I came across Montague's treatment of "John seeks a unicorn". He distinguishes de re and de dicto interpretations of it on the basis that the de dicto meaning does not entail the existence of any unicorn; in other words, John is seeking some set of properties that answers to the conventional description of a unicorn, but this property may not have any instances.
I'm interested in a slightly different example: "Jack seeks a woman". Here there is no doubt that women do in fact exist, but it seems ambiguous as to whether Jack is seeking a particular woman, such as his wife, or any woman, i.e. he just desires some female company. Attempting to represent this sentence in classical predicate logic does not support this distinction.
As I see it there are several options:
We could assimilate it to Montague's unicorn and say on the second interpretation it means Jack seeks some set of properties common to women.
We could go 'modal' and say that on the first interpretation, Jack seeks a set of possible worlds in which he is with a particular woman, while on the second he seeks a set of possible worlds in which he is with any woman.
We could perhaps express the distinction using intuitionistic logic, as the difference between (∃x)(Woman(x) ∧ Seeks(jack,x)) and ¬¬(∃x)(Woman(x) ∧ Seeks(jack,x)).
Maybe we could say there is no semantic ambiguity at all and the difference in the readings is just a matter of pragmatics.
I would appreciate any illumination that theoretical linguistics might shed on it. Thanks.