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Full Idea
There is only one class having a given set of members, whereas there are always many different characteristics by which a given class may be defined.
Gist of Idea
Members define a unique class, whereas defining characteristics are numerous
Source
Bertrand Russell (Introduction to Mathematical Philosophy [1919], II)
Book Ref
Russell,Bertrand: 'Introduction to Mathematical Philosophy' [George Allen and Unwin 1975], p.13
| 14428 | Members define a unique class, whereas defining characteristics are numerous [Russell] |
| 16449 | In modal set theory, sets only exist in a possible world if that world contains all of its members [Stalnaker] |
| 13030 | Extensionality: ∀x ∀y (∀z (z ∈ x ↔ z ∈ y) → x = y) [Kunen] |
| 13013 | The Axiom of Extensionality seems to be analytic [Maddy] |
| 13014 | Extensional sets are clearer, simpler, unique and expressive [Maddy] |
| 10097 | Axiom of Extensionality: for all sets x and y, if x and y have the same elements then x = y [George/Velleman] |
| 10872 | Extensionality: Two sets are equal if and only if they have the same elements [Clegg] |
| 18836 | A set may well not consist of its members; the empty set, for example, is a problem [Rumfitt] |
| 18837 | A set can be determinate, because of its concept, and still have vague membership [Rumfitt] |