more from this thinker | more from this text
Full Idea
There seem strong grounds for rejecting the thesis that a set consists of its members. For one thing, the empty set is a perpetual embarrassment for the thesis.
Gist of Idea
A set may well not consist of its members; the empty set, for example, is a problem
Source
Ian Rumfitt (The Boundary Stones of Thought [2015], 8.4)
Book Ref
Rumfitt,Ian: 'The Boundary Stones of Thought' [OUP 2015], p.240
A Reaction
Rumfitt also says that if 'red' has an extension, then membership of that set must be vague. Extensional sets are precise because their objects are decided in advance, but intensional (or logical) sets, decided by a predicate, can be vague.
| 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] |