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Re: [ontolog-forum] Thing and Class

From: Pat Hayes <phayes@ihmc.us>
Date: Tue, 9 Sep 2008 12:16:09 -0500
Message-Id: <p06240800c4ec5717b6ec@[10.100.0.140]>
To: "[ontolog-forum] " <ontolog-forum@ontolog.cim3.net>
Cc: "[ontolog-forum]" <ontolog-forum@ontolog.cim3.net>, James Leigh <james-nospam@leighnet.ca>, SW-forum <semantic-web@w3.org>, "Michael F Uschold" <uschold@gmail.com>
At 2:35 PM -0700 9/8/08, Michael F Uschold wrote:
>Azamat said:
>
>
>Sum up: If Thing goes as the universal class, of which everything is a
>member, it will equivalent to Class, as the class of all classes. Other
>interpretations will be inconsistent, asking for many questions.
>
>
>Whatever you choose to call these things, I find the following 
>distinctions helpful:

I don't find them helpful. They embody and give credence to several 
common errors; they do not conform to established usages that go back 
half a century or more; and they aren't properly defined.

>
>1.	X: the set of all things in the universe of discourse
>2.	Y: the set of all things that have member individuals
>3.	Z: the set of all things that do NOT have member individuals
>4.	U: the set of all things whose members do not themselves have members
>                       (i.e. the set of all things whose members are 
>members of the class Z)
>5.	V: the set of all things whose members also have member individuals 
>               (i.e   the set of all things whose members are all 
>members of the class, Y)
>
>The names I find most useful for these things are (substituting into 
>the text above)
>
>1.	THING: the set of all things in the universe of discourse

What do you mean here by 'universe of discourse'? That sounds like a 
semantic term. A semantic universe of discourse can be very small, 
e.g. {A} is a possible universe of discourse.

>2.	CLASS: the set of all things that have member individuals

Does that exclude the empty set/class? (I hope not.) And do the 
members have to be individuals, or can they also include classes? As 
stated, this seems to exclude METACLASS, whose elements don't have 
individuals as members. I presume you did not intend this, though.

>3.	INDIVIDUAL: the set of all things that do NOT have member individuals

But not including the empty set/class, I presume.

>4.	ORDINARYCLASS: the set of all things whose members do not 
>themselves have members
>                       (i.e. the set of all things whose members are 
>members of the class INDIVIDUAL)
>5.	METACLASS: the set of all things whose members also have 
>member individuals 
>               (i.e   the set of all things whose members are all 
>members of the class, CLASS)

It might be worth remarking that your 'ORDINARYCLASS' and 'METACLASS' 
classifications are not recognized by set theory, and seem to have no 
purpose that I can determine; that the distinction between them isn't 
exhaustive, since it omits the (common) case of a set containing both 
sets and non-sets; and that it has been shown quite rigorously that 
if set theory is consistent at all, then it is also consistent to 
assume that there are no INDIVIDUALs in the above sense, i.e. that 
everything can be treated as a class.

More importantly, the term "individual" as used in logic does not 
have anything like this meaning: it simply means anything in the 
universe of discourse, i.e. anything that one is quantifying over. 
This may include classes, of course, just as it may include anything 
else. Logical individuals can be any kind of thing: the term does not 
act there as a classifier. It is therefore very misleading and 
confusing to treat it as one, as you do here. Looked at from a 
logical point of view, it seems crazy to single out lack of one 
particular relation as being a defining characteristic for 
individual-hood. Why choose lack of class-membership? Why not say 
that anything that isn't married is an INDIVIDUAL, or anything that 
doesn't have more than three parts, or ...?

The recognized term in set theory for INDIVIDUALs in your sense is 
'ur-elements', from the German "urelemente". Maybe we could call them 
"irreducible individuals" or some such formulation, to avoid this 
(recurrent and exasperating) confusion? Or simply NON-CLASS ?

>Here is the class hierarchy:

Um... it's not a hierarchy.

>
>THING (the most general anything)
>
>CLASS (the most general class)
>
>ORDINARYCLASS
>METACLASS
>
>INDIVIDUAL (the top of the ordinary class hierarchy)

This is a horribly misleading mis-use of a widely used, almost 
universal, nomenclature. Why screw up a terminology that has worked 
well for 50 years? Its not even the terminology that is used in set 
theory itself, which (unlike logic) actually deals with these 
distinctions.

