CathInfo.com

Two different animals, both have only one thing in common, the word implicit

A)The theory of salvation by implicit desire for baptism of St. Thomas, which required an explicit desire to be a Catholic and the  belief in the Trinity and the incarnation. Example: a person who desires to be a Catholic, and believes in the Trinity and the Incarnation, but he has no one to baptize him, or he does not know that he needs to be baptized, and he dies.

F) The theory of salvation by implicit faith in Jesus Christ,  which DOES NOT required an explicit desire to be a Catholic and the  belief in the Trinity and the incarnation. Example: A Jew, Muslim, or Bhuddist who worships his god in all love and belief can be saved, although he does not believe in Christ or his Church. (place your own example here if you don't like mine)

No man ever had the grace of the Holy Ghost except through faith in Christ either explicit or implicit: and by faith in Christ man belongs to the New Testament. Consequently whoever had the law of grace instilled into them belonged to the New Testament. (Summa Theologica, Ia IIae, q.106, a.1, ad 3)

Therefore, as regards the primary points or articles of faith, man is bound to believe them, just as he is bound to have faith; but as to other points of faith, man is not bound to believe them explicitly, but only implicitly, or to be ready to believe them, in so far as he is prepared to believe whatever is contained in the Divine Scriptures. Then alone is he bound to believe such things explicitly, when it is clear to him that they are contained in the doctrine of faith. (Summa Theologica, IIa IIae, q.2, a.5)

It is impossible to believe explicitly in the mystery of Christ, without faith in the Trinity, since the mystery of Christ includes that the Son of God took flesh; that He renewed the world through the grace of the Holy Ghost; and again, that He was conceived by the Holy Ghost. Wherefore just as, before Christ, the mystery of Christ was believed explicitly by the learned, but implicitly and under a veil, so to speak, by the simple, so too was it with the mystery of the Trinity. And consequently, when once grace had been revealed, all were bound to explicit faith in the mystery of the Trinity: and all who are born again in Christ, have this bestowed on them by the invocation of the Trinity, according to Mat. 28:19: “Going therefore teach ye all nations, baptizing them in the name of the Father, and of the Son and of the Holy Ghost.” (Summa Theologica, IIa IIae, q.2, a.8)

Many of the gentiles received revelations of Christ, as is clear from their predictions. Thus we read (Job 19:25): “I know that my Redeemer liveth.” The Sibyl too foretold certain things about Christ, as Augustine states (Contra Faust. xiii, 15). Moreover, we read in the history of the Romans, that at the time of Constantine Augustus and his mother Irene a tomb was discovered, wherein lay a man on whose breast was a golden plate with the inscription: “Christ shall be born of a virgin, and in Him, I believe. O sun, during the lifetime of Irene and Constantine, thou shalt see me again”*. If, however, some were saved without receiving any revelation, they were not saved without faith in a Mediator, for, though they did not believe in Him explicitly, they did, nevertheless, have implicit faith through believing in Divine providence, since they believed that God would deliver mankind in whatever way was pleasing to Him, and according to the revelation of the Spirit to those who knew the truth, as stated in Job 35:11: “Who teacheth us more than the beasts of the earth.” (Summa Theologica, IIa IIae, q.2, a.7, ad 3)

Unbelief does not so wholly destroy natural reason in unbelievers, but that some knowledge of the truth remains in them, whereby they are able to do deeds that are generically good. With regard, however, to Cornelius, it is to be observed that he was not an unbeliever, else his works would not have been acceptable to God, whom none can please without faith. Now he had implicit faith, as the truth of the Gospel was not yet made manifest: hence Peter was sent to him to give him fuller instruction in the faith. (Summa Theologica, IIa IIae, q.10, a.4, ad 3)

Though all do not know explicitly the power of the sacrifices, they know it implicitly, even as they have implicit faith, as stated above (q. 2, AA 6,7). (Summa Theologica, IIa IIae, q.85 a.4, ad 2)

As stated above (a. 1, ad 2; q. 68, a. 2) man receives the forgiveness of sins before Baptism in so far as he has Baptism of desire, explicitly or implicitly; and yet when he actually receives Baptism, he receives a fuller remission, as to the remission of the entire punishment. So also before Baptism Cornelius and others like him receive grace and virtues through their faith in Christ and their desire for Baptism, implicit or explicit: but aferwards when baptized, they receive a yet greater fulness of grace and virtues. Hence in Ps. 22:2, “He hath brought me up on the water of refreshment,” a gloss says: “He has brought us up by an increase of virtue and good deeds in Baptism.” (Summa Theologica, IIIa q.69, a.4, ad 2)

Venial sin is never forgiven without some act, explicit or implicit, of the virtue of penance, as stated above (a. 1): it can, however, be forgiven without the sacrament of Penance, which is formally perfected by the priestly absolution, as stated above (q. 87, a. 2). Hence it does not follow that infusion of grace is required for the forgiveness of venial sin, for although this infusion takes place in every sacrament, it does not occur in every act of virtue. (Summa Theologica, IIIa, q.87, a.2, ad 2)

As stated above (a. 2), no infusion of fresh grace is required for the forgiveness of a venial sin, but it is enough to have an act proceeding from grace, in detestation of that venial sin, either explicit or at least implicit, as when one is moved fervently to God. Hence, for three reasons... (Summa Theologica, IIIa, q.87, a.3)

Ambrose here gives this reason why exception could, without inconsistency, be allowed in the primitive Church; namely, because the whole Trinity is implied in the name of Christ, and therefore the form prescribed by Christ in the Gospel was observed in its integrity, at least implicitly. (Summa Theologica, IIIa, q.66, a.6, ad 2)

What about the pagans who were alive at the First Coming of Jesus Christ, say, those living in North America at the time?