Papal Infallibility - Specifics

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Calvin:
As a seeker, it seems to me that the only way one can “prove” that a Pope might have taught error (and thus is fallible) is if one can find two “infallible” statements that contradict each other. I’ve noticed a pattern when I read Catholic apologetic materials where a Protestant will claim to find just such a contradiction and a Catholic apologist either responds with: 1) “that really wasn’t an error” (and then harmonizes the two views) or 2) “that statement wasn’t infallible” (and then points out the narrow criteria for making a statement ex cathedra). The problem is that, unless we have a definite list of the supposed infallible statements we can’t evaluate whether or not any of them contradict each other.
We could probably do something similar with regards to the inerrancy of Scripture. Critics of Christianity often point out the number of verses in which Scripture appears to contradict itself. Of course, since Christians already presuppose that Scripture is inerrant, they might address these apparent contradictions, for example, by showing that what’s there is a paradox, rather than a contradiction. Or Christians could show how the critic misunderstood the verses.

You might want to be a little bit more specific about Orientalium Ecclesiarum and Unam Sanctam, but that probably deserves a thread of its own.
 
Br. Rich
  • “Would then, Ordinatio Sacerdotalis meet the criteria for a papal “ex cathedra’ statement?”
No, because it was already an infallible teaching of the Deposit of Faith. The Doctrine was not defined, but restated in Ordinatio Sacerdotalis.*

The Pope may not be defining a new doctrine, but his is saying that his judgement must be “definitively” held by all the Church’s faithful.

I declare that the Church has no authority whatsoever to confer priestly ordination on women and that this judgment is to be definitively held by all the Church’s faithful.

OK, there is a difference between defining a doctrine, and declaring that a judgement must be definitively held – but that doesn’t really make things all that clear for me. 😦

Cardinal Ratzinger mentions the “ordinary Papal Magisterium”, i.e.:

In this case, an act of the ordinary Papal Magisterium, in itself not infallible, witnesses to the infallibility of the teaching of a doctrine already possessed by the Church.

Can there be ex cathedra statements from the ordinary Papal Magesterium, or are ex cathedra statements, by definition, restricted to exercises of the extraordinary Papal Magesterium that are defining new dogma?

Pius IX’s Ineffabilis Deus is considered to be a papal ex cathedra statement that solemnly declared the Dogma of the Immaculate Conception. How does one know that Ineffabilis Deus is a document that contains an ex cathedra teaching that is infallible?

I guess my question is this, how can Catholics tell when a papal document falls into either the infallible Ineffabilis Deus category, the Ordinatio Sacerdotalis category that affirms an infallible doctrine, or a category that is fallible pious opinion of the pope?

For example, does Humanae Vitae fall into the Ordinatio Sacerdotalis category? I think that one could easily make the case that in Humanae Vitae, that Pope Paul IV affirms moral truths that are “founded on the written Word of God, and constantly held and applied in the Tradition of the Church”, and these moral truths have “been set forth infallibly by the ordinary universal Magisterium”.
 
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Matt16_18:
For example, does Humanae Vitae fall into the Ordinatio Sacerdotalis category? I think that one could easily make the case that in Humanae Vitae, that Pope Paul IV affirms moral truths that are “founded on the written Word of God, and constantly held and applied in the Tradition of the Church”, and these moral truths have “been set forth infallibly by the ordinary universal Magisterium”.
Fr. Brian Harrison does that and more in his article, " Status of the Encyclical *Ex Cathedra *Humanae Vitae".

Some of his reasons include his conclusion that the teaching against contraception in HV is a “doctrine to be held” (tenenda), and that the object of papal infallibility in the 1870 definition included moral teaching to be held (tenenda). Thus, not only would it be in the *Ordinatio Sacerdotalis * category, but it is also Ex Cathedra.

I find his arguments interesting, but I need to do further research on this issue before I find this totally convincing .
 
Vincent

The CDF’s Doctrinal Commentary on the Professio Fidei includes sententia definitive tenenda as another category of doctrine that can be defined solemnly when the Pope speaks ex cathedra. … And guess what: … “The doctrine that priestly ordination is reserved only to men” (Ordinatio Sacerdotalis) was listed by the CDF as an example of a doctrine in this category.

Hmm … if you have this right, the CDF is saying that the pope was speaking ex cathedra when he issued Ordinatio Sacerdotalis.

