Blinker hood

Protestantism itself has no visible catholic Church. It has only denominations, congregations, believers and their children. 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...What allowed the authors of the Westminster Confession to believe sincerely that there was a “visible catholic Church” other than the Catholic Church headed by the Pope, was a philosophical error. 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. For example, all the crosses that presently exist all have something in common; they are each the same type of thing, i.e. a cross. But they do not form a unified whole composed of each individual cross around the world. This crucifix, for example, in the St. Louis Cathedral Basilica, is not a part of a unified whole consisting of all the crucifixes in the world. All crucifixes are things of the same specific type, but that does not in itself make them parts that compose a unified whole spread out around the world...One way to determine whether something is an actual whole or merely a plurality of things...

...when Matthew records Jesus saying to Peter in Matthew 16:18, “upon this rock I will build My Church”, and then saying, in Matthew 18:17, “tell it to the Church”, and “listen to the Church”, the most natural way of understanding these passages is that the term ‘ekklesia’ (‘Church’) is being used in the same way in all three places. And it is clear in the Matthew 18 passages that ‘ekklesia’ there refers to the visible Church, not a merely spiritual entity. 

http://www.calledtocommunion.com/2009/09/why-protestantism-has-no-visible-catholic-church/

i) Catholic convert Bryan Cross is unintentionally comical because he wears a blinker hood. All he's done here is to invent his own definition of visibility, then proclaim that the Protestant faith fails to measure up to his idiosyncratic definition. But Bryan's tendentious yardstick was never our standard of comparison.

ii) Actually, it's unlikely that Matthew is using ekklesia in quite the same way in Mt 16 & 18. Mt 16 is a statement about the church in general while Mt 18 is a statement about local church discipline.

iii) To play along with Bryan's illustration, individual crucifixes aren't "merely a plurality of things". Bryan must know that's a false description. A "mere plurality of things" would be disparate things that share nothing essential in common. By contrast, individual crucifixes are samples or instances of the same kind of thing. They all have the same basic design. Similar shape. As well as the same symbolic purpose and significance. 

Bryan says that's insufficient for unity of composition. Suppose he's right. So what? Why should unity of composition in his specialized sense be the criterion for visibility? That's a highly idiosyncratic definition of visibility. 

iv) Variation on a theme are an interesting phenomenon. Take snowflakes. Pachelbel's canon. The Mandelbrot set. Are they "merely a plurality of things"? No. They share essential unity. 

Take da Vinci's Virgin of the Rocks. Da Vinci painted two versions of the same scene. Are they one painting or two? In a certain respect they're two different paintings, but there are degrees of difference. You can have two paintings on a different subject or two paintings on the same subject. Two paintings by different painters or two paintings by the same painter. In this case, they exemplify the one idea. Whether we count them as one or two depends on the level of abstraction.  

v) Both in principle and practice, the concept of the church is not univocal. It can stand for different things. The church has some perennial elements, like church office and sacraments. These continue from one generation to the next. 

Christianity has a corporate dimension because humans are social creatures. Moreover, humans who are otherwise unrelated can share the same experience of saving grace. That makes them a spiritual family.

But there's an interplay and overlay between the natural family and the spiritual family. In this life, natural and spiritual affinities intersect but they don't coincide. Three overlapping circles. And there's a sorting process after death.