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 Maarten Maartensz:    Philosophical Dictionary | Filosofisch Woordenboek                      

 C - Collection

 

Collection: Term for the things that may somehow be collected.

The terms "set" and "class" are often offered as synonyms, but there are good reasons to keep these three terms apart, and use them according to the following assumptions, as is done in this Dictionary: Every set is a class, every set and every class is a collection, but there may be collections that are not classes nor sets, and there may be classes that are not sets.

One example of such a class that is not a set is a proper class. And one example of a collection that seems neither a class nor a set is the collection of all classes and all sets, including such as are not elements of themselves. See: Russell's Paradox.

Note that the sense of "collected" is wide: Whether by physical means or only by means of thought, imaginatively. Thus, there are, it would seem, for a given large enough set, subsets of the set that may be thought of somehow, if only by noting that all the elements of the subset are elements of the set, but that subset need not in any way be physically collected or even physically collectable. Presumably, you never before thought of the set of {the oldest living platypus, your grandmother, the Pope}, but even so it is a subset of the set of things in this world, which is a set you spend considerable thought about - and that the subset mentioned is such a subset I have just pointed out to you.

 


See also: Class, Logic, Set,


Literature:

Carnap, Halmos, Quine
 

 Original: Sep 2, 2004                                                Last edited: 12 December 2011.   Top