ok based on that reference and the ones provided in the OP
**
As used in context in the NT**
Are there any believers who are not part of the ekklesia ( I don’t need to paste the OP; right?)
Are there any unbelievers included in the ekklesia?
Only actual baptism makes one a formal member of the Church; baptism of desire does not do so. Since justification can be received by desire for baptism, as Trent states, justification and thus the state of grace can be received without formal membership in the Church. The desire for baptism is sufficient.
**Implicit Desire **
Later Catholic teaching has clarified the nature of this desire and shown it can be either explicit or implicit. One has explicit desire for baptism if he consciously desires and resolves to be baptized (as with catechumens and others). One has an implicit desire if he would resolve to be baptized if he knew the truth about it.
How does implicit desire work? Consider the following analogy: Suppose there is a person who is sick and needs a shot of penicillin to make him better. He tells his physician, “Doc, you’ve got to give me something to help me get well!” The doctor looks at his chart and says, “Oh, what you want is penicillin. That’s the right drug for you.” In this case the man had an explicit desire for a drug to make him better – whatever that drug might be – and the appropriate one was penicillin. He thus had an implicit desire for penicillin even if he had not heard of it before. Thus the doctor said: “What you want is penicillin.” This shows that it is possible to want something without knowing what it is.
A person who has a desire to be saved and come to the truth, regardless of what that truth turns out to be, has an implicit desire for Catholicism and for the Catholic Church, because that is where truth and salvation are obtained. By resolving to pursue salvation and truth, he resolves to pursue the Catholic Church, even though he does not know that is what he is seeking. He thus implicitly longs to be a Catholic by explicitly longing and resolving to seek salvation and truth.
Papal and conciliar writings in the last hundred years have clarified that those who are consciously non-Catholic in their theology may still have an overriding implicit desire for the truth and hence for Catholicism. Pope Pius XII stated that concerning some of “those who do not belong to the visible Body of the Catholic Church . . . by an unconscious desire and longing they have a certain relationship with the Mystical Body of the Redeemer” (Mystici Corporis 103).
How does this work? Consider our example of the sick man who needs penicillin. Suppose that he thinks that a sulfa drug will cure him and he explicitly desires it. So he tells the doctor, “Doc, I’m real sick, and you’ve got to give me that sulfa drug to make me better.” But the doctor notices on his chart that he has an allergy to sulfa drugs, and says, “No, you don’t want that; what you really want is penicillin.” In this case the person’s primary desire is to get well; he has simply mistaken what will bring that about. Since his primary desire to be well, he implicitly desires whatever will cause that to happen. He thus implicitly desires the correct drug and will explicitly desire that drug as soon as he realizes the sulfa would not work.
As papal and conciliar writings have indicated, the same thing is possible in religion.** If a person’s primary desire is for salvation and truth then he implicitly desires Catholicism even if he is consciously mistaken about what will bring him salvation and truth. He might be a member of some other church, yet desire salvation and truth so much that he would instantly become a Catholic if he knew the truth concerning it. In this case, his primary desire would be for salvation and truth – wherever that might be found – rather than his primary desire being membership in a non-Catholic church. **
However, the situation could be reversed. It is possible for a person to have a stronger desire not to be a Catholic than to come to the truth. This would be the case when people resist evidence for the truth of Catholicism out of a desire to remain non-Catholic. In this case their primary desire would not be for the truth but for remaining a non-Catholic. Thus their ignorance of the truth would not be innocent (because they desired something else more than the truth), and it would constitute mortal sin.
Even though some radical traditionalists are disobedient to the papal and conciliar documents which teach the possibility of implicit desire sufficing for salvation, the Church has still taught for centuries that formal membership in the Church is not an absolute necessity for salvation. This was the point made by Trent when it spoke of desire for baptism bringing justification. The issue of whether desire for baptism saves and the issue of whether that desire can be explicit or implicit are two separate subjects which radical traditionalists often confuse. If we keep them separate, it is extremely clear from the Church’s historic documents that formal membership in the Church is not necessary for salvation.
Taken from:
The Necessity of Being Catholic
by James Akin
catholicculture.org/culture/library/view.cfm?recnum=3447
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I encourage you to read the entire article.
