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Full Idea
Suppose the relation of member to singleton is external. Why must Possum be a member of one singleton rather than another? Why isn't it contingent which singleton is his?
Clarification
Possum was David Lewis's cat
Gist of Idea
If singleton membership is external, why is an object a member of one rather than another?
Source
David Lewis (Parts of Classes [1991], 2.2)
Book Ref
Lewis,David: 'Parts of Classes' [Blackwell 1991], p.37
A Reaction
He cites Van Inwagen for raising this question, and answers it in terms of counterparts. So is the relation internal or external? I think of sets as pairs of curly brackets, not existing entities, so the question doesn't bother me.
| 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] |