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Full Idea
Vagueness in respect of membership is consistent with determinacy of the set's identity, so long as a set's identity is taken to consist, not in its having such-and-such members, but in its being the extension of the concept A.
Gist of Idea
A set can be determinate, because of its concept, and still have vague membership
Source
Ian Rumfitt (The Boundary Stones of Thought [2015], 8.4)
Book Ref
Rumfitt,Ian: 'The Boundary Stones of Thought' [OUP 2015], p.241
A Reaction
To be determinate, it must be presumed that there is some test which will decide what falls under the concept. The rule can say 'if it is vague, reject it' or 'if it is vague, accept it'. Without one of those, how could the set have a clear identity?
| 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] |