>
>INDIVIDUAL and CLASS form a partition of THING
>ORDINARYCLASS and METACLASS form a partition of CLASS

No, they most definitely don't. If A is an individual then {A, {A}} 
isn't either ordinary or meta.

Pat

>
>THING and CLASS have all of the five things below as members:
>
>THING
>CLASS
>ORDINARYCLASS
>METACLASS
>INDIVIDUAL
>ORDINARYCLASS has members:
>
>INDIVIDUAL (any any of its subclasses)
>
>METACLASS has members:
>
>CLASS
>METACLASS
>ORDINARYCLASS
>INDIVIDUAL has members that are inherited from any of its subclasses 
>(e.g. individual persons, or companies, or drugs, depending on the 
>domain).
>
>Michael
>
>On Thu, Aug 28, 2008 at 12:58 AM, Azamat 
><<mailto:abdoul@cytanet.com.cy>abdoul@cytanet.com.cy> wrote:
>
>As a devil's advocate, seemingly unsanctioned with the 3WC, Richard is doing
>a useful work raising sometimes justified objections for SW candidates
>looking for canonization (standardization).
>As for James's reading of Thing and Class, it looks more as punning,
>possibly intentionally.
>
>The interrelations of classes as well as classes and things are actually
>more subtle and deep, than generally presented in various specifications.
>A member of a class may itself be a class. For example, the class of humans
>is a member of the class of species of animals. An individual human, even
>being a member of its class, is not a member of the latter one,  the class
>of species of animals. For a human is not a species of animal.
>Whatever the number of human beings, it will not affect the number of
>species of animals. This goes as a kind of ontological rule of all
>taxonomies: whatever the number of instances, objects, particulars, it will
>not change the number of classes of things. Again, this means that
>relationships of class inclusion (subsumption) and class membership have
>some principal differences. Namely, the class inclusion is a transitive
>relation, while the CLASS MEMBERSHIP IS NOT TRANSITIVE. This fundamental
>fact is missing in some large scale, common sense ontologies, making the
>whole hierarchy just as invalid for computing applications.
>Sum up: If Thing goes as the universal class, of which everything is a
>member, it will equivalent to Class, as the class of all classes. Other
>interpretations will be inconsistent, asking for many questions.
>
>Hope this will be of use,
>Azamat Abdoullaev
>
>
>----- Original Message -----
>From: "James Leigh" 
><<mailto:james-nospam@leighnet.ca>james-nospam@leighnet.ca>
>To: "Richard H. McCullough" <<mailto:rhm@pioneerca.com>rhm@pioneerca.com>
>Cc: "Semantic Web at W3C" <<mailto:semantic-web@w3.org>semantic-web@w3.org>
>Sent: Thursday, August 28, 2008 4:30 AM
>Subject: Re: Thing and Class
>
>
>>
>>  Hi Richard et al.
>>
>>  Here is an informal interpretation of some of the spec written in plain
>>  English.
>>
>>  Class stands for classification.
>>  We use Class to classify things.
>>  Class is a set of Things.
>>  "I am a Human" - I just classified myself as Human (I hope I'm right).
>>  "I am a Thing" - that is true for everything.
>>  Human is a classification of all people.
>>  Thing is a classification of all things.
>>  Every Human is a Thing. Therefore Thing is a super set of Human.
>>  Is Human a Thing? No! its a Class!
>>  Everything Thing is an individual.
>>  Human is not an individual, it is a classification of individuals.
>>  Thing is not an individual, it is a classification of individuals.
>>  Can we classify Classes? Yes we can! Human is a classification - I just
>>  classified Human as a classification.
>>  Human is a Class.
>>  Thing is a Class.
>>  Are all Things Classes? No! I am a Thing, but I am not a classification.
>>  Is Thing the same as Class? No! Human is not a Thing, but Human is a
>>  Class.
>>
>>  Hope this helps,
>  > James
>>
>>
>>
>>
>
>
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Received on Tuesday, 9 September 2008 17:16:58 GMT

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