Within Protestantism there is not some one additional entity to which the term “visible catholic Church” refers, consisting of these denominations, congregations, believers and their children.

As opposed to the one entity which is the Roman Catholic Church, of course.

Unfortunately, the only thing the author shows is that philosophy students should be forced, at gunpoint if necessary, to take a formal course in logic before they graduate.

His argument is as follows:

This was the error of assuming that unity of type is sufficient for unity of composition. In actuality, things of the same type do not by that very fact compose a unified whole.

At first glance this might suffice for a Platonist, but consider this: who gets to decide which collections of things of the same type get their own unified whole, and which don’t?

If the Westminster Confession defines the “visible catholic Church” as the unity of Protestant Christians, then who is the author to claim that that entity does not exist, whilst the entity known as the Roman Catholic Church does?

I assume that the author would assert that the doctrines of the Roman Catholic church hold more authority than the Westminster Confession. But this is not an argument, it is an axiom: he has not “shown” anything, but simply restated his underlying assumption.

I can, in fact, refute his argument by construction.

Consider the set C, defined as the set of persons adhering to a Christian tradition descended from those developed in the Protestant Reformation.

If mathematics has any access at all to the world of Platonic ideals, then I have just shown that there exists, both in our world and in the ideal world, an entity, C, which is identical to the “visible catholic Church” as defined in the Westminster Confession.

Quod Erat Demonstrandum