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Re: [ontolog-forum] Thing and Class

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
Cc: tim.glover@xxxxxx
From: "Michael F Uschold" <uschold@xxxxxxxxx>
Date: Wed, 10 Sep 2008 10:30:48 -0700
Message-id: <406b38b50809101030q70616a98k60ecd568eb426c03@xxxxxxxxxxxxxx>
Usefulness is in the eyes of the beholder.  I was reporting the news: I, Michael Uschold,  find the distinctions helpful.  I tossed them out there in case there are others who also find them useful, not to convince anyone that they are.

I was not using the word 'set' in a rigorous mathematical sense, I really meant any way you wish to think of a group or collection of things. I understand that the details are important, I was not addressing them.

From the responses, it seems that if any of the distinctions that I find helpful are to be helpful to a broader number of people, one would have to be more clear about distinctions like set/type intension/extension.  Replacing 'set' with 'type' as Pat suggests may be a step in the right direction.

Michael

On Wed, Sep 10, 2008 at 9:37 AM, Pat Hayes <phayes@xxxxxxx> wrote:


tim.glover@xxxxxx wrote:
>
> Pat, noting John Sowas comments about the difference between
> extensional sets, and intensional types, would the situation  be
> improved by substituting "type" for "set" throughout, eg
>
> X: the universal type
> Y: the type of things that have members
> Z: the type of things that do not have members.
> U: the type of things whose members are all of type Y
> V: the type of things whose members are all of type Z
>
Nice thought, but the problem is that these notions are all defined
purely in extensional terms, i.e. in terms of membership. Every
intensional type has a corresponding extension, which is the set of all
things which are of the type; and Michael's taxonomy, above, only refers
to the extensions.
> U and V might be useful types, even if they are not useful sets?
Maybe I spoke too harshly if I said they were useless. They are
obviously widely used notions. But it is dangerous to assume that they
are the only possibilities.

Pat
>
>

> Tim.
>
>
>
> ------------------------------------------------------------------------
> *From:* semantic-web-request@xxxxxx
> [mailto:semantic-web-request@xxxxxx] *On Behalf Of *Pat Hayes
> *Sent:* 09 September 2008 18:16
> *To:* [ontolog-forum]
> *Cc:* [ontolog-forum]; James Leigh; SW-forum; Michael F Uschold
> *Subject:* Re: [ontolog-forum] Thing and Class
>
> 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 <abdoul@xxxxxxxxxxxxxx
>> <mailto:abdoul@xxxxxxxxxxxxxx>> 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" <james-nospam@xxxxxxxxxxx
>>     <mailto:james-nospam@xxxxxxxxxxx>>
>>     To: "Richard H. McCullough" <rhm@xxxxxxxxxxxxx
>>     <mailto:rhm@xxxxxxxxxxxxx>>
>>     Cc: "Semantic Web at W3C" <semantic-web@xxxxxx
>>     <mailto:semantic-web@xxxxxx>>
>>     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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