This study investigates the problem of quantifier scope ambiguity in natural languages and the various ways with which it has been accounted for, some of which are problematic for monotonic theories of grammar like Combinatory Categorial Grammar (CCG) which strive for solutions that avoid non-monotonic functional application, and assume complete transparency between the syntax and the semantics interface of a language. Another purpose of this thesis is to explore these proposals on examples from Turkish and to try to account for the meaning differences that may be caused by word order and see how the observations from Turkish fit within the framework of CCG.