class

class

A <class> is a <thing> that is an understanding of the nature of things and that divides things into those which are members of the class and those which are not according to one or more criteria.

The identity of a <class> is ultimately defined by its members. No two classes have the same membership. However, a distinction must be made between a <class> having members, and those members being known, so within an information system the members recorded may change over time, even though the true membership does not change.

NOTE 1 The membership of a <class> is unchanging as a result of the spatio-temporal paradigm upon which this schema is based. In another paradigm it might be stated that a car is red at one time, and green at another time, indicating that the class of red things and class of green things changed members. However, using a spatio-temporal paradigm, a temporal part, state 1, of the car is red, and another temporal part of the car, state 2, is green. In this way the members of the classes red and green are unchanging. The same principle applies to future temporal parts as to past temporal parts, it is just more likely that the membership of these is not known.

A class may be a member of another class or itself.

NOTE 2 The set theory that applies to classes in this model is non-wellfounded set theory [3]. This permits statements like "class is a member of class", unlike traditional set theories such as Zermelo-Fraenkel set theory found in standard texts [4].

There is a null <class> that has no members.

NOTE 3 The known members of a <class> are identified by <classification>.

EXAMPLE 1 Centrifugal pump is a <class>.

EXAMPLE 2 Mechanical equipment type is a <class>.

EXAMPLE 3 Temperature is a <class>.

EXAMPLE 4 Commercial fusion reactor is a <class>.

NOTE 4 Although there is only one <class> that has no members, there can be a <class> that has no members in the actual world, but which does have members in other possible worlds.

EXAMPLE 5 Centigrade scale is a <class>.

BIBLIOGRAPHY

[3] ACZEL, Peter. Non-Well-Founded Sets, Center for the Study of
Language and Information, Stanford, California, 1988, ISBN 0937073229.
[4] ITÔ, K. (editor). Encyclopedic Dictionary of Mathematics,
Mathematical Society of Japan, Edition 2, Cambridge, Massachusetts, MIT
Press, 1993, ISBN 0262590204.