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Single Idea 13821

[filed under theme 5. Theory of Logic / I. Semantics of Logic / 5. Extensionalism ]

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.

The 5 ideas with the same theme [semantic system built on reference to objects]:

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]