It's unbelievable that he is trying to say that St. Paul taught that the Gentiles could be saved without the Faith. St. Paul says "For not the hearers of the law are just before God: but the doers of the law shall be justified." This is not saying that the Gentiles were justified!

Saint Paul literally says "they have not the law". He says they "do by nature those things that are of the law; these, having not the law, are a law to themselves"

Only the doers of the law are justified..the law which the gentiles do not have! They do by nature things that are of the law (those "things" being the natural law), he does not say that they do the law. (Natural and divine)

2:12 For whosoever have sinned without the law shall perish without the law: and whosoever have sinned in the law shall be judged by the law

2:15 Who shew the work of the law written in their hearts, their conscience bearing witness to them: and their thoughts between themselves accusing or also defending one another,

It's unbelievable that he is trying to say that St. Paul taught that the Gentiles could be saved without the Faith. St. Paul says "For not the hearers of the law are just before God: but the doers of the law shall be justified." This is not saying that the Gentiles were justified!

Saint Paul literally says "they have not the law". He says they "do by nature those things that are of the law; these, having not the law, are a law to themselves"

Only the doers of the law are justified..the law which the gentiles do not have! They do by nature things that are of the law (those "things" being the natural law), he does not say that they do the law. (Natural and divine)

Now you are just lying. I quoted Aquinas and highlighted an underlined the phrase (look back at my prior post). I'll make it red now so you can't miss it:

Hence by nature should mean nature reformed by grace. For he is speaking of gentiles converted to the faith, who began to obey the moral precepts of the law by the help of Christ’s grace. Or by nature can mean by the natural law showing them what should be done, as in a psalm: there are many who say, ‘who shows us good things?’ The light of your countenance, O Lord, is signed upon us (Ps 4:6), i.e., the light of natural reason, in which is God’s image. All this does not rule out the need of grace to move the affections any more than the knowledge of sin through the law (Rom 3:20) exempts from the need of grace to move the affections.

It is clearly established from this same epistle [to the Romans], chap. 3 and 4, that no one is justified without faith in Christ.

...

For in the first part of his epistle [to the Romans] he wished to show the necessity of the Christian faith, without which no man can be justified before God, whether he is a gentile or a Judean.

...

For when the Apostle says the doers of the Law shall be justified, he speaks of those who observe the whole Law. For, as stated in James 2, 'He who offends in one point has become guilty of all.' However, in this passage [Romans 2:13-15] the Apostle does not teach that gentiles, who do not have the Law, by nature observe the whole Law; but he says that they show that the work of the Law has been written in their hearts when they do things that belong to the Law, that is, when they perform something according to the rule of the Law.

St. Robert Bellarmine, De Gratia et Libero Arbitrio, Book 5, Chapter 2

Your last sentence is just silly. That is not what Pius IX is talking about. You are interpreting the Pope (incorrectly) as saying that the people he refers to will become Catholic before they die

Now, it is logically impossible to claim that those people discussed in the second section (the invincibly ignorant) are NOT outside of the Church when they die. Why? Because they are described as "invincibly ignorant of our most holy religion." Both groups of people described are outside of the Catholic unity. Neither group is Inside the Church at their death as you try to claim.

So, both groups are non-Catholic and die in that state. But the first group dies in a state of culpable "error," while the second group dies "not guilty." Again, this make perfect sense because, although both are not Catholic, the first group cannot "arrive at eternal salvation" because of its culpable error, while the second group can "attain eternal life" because they are not culpable.

And you still haven't answered by question that I have now asked you at least 4 times: Where do the "invincibly ignorant" who die Outside the Church go immediately after they die?

Whoever wills to be saved, before all things it is necessary that he holds the catholic faith. Unless a person keeps this faith whole and undefiled, without doubt he shall perish eternally. The catholic faith is this, that we worship one God in the Trinity, and the Trinity in unity, neither confounding the persons nor dividing the substance. For there is one person of the Father, another of the Son, and another of the holy Spirit. But the Godhead of the Father, of the Son and of the holy Spirit is one, the glory equal, and the majesty co-eternal. Such as the Father is, such is the Son, and such is the holy Spirit. The Father uncreated the Son uncreated and the holy Spirit uncreated. The Father infinite, the Son infinite and the holy Spirit infinite. The Father eternal, the Son eternal and the holy Spirit eternal. Yet they are not three eternals, but one eternal. As also they are not three uncreateds nor three infinites, but one uncreated and one infinite. Likewise the Father is almighty, the Son is almighty and the holy Spirit is almighty. Yet they are not three almighties, but one almighty. Likewise the Father is God, the Son is God and the holy Spirit is God. Yet they are not three gods, but one God. Likewise the Father is Lord, the Son is Lord and the holy Spirit is Lord. Yet they are not three lords, but one Lord. For just as we are compelled by the Christian truth to acknowledge each person by himself to be God and Lord, so we are forbidden by the catholic religion to say there are three gods or three lords. The Father is made by none, neither created nor begotten. The Son is from the Father alone; not made nor created, but begotten. The holy Spirit is from the Father and the Son; not made nor created nor begotten, but proceeding. So there is one Father, not three fathers; one Son, not three sons; one holy Spirit, not three holy spirits. And in this Trinity nothing is before or after, nothing is greater or less; but the whole three persons are co-eternal together and co-equal. So that in all things, as has been said above, the unity in Trinity and the Trinity in unity is to be worshipped. Whoever, therefore, wishes to be saved, let him think thus of the Trinity.

It is also necessary for salvation to believe faithfully the incarnation of our lord Jesus Christ. The right faith, therefore, is that we believe and confess that our lord Jesus Christ, Son of God, is God and man. God, of the substance of the Father, begotten before the ages; and man, of the substance of his mother, born in the world. Perfect God, perfect man, subsisting of a rational soul and human flesh. Equal to the Father according to his Godhead, less than the Father according to his humanity. Although he is God and man, he is not two, but one Christ. One, however, not by conversion of the Godhead into flesh, but by the taking of humanity into God. One altogether, not by confusion of substance, but by unity of person. For as a reasoning soul and flesh is one man, so God and man is one Christ. He suffered for our salvation and descended into hell. On the third day he rose from the dead. He ascended into heaven and sits at the right hand of God the Father almighty. Thence he shall come to judge the living and the dead. At his coming all shall rise again with their bodies, and shall give an account of their own deeds. Those who have done good shall go into eternal life, but those who have done evil shall go into eternal fire.

This is the catholic faith. Unless a person believes it faithfully and firmly, he cannot be saved.

So you think St. Paul is giving a history lesson about "the gentiles?" Read more closely. Pay attention to verb tenses. If you are not familiar with the importance of verb tenses, maybe you should not be arguing with me and calling me a heretic?

Then you bring up the necessity of explicit faith in the Trinity and Incarnation. Are you drunk? That is exactly what the doctrine of "invincible ignorance concerning our most holy religion" excludes.

Pius IX says those people who do not know about the Trinity or the Incarnation, through no fault of their own, are not going to be punished. Why? Because they are not culpable for not knowing such things. It is not their fault that a Catholic priest did not penetrate the Amazon jungle before they died. But they were required to cooperate with divine grace and follow the natural law (a rare feat). And if they do that, they will "attain eternal life."

Yes, a person who is aware of the Catholic faith (i.e., one that is not invincibly ignorant) must believe the Catholic faith to be saved. Duh. We are discussing people who, for whatever reason, have not heard about the Catholic faith.