So do we have at least two types of papal documents that have been received by the faithful by the pope speaking ex cathedra? :confused: ------

One, the document that solemnly defines a new dogma, e.g. Ineffabilis Deus;

and

two, the document “that is not in itself infallible”, but is instead a “formal declaration” that requires that all the faithful to give their give their “definitive and irrevocable assent” to an infallible doctrine of the depositum fide that is taught by the ordinary and universal Magisterium, e.g. Ordinatio Sacerdotalis.
 
Vincent

You slipped in your post #23 while I was writing my post #24. I see that you answered my questions.

Now I need to read the article you referenced ….
 
Vincent

Very interesting article. 👍

… the thesis is sustained that the teaching against contraception in Pope Paul VI’s encyclical letter Humanae Vitae (25 July 1968) is infallible, not merely by virtue of being an instance of the constant, ordinary and universal magisterium of the Popes and Catholic Bishops against this practice, but because the encyclical itself contains (in article 14) an ex cathedra definition.’

The article states that ex cathedra definitions are not restricted to dogma alone:

Certainly, Lio’s thesis goes against the common view of theologians (both those who assent to Humanae Vitae and those who dissent from it), who have usually described the encyclical as being, in itself, a “non-infallible” document. Very often this conclusion seems to be drawn merely from the fact that there is no definition of a dogma - a point of revealed truth to be held as “of faith” (de fide) - in Pope Paul’s encyclical. But Lio’s point is that such definitions, while they represent the most solemn form of papal teaching, are not the only form which satisfied the conditions for an ex cathedra definition as laid down by the constitution Pastor Aeternus of Vatican I.
 
Calvin
  • I’m predicting right now that the Catholic apologetic will be to point out that Boniface’s decree was, for whatever reason, not an ex cathedra statement.*
No need to do that. You are misinterpreting Unam Sanctum and * Orientalium Ecclesarum* when you come to the conclusion that they contradict each other. To understand these documents you need to know that the Church makes a distinction between material heretics and formal heretics, and between material schismatics and formal schismatics. The church teaches that material schismatics and material heretics that are invincibly ignorant, and that lead moral lives aided by grace, have the possibility of salvation. An invincibly ignorant pagan that leads a moral life aided by the grace of God can be saved.

When Unam Sanctum says that the Orthodox are “not of Christ’s sheep”, it is a reference to formal schismatics and formal heretics, not material heretics and material schismatics.

*In Orientalium Ecclesarum, as is well known, Pope Paul VI decreed that the Orthodox sacraments are valid and even referrs to the Orthodox as “the Eastern Churches.” *

The Orthodox sacraments are valid, but illicit. A formal schismatic or a formal heretic brings condemnation by receiving a valid sacrament, because formal heresy and formal schism are mortal sins. A person can be a member of the RCC and be in a state of mortal sin. It would be a grave sin for that person to receive a validly consecrated Eucharist in a state of mortal sin.

A material heretic or a material schismatic would not be culpable of mortal sin because of their invincible ignorance.

I agree with Vincent that this topic deserves its own thead.
 
Can there be ex cathedra statements from the ordinary Papal Magesterium, or are ex cathedra statements, by definition, restricted to exercises of the extraordinary Papal Magesterium that are defining new dogma?

They are restricted to the Extraordinary Papal Magisterium.

Pius IX’s Ineffabilis Deus is considered to be a papal ex cathedra statement that solemnly declared the Dogma of the Immaculate Conception. How does one know that Ineffabilis Deus is a document that contains an ex cathedra teaching that is infallible?

Not because you or I think it is or is not, but because the Church has pointed out that it is.

I guess my question is this, how can Catholics tell when a papal document falls into either the infallible Ineffabilis Deus category, the Ordinatio Sacerdotalis category that affirms an infallible doctrine, or a category that is fallible pious opinion of the pope?

It would have be something that has not been up to that point in time defined solemnly by the Magisterium of the Church to be ex cathedra.

For example, does Humanae Vitae fall into the Ordinatio Sacerdotalis category? I think that one could easily make the case that in Humanae Vitae, that Pope Paul IV affirms moral truths that are “founded on the written Word of God, and constantly held and applied in the Tradition of the Church”, and these moral truths have “been set forth infallibly by the ordinary universal Magisterium”.

