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### 4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Set

#### [status of a set having a single member]

12 ideas
 15505 If a set is 'a many thought of as one', beginners should protest against singleton sets [Cantor, by Lewis]
 6103 Normally a class with only one member is a problem, because the class and the member are identical [Russell]
 13203 The singleton is defined using the pairing axiom (as {x,x}) [Enderton]
 10813 What on earth is the relationship between a singleton and an element? [Lewis]
 10814 Are all singletons exact intrinsic duplicates? [Lewis]
 15497 We can replace the membership relation with the member-singleton relation (plus mereology) [Lewis]
 15506 If we don't understand the singleton, then we don't understand classes [Lewis]
 15511 If singleton membership is external, why is an object a member of one rather than another? [Lewis]
 15513 Maybe singletons have a structure, of a thing and a lasso? [Lewis]
 9551 What is special about Bill Clinton's unit set, in comparison with all the others? [Chihara]
 8956 What is a singleton set, if a set is meant to be a collection of objects? [Szabó]
 14243 The unit set may be needed to express intersections that leave a single member [Oliver/Smiley]