   SetOrClass
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Sigma KEE - SetOrClass
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Relationships
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Abstract |
Properties or qualities as distinguished from any particular embodiment of the properties/qualities in a physical medium. Instances of Abstract can be said to exist in the same sense as mathematical objects such as sets and relations, but they cannot exist at a particular place and time without some physical encoding or embodiment.
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Class | Classes differ from Sets in three important respects. First, Classes are not assumed to be extensional. That is, distinct Classes might well have exactly the same instances. Second, Classes typically have an associated `condition' that determines the instances of the Class. So, for example, the condition `human' determines the Class of Humans. Note that some Classes might satisfy their own condition (e.g., the Class of Abstract things is Abstract) and hence be instances of themselves. Third, the instances of a class may occur only once within the class, i.e. a class cannot contain duplicate instances. | | | Set | A SetOrClass that satisfies extensionality as well as other constraints specified by some choice of set theory. Sets differ from Classes in two important respects. First, Sets are extensional - two Sets with the same elements are identical. Second, a Set can be an arbitrary stock of objects. That is, there is no requirement that Sets have an associated condition that determines their membership. Note that Sets are not assumed to be unique sets, i.e. elements of a Set may occur more than once in the Set. |
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