|Extensionality, philosophy: (also extensionality principle, extensionality thesis) an attempt to make the language distinct by taking complete sets of denoted objects as the meaning of the referring words. See also extensions, intensions, extensional language, ambiguity, propositional attitudes.|
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|Extensionality||EMD II 306
Inference rule/lambda operator/Grandy/Wiggins: Rl: if l-((xi1 ... xin) (A ↔ B)) and when ---- (lxi1 ... lxin) [A] ----, then ---- (lxi1 ... lxin) [B] ----. would conclude - Necessary: necessary for predicates.
Problems: extensionality: Expressions in a Necessary-sentence are open to substitution of identical and existential generalization but problem: predicates: E.g. if something was the only ring of Gyges, we do not want to conclude that it was essentially magical - solution: relational view of predication> participation (Frege: fall under the expression) - if (lx1) [fX1] and (lx1) [Yx1] do not designate the same property, but are coextensive, then in extensional contexts one will include(entail) the other - which is maintained when the operator Necessary is prefixed - whereby the theory Necessary does not decide whether it is the same property or not - participation/Bradley (+).
Essays on Identity and Substance Oxford 2016
G. Evans/J. McDowell
Truth and Meaning Oxford 1977
The Varieties of Reference (Clarendon Paperbacks) Oxford 1989