I think so. Humanae Vitae and Ordinatio Sacerdotalis are not infallible statements. They are Papal documents that contain infallible teachings, teachings that already have been defined and taught by the Magisterium. Yes, the teaching of Humanae Vitae is infallible and therefore will not change as is hoped for by some. Such is also the case of *Ordinatio Sacerdotalis. *
 
Matt16_18:

At the risk of oversimplification:
  • Ineffabilis Deus → “de fide credenda
    (to be believed as divinely revealed on the authority of God who reveals).
  • Ordinatio Sacerdotalis → “de fide tenenda
    (to be held definitively on the authority of the Church which is rendered infallible by the Holy Spirit).
Both* de fide credenda * and de fide tenenda can be promulgated ex cathedra. In fact, *ID * was.

Cardinal Ratzinger and the CDF seem to argue that although *OS * could’ve been promulgated ex cathedra, it wasn’t.

Fr. Peter Pilsner and Brother Ansgar Santogrossi argue that OS was promulgated * ex cathedra*.

Cardinal Ratzinger and the CDF assert that the Pope explictly reaffirmed or confirmed something that already belongs to the teaching of the ordinary and universal magisterium. In other words, they seem to say that if the Pope hadn’t reaffirmed or confirmed that it is taught by the ordinary and universal magisterium, then it would’ve been a “defining” act (ex cathedra). The CDF thus would categorize *OS * as a “non-defining” act.

The position of Fr. Pilsner and Bro. Santogrossi and quite possibly, Fr. Harrison (see also I. Shawn McElhinney’s “Papal Infallibility Explained”) appear to differ from that of Cardinal Ratzinger and the CDF.

Even though they may disagree on the *ex cathedra * status of OS, when it comes down to it, they all agree that it is infallible and irreformable, and it is to be obeyed.
 
INFALLIBILITY. Freedom from error in teaching the universal Church in matters of faith or morals. As defined by the First Vatican Council, “The Roman Pontiff, when he speaks ex cathedra – that is, when in discharge of the office of pastor and teacher of all Christians, by virtue of his supreme apostolic authority, he defines a doctrine regarding faith or morals to be held by the universal Church, by the divine assistance promised to him in Blessed Peter, is possessed of that infallibility with which the divine Redeemer willed that his Church should be endowed in defining doctrine regarding faith or morals; and therefore such definitions are irreformable of themselves, and not in virtue of consent of the Church” (Denzinger 3074).

The bearer of the infallibility is every lawful Pope as successor of Peter, the Prince of the Apostles. But the Pope alone is infallible, not others to whom he delegates a part of his teaching authority, for example, the Roman congregations.

The object of his infallibility is his teaching of faith and morals. This means especially revealed doctrine like the Incarnation. But it also includes any nonrevealed teaching that is in any way connected with revelation.

The condition of the infallibility is that the Pope speaks ex cathedra. For this is required that: 1. he have the intention of declaring something unchangeably true; and 2. he speak as shepherd and teacher of all the faithful with the full weight of his apostolic authority, and not merely as a private theologian or even merely for the people of Rome or some particular segment of the Church of God.

The source of the infallibility is the supernatural assistance of the Holy Spirit, who protects the supreme teacher of the Church from error and therefore from misleading the people of God.

As a result, the ex cathedra pronouncements of the Pope are unchangeable “of themselves,” that is, not because others in the Church either first instructed the Pope or agree to what he says. (Etym. Latin in-, not + fallibilis; from fallere, to deceive: infallibilis not able to deceive, or err.)

Pocket Catholic Dictionary - John A. Hardon, S.J.
 
Br. Rich
  • Humanae Vitae and Ordinatio Sacerdotalis are not infallible statements. They are Papal documents that contain infallible teachings, teachings that already have been defined and taught by the Magisterium. Yes, the teaching of Humanae Vitae is infallible and therefore will not change as is hoped for by some.*
What do you mean by “infallible”? Both you and Cardinal Ratzinger seem to be using “infallible” in some technical sense that is beyond the ordinary definitions that I can find - i.e. infallible: Freedom from error in teaching the universal Church in matters of faith or morals.

Does * Ordinatio Sacerdotalis* requirements of infallibility as listed by Fr. Hardon?

“The object of his infallibility is his teaching of faith and morals.”

Check, OS is a matter of the faith, not discipline.

“The object of his infallibility is his teaching of faith and morals. This means especially revealed doctrine like the Incarnation. But it also includes any nonrevealed teaching that is in any way connected with revelation.”

Check, in OS meets this criteria.

“The condition of the infallibility is that the Pope speaks ex cathedra. For this is required that: 1. he have the intention of declaring something unchangeably true; and 2. he speak as shepherd and teacher of all the faithful with the full weight of his apostolic authority, and not merely as a private theologian or even merely for the people of Rome or some particular segment of the Church of God.”

