Catholicam Ecclesiam: Cyril vs. Turretin on the Church's Catholicity

According to the Nicene Creed, the third mark of the church is its “catholicity” (“We believe in one holy catholic and apostolic church”). Defending the Catholic position in this post will be Cyril of Jerusalem (Catacheses, No. 18:23; 17:14, c. 347 A.D.), and rebutting that position from the Protestant perspective will be Francis Turretin (Institutes of Elenctic Theology, Eighteenth Topic, Thirteenth Question, c. 1685).

First, Cyril of Jerusalem:

“The Church is called Catholic or universal because it has spread throughout the entire world, from one end of the earth to the other. Again, it is called Catholic because it teaches fully and unfailingly all the doctrines which ought to be brought to men’s knowledge, whether concerned with visible or invisible things, with the realities of heaven or the things of earth. Another reason for the name Catholic is that the Church brings under religious obedience all classes of men, rulers and subjects, learned and unlettered. Finally, it deserves the title Catholic because it heals and cures unrestrictedly every type of sin that can be committed in soul or in body, and because it possesses within itself every kind of virtue that can be named, whether exercised in actions or in words or in some kind of spiritual charism.

“And if ever you are sojourning in cities, inquire not simply where the Lord’s House is (for the other sects of the profane also attempt to call their own dens houses of the Lord), nor merely where the Church is, but where is the Catholic Church. For this is the peculiar name of this Holy Church, the mother of us all.”

And Francis Turretin:

“If to be called catholic is a mark of the church, this arises from God; but the Scripture is entirely silent about it. Or it arises from opponents; but they are not our judges. Or it arises from their own people; but what right have they to assume for a mark the name which they ascribe to themselves, since heretics are accustomed to set up in front of themselves specious names? … If the fathers formerly distinguished the orthodox from heretics by the name catholic, they did this… on account of the catholic and orthodox doctrine that they held…. Cyril teaches that ‘the church is called Catholic because it teaches fully and unfailingly all the doctrines which ought to be brought to men’s knowledge.’”

The issue here is not whether a church's catholicity is a matter of doctrine or not (for it surely is). The issue, rather, is whether it is by a church's doctrine alone that such a determination is to be made, or whether other factors, like pedigree and universality, are to be taken into account.

Well...?