structure for 'Formal Logic'    |     alphabetical list of themes    |     expand these ideas

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