Randy,
Perhaps I can continue the dialogue with you since your counterpart has disappeared. I think your question is answered quite concretely through the philosophical and natural argumentation by these theologians. It rang like loud church bells of truth in my ear when I read this.
Hans Urs von Balthaser: “The only unifying factor among them is the denial of papal primacy. The
negation created a purely formal unity, but this unity, deriving from
negation -within every non-Catholic church as well as between them - remains
abstract in consent, because the most concrete factor of unity has been eliminated.”
Ignatz Döllinger quoting a prominent German Protestant theologian [regarding the nature of Protestant churches]: “It is untrue and confusing to speak of unity when this is merely sought after, existing only as a concept, and when nothing can be presented that shows the alleged unity
numerically.”
Johann Adam Möhler says in his
Die Einheit in der Kirche: "To call the external manifestation of internal unity the “empirical concept” of the Church, which must be replaced by the “ideal”, means to put an abstraction, an empty concept, death, in the place of
life. [In other words, non-Catholics would rather have the “invisible abstract” church(es), possessing the mark of disunity, replace the “visible concrete” Church, which possesses unity.]
The once-Anglican bishop
John Henry Newman complained that “the (then) existing unity of the English church was
abstract; in truth one should speak about ‘churches’.”
Funny that I quoted several Germans and one Englishman to make the point.