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Full Idea
Extensionality is built into the semantics of ordinary logic. When a name-letter is interpreted as denoting something, we just provide the object denoted. All that we provide for a one-place predicate-letter is the set of objects that it is true of..
Gist of Idea
Extensionality is built into ordinary logic semantics; names have objects, predicates have sets of objects
Source
David Bostock (Intermediate Logic [1997])
Book Ref
Bostock,David: 'Intermediate Logic' [OUP 1997], p.356
A Reaction
Could we keep the syntax of ordinary logic, and provide a wildly different semantics, much closer to real life? We could give up these dreadful 'objects' that Frege lumbered us with. Logic for processes, etc.
13606 | Humean conceptions of reality drive the adoption of extensional logic [Ellis] |
13821 | Extensionality is built into ordinary logic semantics; names have objects, predicates have sets of objects [Bostock] |
13362 | If an object has two names, truth is undisturbed if the names are swapped; this is Extensionality [Bostock] |
9458 | Extensionalists say that quantifiers presuppose the existence of their objects [Jacquette] |
21719 | Extensionalism means what is true of a function is true of coextensive functions [Linsky,B] |