Check. 1.The pope had the intention of declaring that only men can be ordained is unchangebly true (the doctrine requires definitive assent and is irrevokable) 2. The pope spoke as the shepherd of all the faithful in OS.

How can OS be affirming an infallible doctrine, and yet not be a document that is an infallible in its affirmation of that teaching? :confused:

They are restricted to the Extraordinary Papal Magisterium.

Can you show me anything that would support this? Why should papal infallibilty be restricted to only the extraordinary Magisterium when we can receive infallible teachings through the ordinary universal Magisterium? The pope said that the infallible doctrine in OS has been taught by the ordinary universal Magisterium. Surely, as pope he has a share in the ordinary Magisterium.
  • It would have be something that has not been up to that point in time defined solemnly by the Magisterium of the Church to be ex cathedra.*
The doctrine that restricts men to the priesthood has never been solemnly defined, (i.e. it has not been taught by the bishops exercising the extraordinary Magisterium in an Ecumenical Council). The pope says that this doctrine is known to be an infallible doctrine in the same way that the vast majority of our doctrines are known to be infallible - because it is a teaching of the ordinary universal Magisterium. Are you saying that only an Ecumenical Council could solemnly define the doctrine of restricting the priesthood to males and that the pope could not do that with an ex cathedra statement?
 
vincent
  • Even though they may disagree on the ex cathedra status of OS, when it comes down to it, they all agree that it is infallible and irreformable, and it is to be obeyed.*
That much is obvious. What seems strange to me is that even well educated and solidly orthodox Catholics cannot agree on when the pope is speaking ex cathedra. So I suppose that I am in good company when I admit that am confused too!

:crying:
 
Can anyone tell me when in the history of the church was the word ‘infallibility’ and its concept first used explicitely, not just some implicit reference to the concept? Was it before the break with Eastern Orthodoxy or afterwards?
 
Dolly
  • Can anyone tell me when in the history of the church was the word ‘infallibility’ and its concept first used explicitly, not just some implicit reference to the concept? Was it before the break with Eastern Orthodoxy or afterwards?*
Jesus is being explicit that Simon spoke infallibly when Jesus said to Simon, “flesh and blood has not revealed this to you, but my heavenly Father”. Immediately after Jesus affirms that Peter spoke infallibly, he makes Simon son of Jonah the first pope:

He said to them, “But who do you say that I am?” Simon Peter said in reply, “You are the Messiah, the Son of the living God.” Jesus said to him in reply, “Blessed are you, Simon son of Jonah. For flesh and blood has not revealed this to you, but my heavenly Father. And so I say to you, you are Peter, and upon this rock I will build my church, and the gates of the netherworld shall not prevail against it. I will give you the keys to the kingdom of heaven. Whatever you bind on earth shall be bound in heaven; and whatever you loose on earth shall be loosed in heaven.”
Matt. 16:15-19
 
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Vincent:
We could probably do something similar with regards to the inerrancy of Scripture. Critics of Christianity often point out the number of verses in which Scripture appears to contradict itself. Of course, since Christians already presuppose that Scripture is inerrant, they might address these apparent contradictions, for example, by showing that what’s there is a paradox, rather than a contradiction. Or Christians could show how the critic misunderstood the verses.
You are absolutely correct and that is why I abandoned sola scriptura. I need some sort of authority, I’m just not sure which one (Rome or Constantinople) to accept.

-C
 
What do you mean by “infallible”? Both you and Cardinal Ratzinger seem to be using “infallible” in some technical sense that is beyond the ordinary definitions that I can find - i.e. infallible: Freedom from error in teaching the universal Church in matters of faith or morals.

An Infallible teaching conveys a Truth without the possibility of error. What it says, is!

How can OS be affirming an infallible doctrine, and yet not be a document that is an infallible in its affirmation of that teaching? :confused:

Your missing my point. It is the Doctrine taught in the document that is infallible not the document. If you look in Denzinger you notice as you read. There is one sentence or paragraph presented as “of the Faith” out of a document that might be 20, 50 or 100 pages long.

They are restricted to the Extraordinary Papal Magisterium.

Can you show me anything that would support this? Why should papal infallibilty be restricted to only the extraordinary Magisterium when we can receive infallible teachings through the ordinary universal Magisterium? The pope said that the infallible doctrine in OS has been taught by the ordinary universal Magisterium. Surely, as pope he has a share in the ordinary Magisterium.

Not Papal Infallibility, but the ex cathedra means by which that Infallibility is exercised that is restricted to the Extraordinary Papal Magisterium.

