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Single Idea 18837

[from 'The Boundary Stones of Thought' by Ian Rumfitt, in 4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I ]

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 Reference

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?