Baude on the nature of a university

One ambiguity in Will Baude's post on Catholic universities is whether he thinks that a Catholic university committed to Ex Corde Ecclesiae could even lay claim to the title of "university." Or is it that such a university could not be considered "great." He seems to have an "essence" of a university in mind that would exclude such an institution from the category of "university" altogether. Under Ex Corde, the main task of a Catholic university is to be consecrated to the cause of the truth. The essence of a university, according to Baude, is to remain ideologically neutral and to be in a state of perpetual opposition to the existing order. Under Baude's view, what is a university for?

Under Baude's thinking, is Harvard even a university? or is it only a university because no one thinks that it takes its motto ("Veritas") seriously?

Richard