In order for theology to have a cognitive dimension, it is necessary to have procedures for testing and critically evaluating theological models. We make use of certain features of scientific models to show how science has been able to move beyond the poles of foundationalism, represented by logical positivism, and antifoundationalism or relativism, represented by the sociologists of knowledge. These ideas are generalized to show that constructing and testing theological models similarly offers a means by which theology can move beyond confessionalism and postmodernism. Our starting point is Paul Tillich's concept of God as the ground of being and the different levels of consciousness and thinking that accompany his understanding of theology. The ontological argument of Anselm is shown to play a key role, not as a proof for the existence of God but as a means for testing theological models. An example of a theological model, drawn from the domain of philosophy of science, is presented to show how theological models are constructed and tested.