word mean anything you want it to mean. But then you have
the obligation to state precisely what you mean. (018)
John (019)
_________________________________________________________________
Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/
Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
Shared Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/
To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J (020)
|