Definition of "class"

[zhengj2007]

From [email protected] on May 14, 2013 16:53:35

In 2.5 Universals and classes, the term "class" is used but not clearly defined:

"Universals have instances, which are in every case particulars (entities located in space and time). Universals also have extensions, which we can think of (set-theoretically) as collections of their instances.
Such extensions fall outside the scope of this specification, but it is important for the understanding of BFO that the distinction is recognized. It implies further distinctions not only between universals and their extensions but also between universals and classes in general, including arbitrary classes such as: {the moon, Napoleon, redness}. "

It would be helpful to clarify whether "extension" mean "class". I would also propose to introduce a (functional) relation like "extension of", which links classes with universals.

Original issue: http://code.google.com/p/bfo/issues/detail?id=174

[zhengj2007]

From [email protected] on May 15, 2013 03:28:14

I have understood classes to mean also logical combinations of universals that are not themselves universals. For examples (Apples OR Oranges). I think extension here is not the same as class. Universals (as well as classes) have extensions which may change from moment to moment. The phrase "classes such as: {the moon, Napoleon, redness}" means, the class with extension {the moon, Napoleon, redness}, presumably whenever the members exist, since, as far as I know, it does not make sense to have, in BFO, either a class nor universal whose extensions contain, at a moment, things that don't exists at the time that the class or universal exists.

I imagine one could extend the notion of class to allow this, but then the notion of extension would be confusing, meaning something different for classes than for universals.

Part of the confusion in the above is in the phrase "collections of their instances", since instantiation is time dependent we don't know if it means "at a time", or whether it means "ever". In the latter case it would be a strange entity as it would include all instance in history but also in the future.

[zhengj2007]

From [email protected] on May 15, 2013 03:28:51

Also, what is the use case for having the relation "extension of".

[zhengj2007]

From [email protected] on May 15, 2013 03:35:32

Labels: Milestone-BFO2-Release

[zhengj2007]

From [email protected] on June 05, 2013 11:25:30

Status: Accepted
Labels: -Milestone-BFO2-Release