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Single Idea 6103

[from 'The Philosophy of Logical Atomism' by Bertrand Russell, in 4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets ]

Full Idea

With the ordinary view of classes you would say that a class that has only one member was the same as that one member; that will land you in terrible difficulties, because in that case that one member is a member of that class, namely, itself.

Clarification

(the problem is classes that turn out to be members of themselves)

Gist of Idea

Normally a class with only one member is a problem, because the class and the member are identical

Source

Bertrand Russell (The Philosophy of Logical Atomism [1918], §VII)

Book Reference

Russell,Bertrand: 'Russell's Logical Atomism', ed/tr. Pears,David [Fontana 1972], p.126


A Reaction

The problem (I think) is that classes (sets) were defined by Frege as being identical with their members (their extension). With hindsight this may have been a mistake. The question is always 'why is that particular a member of that set?'