Saint Robert Bellarmine's Definition of the Church

"Now, our opinion is that the Church is only one, and not two; and that one and true [Church] is the assembly of men gathered in the profession of the same Christian faith, and in the communion of the same sacraments, under the reign of legitimate pastors, and especially of the one vicar of Christ on earth, the Roman Pontiff. From which definition, one can easily gather which men pertain to the Church, and indeed those who do not pertain to her. For there are three parts of this definition: the profession of the true faith, the communion of the sacraments, and subjection to the legitimate shepherd, the Roman Pontiff. By reason of the first part all infidels are excluded, both those who were never in the Church, such as Jews, Turks, and pagans; and those who were, and went back, such as heretics and apostates. By reason of the second part catechumens and excommunicates are excluded, the former because they are not admitted to the communion of the sacraments, and the latter because they are cast out. By reason of the third part are excluded schismatics, who have faith and sacraments, but are not subject to the legitimate pastors, and therefore they profess the faith and receive the sacraments outside [of the Church]. But all others are included, even the reprobate, the wicked, and the impious.

"And so there is this difference between our opinion and all others, that all others require internal virtues to constitute someone in the Church, and on that account they make the true Church invisible; but we, although we believe that all virtues, such as faith, hope, charity, etc., are found in the Church, yet that anyone can in some way be called a part of the true Church, about which Scripture speaks, we do not believe any internal virtues are required, but only external profession of the faith, and communion of the sacraments, which are perceived by the senses. For the Church is a assembly of men as visible and palpable as is the assembly of the people of Rome, or the kingdom of France, or the republic of Venice."