Our concern is to deal with the notion of existence and its status in onto-logical approach among analytic philosophers of the last century. As a draft of this critique we are using works of american philosopher William F. Vallicella, especially his three works: A Critique of the Quantificational Account of Existence (1983), A Paradigm Theory of Existence: Onto-Theology Vindicated (2002) and Existence: Two Dogmas of Analysis (2014). We criticise and analyse the philosophical view which suggests that to exist is what instantiation of existence is. This view is established in the works of Gottlob Frege, Bertrand Russell and Willard V. O. Quine. We also cope with the Vallicella's critique of ontology, which validates the statements about non-existent objects, and with his critique of existence being a first order property.