From the very beginning up to now the concept of existence has been one of the most controversial ones among the philosophers. Such discussions can be divided into two main parts. The first one refers to the ontological aspects of existence for which one is involved with two schools namely Possibilism and Actualism anyone of which tries to talk of the scope and limit of things within their own metaphysical principles. The second part includes the issues about existence as a predicate. For these discussions and because we want to consider existence as a first or a second order predicate, we can either talk about the possible existence or its counterpart i.e., the necessary existence of the things. The necessary existence is one of the formula which, in the simplest quantified modal logic of S5 and just like those formula such as BF and CBF, is provable and valid. Although talking of the validity of necessary existence things needs to provide a second degree concept of existence but discussing the validity of Barcan formula needs an existential commitment to the possible things which the possibilists believe are not among the existent things. Following Linsky and Zalta and for defending BF and NE formula, Timotty Williamson has excluded the validity issue of Barcan formula from the first part and he has transferred it to the second part. Thus using the modal properties he provides a new definition of possible things through which one can defend the validity of Barcan formula as well as the necessary existence of things without having any existential commitment to the possibilia. Afterwards, Williamson provides the conditions for talking of the logical existence for things by providing a second-order concept of existence in unrestricted quantification theory and in this way one can have a better understanding of necessary existence.