John makes an important addition to my list. In addition to defining a concept
as the union of a set of 'subordinate' concepts', it is also possible to define
a 'class' or a 'term' (less clearly a 'concept') as a specific set of named
things. This latter is also referred to as an "extensional definition". One
can define 'primary color' as "one of red, orange, yellow, green, blue, indigo,
violet," without being at all clear about what the distinguishing properties
are. (01)
(I tend to think that a 'concept' should have a definition that involves
specifying properties, but then "being the color red" and "being John
Malkovich" can be considered properties.) (02)
-Ed (03)
> -----Original Message-----
> From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-
> bounces@xxxxxxxxxxxxxxxx] On Behalf Of John F Sowa
> Sent: Monday, June 23, 2014 4:47 PM
> To: ontolog-forum@xxxxxxxxxxxxxxxx
> Subject: Re: [ontolog-forum] Types of Formal (logical) Definitions in ontology
>
> Ed and Pat,
>
> Pat raises an important point:
>
> PJH
> > If all classes are defined in terms of other classes, where does the
> > whole process get started?
>
> All three of those methods assume you have some classes to start:
>
> EJB
> > 1) identify a more general concept and the delimiting characteristics
> > of the subordinate concept being defined
> > This is exactly: An A is a B that C.
> > 2) identify a list of subordinate concepts that together cover the
> > more general concept being defined - the union of other defined classes:
> > An A is a B or a C or a D.
> > 3) One can also define a Class as the intersection of two or more classes,
> > but that is just a special case of (1): An A is a B that is also a C.
>
> Those are all set forming operations. Set theory has a starting method:
> {x | P(x)} -- the set of all x for which some property P is true.
>
> That property P can also be specified by enumeration:
> {x | x=a or x=b or x=c}
>
> What distinguishes a class from a set are the identity criteria:
>
> 1. Two sets S1 and S2 are identical if they have the same elements.
>
> 2. Two classes or concepts C1 and C2 are identical if they have the
> same or logically equivalent defining property or predicate P.
>
> The set of all cows, for example, changes with every birth or death.
> But the concept cow is determined by an unchanging predicate P.
>
> John
>
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