What is the church? St Bellarmine gives the following definition
As thus understood, the definition of the Church given by Bellarmine is that usually adopted by Catholic theologians: "A body of men united together by the profession of the same Christian Faith, and by participation in the same sacraments, under the governance of lawful pastors, more especially of the Roman Pontiff, the sole vicar of Christ on earth"
Catholic ecclesiology states that one must possess the external and internal bonds of unity, ecclesiastical and sacramental. One is bound interiorly through the supernatural virtues of faith, hope and charity and externally by submission to the hierarchy, profession of faith and sacramental unity. St Pius X clarified that the church is one and the same and these are different angles to view the one church, the interior bonds of communion with the church does not extend beyond the visible society of the church, and while baptized non Catholics have imperfect sacramental communion, that alone does not allow salvation.
St Chrysostom says the following about an invisible church
“It is an easier thing for the sun to be quenched, than for the church to be made invisible.”
Here are the three acts of the extra ordinary magesterium we must read all subsequent interpretation in light of
It firmly believes, professes, and proclaims that those not living within the Catholic Church, not only pagans, but also Jews and heretics and schismatics cannot become participants in eternal life, but will depart “into everlasting fire which was prepared for the devil and his angels” [Matt. 25:41], unless before the end of life the same have been added to the flock; and that the unity of the ecclesiastical body is so strong that only to those remaining in it are the sacraments of the Church of benefit for salvation, and do fastings, almsgiving, and other functions of piety and exercises of Christian service produce eternal reward, and that no one, whatever almsgiving he has practiced, even if he has shed blood for the name of Christ, can be saved, unless he has remained in the bosom and unity of the Catholic Church.
Pope Innocent III and Lateran Council IV (A.D. 1215): “One indeed is the universal Church of the faithful outside which no one at all is saved…”
Pope Boniface VIII in his Papal Bull Unam Sanctam (A.D. 1302): “We declare, say, define, and pronounce that it is absolutely necessary for the salvation of every human creature to be subject to the Roman Pontiff.”
Vatican II upheld this teaching fully and Lumen Gentium and the catechism state that it is impossible for one to knowingly reject the church and be saved, salvation outside the church is due to exceptions made by God of baptized persons due to ignorance, Protestant churches are not a normative avenue of salvation
Remember the Church is One, Holy, Catholic and Apostolic, bearing the marks of infallibility, authority and indefectability. The church is a visible society composed of men, when Jesus instructed us on how to deal with a heretic, when he was expelled and treated as a heathen and a publican there was no other church to join, the same case in 1 John, the one church is the body of Christ alone.
Do not err, my brethren: if anyone follow a schismatic, he will not inherit the Kingdom of God. If any man walk about with strange doctrine, he cannot lie down with the passion. Take care, then, to use one Eucharist, so that whatever you do, you do according to God: for there is one Flesh of our Lord Jesus Christ, and one cup in the union of His Blood; one altar, as there is one bishop with the presbytery and my fellow servants, the deacons.”
— St. Ignatius Of Antioch, Epistle to the Philadelphians, 3:2-4:1, 110 A.D.
Saint Ambrose (died A.D. 397): “Where Peter is therefore, there is the Church. Where the Church is there is not death but life eternal. …Although many call themselves Christians, they usurp the name and do not have the reward.” (The Fathers of the Church )
Saint Jerome (died A.D. 420): “As I follow no leader save Christ, so I communicate with none but your blessedness, that is, with the Chair of Peter. For this, I know, is the rock on which the Church is built. …This is the ark of Noah, and he who is not found in it shall perish when the flood prevails. …And as for heretics, I have never spared them; on the contrary, I have seen to it in every possible way that the Church’s enemies are also my enemies.” (Manual of Patrology and History of Theology )
Saint Augustine (died A.D. 430): “No man can find salvation except in the Catholic Church. Outside the Catholic Church one can have everything except salvation. One can have honor, one can have the sacraments, one can sing alleluia, one can answer amen, one can have faith in the name of the Father and of the Son and of the Holy Ghost, and preach it too, but never can one find salvation except in the Catholic Church.” (Sermo ad Caesariensis Ecclesia plebem )