John, (01)
I wasn't taking the view that sharing a spatial-temporal extent (i.e., life
cycle) was a definition of an individual. That was Matthew's point, but I
can understand how using that criteria when faced with deciding whether two
or more observations of some "entity" in the real world were the same entity
or not is a reasonable approach. A lot of systems that detect objects in
their environment operate on that principle if the objects don't have
explicitly observable (and reliable) identifiers. (02)
Having said that, I believe our discussion really centered around the
observation that what constitutes an individual is a function of context,
and whether that context requires individuation of entities described within
it. And if it does, the issue of how to identify the individual entities in
a way that is both detectable and sharable among parties that operate in
that shared context needs to be addressed. Furthermore, when operating with
parties in related but distinct contexts that treat those same entities at a
different level of aggregation, some means of relating the identities of
entities at these different levels of aggregation are required. I suppose
this maps to named sets of individuals and named sets of sets, and so on. (03)
We don't need to do this for all entities. For example, I would be surprised
if anyone wanted to individually identify each lump of coal in the bulk
cargo hold of a collier, even though the cargo shipment probably has an
identifier in some business context. Coal is consider a fungible commodity.
But every iPhone in the hold of a container ship, and every container and
pallets within each container will have a specific individual identifier.
And it's important in some contexts (but not all) to know which containers
have iPhones in them and which pallets are destined for which store or
distributor. Shouldn't ontologies describing such a commercial supply chain
include which entity types require identifiers for individual entity
instances? And describe which entity types with individual identities can
contain (or otherwise represent an aggregate of, as in the flight data
object example) other entity types whose instances have individual
identities? I'm obviously not conversant with set theory, but it seems to me
that this supply chain example requires naming sets so that they can be
treated as individuals in some contexts and as sets of individuals or of
other sets in other contexts. (04)
Hans (05)
-----Original Message-----
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Richard
Dapoigny
Sent: Sunday, December 16, 2012 12:56 PM
To: ontolog-forum@xxxxxxxxxxxxxxxx
Subject: Re: [ontolog-forum] Ontologies and individuals (06)
Le 16/12/2012 18:39, John F Sowa a écrit :
> Hans, Doug, William, Pat, et al.,
>
> 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.
>
> HP
>> Remember that the conceptual flight object also has a life cycle, not
>> just the individual flight instances...
> DF
>> Just because something has properties, it doesn't mean that that
>> thing is an individual...
> WF
>> As Hans and Mathew emphasize, the sine-qua-non of an *individual* is
>> that it has a life cycle...
> 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.
>
> I agree with Pat:
>
> 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.)
> 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.
>
> 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:
>
> "To be is to be the value of a quantified variable."
>
> 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:
>
> 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.
>
> 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:
>
> 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.
>
> 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.
>
> 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.
>
> 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.
>
> John
Hi all,
John , you are right but the problem with mereology and set theory is that
many works choose the framework of set theory and use mereological
definitions (e.g., part-of, proper-part-of, weak or strong supplementation
principle and the like) without stating explicitely that they are not in a
"pure" mereological framework.
Richard (07)
>
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--
And the wounded skies above say
it's much too much too late.
Well, maybe we should all be praying for time. (09)
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