It would have be something that has not been up to that point in time defined solemnly by the Magisterium of the Church to be ex cathedra.


The doctrine that restricts men to the priesthood has never been solemnly defined, (i.e. it has not been taught by the bishops exercising the extraordinary Magisterium in an Ecumenical Council). The pope says that this doctrine is known to be an infallible doctrine in the same way that the vast majority of our doctrines are known to be infallible - because it is a teaching of the ordinary universal Magisterium. Are you saying that only an Ecumenical Council could solemnly define the doctrine of restricting the priesthood to males and that the pope could not do that with an ex cathedra statement?

No of course not. The doctrine that restricts the priesthood to males only has always been held and taught by the Church. Pops Paul VI also stated this.
 
Br. Rich sfo
  • An Infallible teaching conveys a Truth without the possibility of error. What it says, is!*
The pope is teaching in OS that all Catholics must accept that it is an infallible doctrine that the priesthood is restricted to males only. How can he be teaching fallibly that we must accept a doctrine that is infallible? Isn’t he infallibly teaching that we must accept an infallible doctrine?
  • Your missing my point. It is the Doctrine taught in the document that is infallible not the document. If you look in Denzinger you notice as you read. There is one sentence or paragraph presented as “of the Faith” out of a document that might be 20, 50 or 100 pages long.*
I understand the point that the doctrine that the priesthood is restricted to males only is the teaching of the ordinary and universal magisterium. The pope is affirming that this teaching of the ordinary universal magisterium belongs to the deposit of faith. But the dogma of the Immaculate Conception belonged to the deposit of faith too. The pope doesn’t add infallible teachings to the deposit of faith by making ex cathedra statements.
  • Not Papal Infallibility, but the ex cathedra means by which that Infallibility is exercised that is restricted to the Extraordinary Papal Magisterium.*
Sorry for being dense, but I don’t understand this sentence.

The Pope is vested with special power because he holds a divinely instituted office in Christ’ Church. As the holder of the keys, the pope can exercise the powers vested in the papal Magisterium (i.e. the teaching office that the pope alone holds). The pope can exercise the papal Magisterium in either an ordinary or extraordinary manner. Where does the church teach that papal ex cathedra statements are restricted to the extraordinary Papal Magisterium? And where is the church teaching that states that the pope is only speaking infallibly (without error) when he is exercising the papal Magisterium in an extraordinary matter? I can’t find that in any document of Vatican I or Vatican II. Perhaps that teaching is there, but I can’t seem to find it!

I am getting the impression that there is some sort of arbitrary technical sense in which “infallible” is being as it applies to papal teachings – i.e. the pope is only speaking Infallibly®™ when he exercises the extraordinary papal Magisterium, otherwise, if he is exercising the ordinary papal Magisterium, he may only be speaking infallibly. A little “i” and big “I” kind of thing.
  • The doctrine that restricts the priesthood to males only has always been held and taught by the Church. Pope Paul VI also stated this.*
Right. Pope John Paul II quotes Inter Insigniores in OS. But saying that the church has always taught something – how does saying that clarify the issue of when the pope is speaking ex cathedra? Any valid doctrine of the church has to be a part of the deposit of faith that Christ handed on to his church. The seeds of all dogmas are found in the divinely revealed teachings that the church has always held. Solemnly defined dogmas are only formal definitions of what the Church has always held to be true. Not every infallible teaching of the Catholic Church has been solemnly defined (de fide definita). In fact, most of the infallible teachings of the Church have never been solemnly defined.
 
Br.Rich sfo

Following is from the link that Vincent gave in his post # 29, (“Papal Infallibility Explained”).

“It is profoundly erroneous to make infallibility out to be a formula because to do this is to misunderstand the teachings of Vatican I. It also introduces a novelty into the mix that does not have historical perspective. Brother Alexis Bugnolo in response to simplistic ‘traditionalist’ notions about papal infallibility made the following notations, which are essential in understanding the extent to which infallibility applies:

Regarding the Definition of Papal Infallibility it should noted that often it is misunderstood as requiring the Pope to be either seated on the Papal Throne when teaching or that the Pope explicitly cite the fact that he is invoking infallibility or further that the Pope has to be issuing a dogmatic or doctrinal definition. Those who hold this view of Papal Infallibility go on to say that in no other circumstance is the Pope Infallible. But a closer look at the definition taught by Vatican I, shows that these are misunderstandings. All that is required is that the Pope be teaching in matters of faith or morals in such a manner that he intended to teach a dogma or doctrine which is to be believed by the faithful as pertaining to Catholic Teaching, in that he do this in his capacity as Roman Pontiff, Shepherd of the entire Church. Thus even the homilies of the Pope, if they meet this criterion, are infallible teachings; and not just solemn dogmatic definitions.”

