Here is some more of the context for
Satis Cognitum that helps us to understand better what is being communicated:
papalencyclicals.net/Leo13/l13satis.htm
Pope Leo here is explaining that the Church is not a body alone or a soul alone but that the true Church has both a body and soul, which is inseparable to the extent that there is not a separate soul of the Church and a separate body but they are united in one Catholic Church.
Exactly The Pius X Catechism SEPARATES them:
"29 Q. But if a man through no fault of his own is outside the Church, can he be saved?
A. If he is outside the Church through no fault of his, that is, if he is in good faith, and if he has received Baptism, or at least has the implicit desire of Baptism; and if, moreover, he sincerely seeks the truth and does God’s will as best he can such a man is indeed separated from the body of the Church, but is united to the soul of the Church and consequently is on the way of salvation"
Now what Pius X’s catechism proposes is that it can be that one could be a member of this Church through being united to the soul while being invincibly ignorant of the necessity of belonging to the body. Such a person would truly be a member and united to the Church but would not be visibly united to the body.
It does not say that see above.
Membership in the Church is not dependent upon any other witness except God alone, and God alone weighs the hearts and its desires. If a person explicitly desires water baptism, but is unable to attain it, and has made an act of perfect contrition and has perfect charity for God, then he is united to the Church through his desire. If he is hindered from receiving the sacrament and dies in such a state, God would judge the person’s heart. His salvation is not dependent upon whether others thought him to be in the Church. It is dependent upon his desire, which unites him to the Church. Now if someone has a simple desire, but is unwilling to act upon it, then this desire would not be salutary but would actually condemn them. Therefore, with such a desire for baptism, the person must have a willingness to complete the action, which only God himself can judge.
All very confusing here. How are they united to the Church?
Do they need to believe in the Trinity? The Incarnation? The necessity of Baptism for salvation?
Which infallible document defines “Baptism of Desire”?
Sources?
Pope Leo is saying it is a grave error to separate soul from the body but it is clearly stated as such in the Pius X catechism:
Pope Leo XIII, Satis Cognitum (# 3), June 29, 1896:
“From this it follows that those who arbitrarily conjure up and picture to themselves a hidden and invisible Church are in grievous and pernicious error:…It is assuredly as impossible that the Church of Jesus Christ can be the one or the other, as that man should be a body alone or a soul alone. The connection and union of both elements is as absolutely necessary to the true Church as the intimate union of the soul and body is to human nature.”
Pius XII understood Leo like me:
Pope Pius XII, Mystici Corporis (# 14), June 29, 1943:*
“Leo XIII, in his Encyclical Satis Cognitum asserts: “the Church is visible because she is a body.” [15] Hence they err in a matter of divine truth, who imagine the Church to be invisible, intangible, a something merely “pneumatological” as they say, by which many Christian communities, though they differ from each other in their profession of faith, are united by an invisible bond.”
link
There are very few people left in the world who could claim invincible ignorance but even so this goes for especially for Protestants, Leo’s same encyclical says:
Pope Leo XIII, Satis Cognitum (# 8), June 29, 1896:
“He requires the assent of the mind to all truths without exception. It was thus the duty of all who heard Jesus Christ, if they wished for eternal salvation, not merely to accept His doctrine as a whole, but to assent with their entire mind to all and every point of it, since it is unlawful to withhold faith from God even in regard to one single point.”
again
“Hence she regarded as rebels and expelled from the ranks of her children all who held beliefs on any point of doctrine different from her own. The Arians, the Montanists, the Novatians, the Quartodecimans, the Eutychians, did not certainly reject all Catholic doctrine: they abandoned only a certain portion of it. Still who does not know that they were declared heretics and banished from the bosom of the Church? In like manner were condemned all authors of heretical tenets who followed them in subsequent ages. “There can be nothing more dangerous than those heretics who admit nearly the whole cycle of doctrine, and yet by one word, as with a drop of poison, infect the real and simple faith taught by our Lord and handed down by Apostolic tradition” (Auctor Tract. de Fide Orthodoxa contra Arianos).”
link to Satis Cognitum
While in general the encyclical seemed to be aimed at Protestants it still well establishes that there is no way a person could belong to the soul of the Church with out belonging to the body but again Pius X catechism says:
“such a man is indeed separated from the body** of the Church, but is united to the soul of the Church and consequently is on the way of salvation”**
clear I think