This paper aims at providing semantics and pragmatics as well as some syntax of various but related kinds of Korean floating quanitifiers. The synax of Categorial Grammar is used, and semantic considerations of NPs denoting nominalized properties (functions) and pragmatic considerations of discourse functions of some kinds of floating quantifiers turn out to be relevant. One of the basic syntactic facts of Korean (and Japanese) Quantifier Floating to be dealt with is as follows: There are two kinds of FQs, i.e. [Number(-Classifier)] such as ‘sey-myeng-i’ and [Number(-Classifier) -CaseMarker] such as ‘sey-myeng-ul’ and only the former shows subject/object asymmetry. The Categorial analysis to deal with these facts is to assign the category of NP/NP to non-case-marked FQs and to assign predicate modifier categories to case-marked FQs: VP/VP to ‘sey-myeng-i’ and TV/TV to ‘sey-myeng-ul’. When an FQ in front of a TV(i.e. S/NP/NP) combine with the TV by function composition, only the object NP is related to the FQ, which results in subject/object asymmetry. But case-marked VP/VP may combine with TV without causing such an effect. The semantics to support such a categorial analysis is that the NPs that FQs of NP/NP combine with are not usual ones denoting Generalized Quanifiers, but NPs with no quanrificational determiners. I use Chierchia’s (1998) notion of nominalized property (function), which should be the meaning of bare (non-quanrificational) NPs, so that the meaning of ‘sey-myeng’ (NP/NP) is provided as follows: sey-myeng => λf[3-myeng’($^{∪}$f)], where f is a nominalized function. A fuller semantic representation should be: sey-myeng => λfλQ[∋X[Q(X) ∧ gmyeng($^{∪}$f)(X) ∧ ｜X｜ = 3]], where g is a domain shifter. Related meanings, which are also based on nominalized functions can be provided for case-marked FQs of categories VP/VP and TV/TV. Another fact to be dealt with is that discourse functional factors intervene with the FQ phenomena. FQs with discourse particles such as ‘-man, -to,-ina, -kkaci’ which mean “only, even, too” and the like render the subject/object asymmetry of FQs not vaild, and unlike other FQs, discourse linked FQs can precede the host NP. In short, Korean FQ are basically NP＼NP but it can be realized as predicate modifiers of VP/VP and TV/TV in three ways: 1) with case-markers, 2) with discourse particles, and 3) in a strong discourse context where number is particularly important.