… The key word “defines” is what is confusing to most people about the decree because often what is imagined is that it is a solemn pronouncement when this is almost never the case at all. Catholic apologists are often at fault here for propagating the particularly noxious error that papal infallibility is a charism that is exercised “rarely”. (Some go so far as to propagate the profound absurdity that the Immaculate Conception in 1854 and the Assumption in 1950 were the last two “exercises of papal infallibility”.) If Catholic apologists cannot understand the extent of papal infallibility, then they cannot properly explain it to Protestants, the Orthodox, or even to inquiring Catholics seeking answers with which to defend challenges to the Church’s claims.​

I want to properly explain papal infallibility in the RCIA class! 🤓
 
Matt16_18 said:
Dolly

Can anyone tell me when in the history of the church was the word ‘infallibility’ and its concept first used explicitly, not just some implicit reference to the concept? Was it before the break with Eastern Orthodoxy or afterwards?

Jesus is being explicit that Simon spoke infallibly when Jesus said to Simon, “flesh and blood has not revealed this to you, but my heavenly Father”. Immediately after Jesus affirms that Peter spoke infallibly, he makes Simon son of Jonah the first pope:

He said to them, “But who do you say that I am?” Simon Peter said in reply, “You are the Messiah, the Son of the living God.” Jesus said to him in reply, “Blessed are you, Simon son of Jonah. For flesh and blood has not revealed this to you, but my heavenly Father. And so I say to you, you are Peter, and upon this rock I will build my church, and the gates of the netherworld shall not prevail against it. I will give you the keys to the kingdom of heaven. Whatever you bind on earth shall be bound in heaven; and whatever you loose on earth shall be loosed in heaven.”

Matt. 16:15-19

I’d like to humbly add to this if I may, but I don’t have the scripture passage. But I know that Jesus also said to his apostles "…**just as the Father has sent Me so I send you…" Them’s pretty strong words. Seems that would have something to do with the church’s infallibility…
 
The pope is teaching in OS that all Catholics must accept that it is an infallible doctrine that the priesthood is restricted to males only. How can he be teaching fallibly that we must accept a doctrine that is infallible? Isn’t he infallibly teaching that we must accept an infallible doctrine?

Yes

Your missing my point. It is the Doctrine taught in the document that is infallible not the document. If you look in Denzinger you notice as you read. There is one sentence or paragraph presented as “of the Faith” out of a document that might be 20, 50 or 100 pages long.

I understand the point that the doctrine that the priesthood is restricted to males only is the teaching of the ordinary and universal magisterium. The pope is affirming that this teaching of the ordinary universal magisterium belongs to the deposit of faith. But the dogma of the Immaculate Conception belonged to the deposit of faith too.

No, the Immaculate Conception even though it was held to and believed in the Church was not De Fide until 1854 when Pius IX defined it as such.

The pope doesn’t add infallible teachings to the deposit of faith by making ex cathedra statements.

In a sense yes he does. He does not invent new doctrines but he does solemnly declare a belief as revealed by God and defines it as De Fide.

Not Papal Infallibility, but the ex cathedra means by which that Infallibility is exercised that is restricted to the Extraordinary Papal Magisterium.

Sorry for being dense, but I don’t understand this sentence.

The Pope is exercising the extraordinary papal magisterium when he teaches ex cathedra. There is no Church teaching that states that the pope is only speaking infallibly (without error) when he is exercising the papal Magisterium in an extraordinary matter.
The pope speaks Infallibly when exercising either the Ordinary or Extraordinary papal magisterium.

The doctrine that restricts the priesthood to males only has always been held and taught by the Church. Pope Paul VI also stated this.

Solemnly defined dogmas are only formal definitions of what the Church has always held to be true. Not every infallible teaching of the Catholic Church has been solemnly defined (de fide definita). In fact, most of the infallible teachings of the Church have never been solemnly defined.

I don’t agree with that. Every Infallible teaching of the Church that is to be held as a matter of Faith has been defined in one way or another by the magisterium of the Church. Either in the Ordinary exercise of the mageristerium, those things found in the Scriptures, Sacred Tradition or the Creeds, or by the extraordinary magisterium as exercised by a Church Council or the pope.
 
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