What denotation do linguists assign to the predicate exists in order to make the right predictions about the truth conditions of sentences like
- Santa does not exist.
- Unicorns do not exist.
- My neighbor Bob exists.
- Dogs exist.
Obviously, the denotation would need to make (1) and (2) true, while also ensuring that sentences like (5) are true and sentences like (6) are false.
- Unicorns have exactly one horn.
- Unicorns have exactly two horns.
Also, how is the semantics of the predicate exists related to the semantics of the quantifier some?