Many Catholics today have no concept of the ordinary magisterium and mistakenly think that doctrines must be dogmatically decreed in order for us to believe them. Nothing could be further from the truth. To prove this, below are quotes from Catholic texts on the lives of the Saints which show that both Arius and Nestorius were condemned as heretics by the Catholic Church before they were condemned by General Council.

Conclusions:
•   When Arius was first publicly condemned by the clergy of the Church in 319, the Church had never yet had any dogmatic (solemn) teaching. Yet all the clergy in the Church still considered Arius a heretic because he was teaching contrary to continuous Christian teaching (the ordinary magisterium). He was later officially condemned in 325 in the Council of Nicaea.
•   When Nestorius was first publicly condemned by the clergy of the Church in 430, the two previous General Councils had not defined the divine maternity of the Blessed Virgin Mary, which he denied. Yet Nestorius was still considered a heretic for opposing the ordinary magisterium (which the First Vatican Council later defined as infallible). Nestorius was later condemned at the Council of Ephesus in 431.
•   Many Catholic beliefs to this day have never been solemnly defined. Examples; that Guardian Angels exist, that ɧoɱosɛҳųαƖ acts are wrong, that Adam and Eve are the first and sole parents of the human race, and that the soul is created immediately by God etc. Yet, as Catholics we would be considered heretics for denying any of these. Again, proof that Catholics must believe what the ordinary magisterium teaches.
•   It should now be evident that Catholics need to STOP insisting that they will not believe teachings of the Catholic Church if they haven't been solemnly defined. It's nothing but heresy to believe otherwise. The examples of Arius and Nestorius below prove definitively that the majority of what Catholics believe comes from the ordinary magisterium, which the First Vatican Council says we MUST believe.

Arius:
The Lives Of The Fathers, Martyrs, And Other Principal Saints ..., Volume 4 By Alban Butler (1902):
"In 319 St. Alexander sent an account of his proceedings against Arius in a circular letter directed to all the bishops of the church, signed by St. Athanasius and many others. In 325 he took the holy deacon with him to the Council of Nice, who there greatly distinguished himself by the extraordinary zeal and learning with which he encountered not only Arius but also Eusebius of Nicomedia, Theognis, and Maris, the principal protectors of that heresiarch; and he had a great share in the disputations and decisions of that venerable assembly, as Theodoret, Sozomen, and St. Gregory nαzιanzen testify."

Orations of St. Athanasius against the Arians (1873) mentions the same:
Page IX: "It was in A.D. 319 that Archbishop Alexander was informed of the dissemination, among Alexandrian church–people, of strange opinions derogatory to the dignity of the Son of God. Their author, it appeared, was Arius, a priest of mature age, who, after a period of misdirected and factious activity, had attained a high position as pastor of the oldest church in Alexandria."
Page XI: "Alexander formally summoned the priests and deacons of the city to sign a letter, in which he exhorted the partizans of Arius to 'renounce their impiety'. This rigorous step was followed up by the assembling of a Council of the suffragan bishops, nearly 100 in number, which drew forth from Arius and his friends, among whom were 2 prelates, a fuller exposition of their belief, and thereupon passed sentence of excommunication and anathema."
Page XI-XII: "There were many letters to be written in defense of the doctrine denied by Arius, and in order to expose his real meaning: the most important of these, the 'Encyclical,' has been assigned, on internal evidence, to the hand of Athanasius, now, apparently, Archdeacon of Alexandria. Adjusting itself to all Christian prelates, the letter insisted that the propositions of Arius were at variance alike with Scripture and with continuous Christian teaching: and in one sentence, eminently 'Athanasian,' called on its readers to 'hold aloof, as Christians, from those who spoke or thought in opposition to Christ.' Athanasius was among the 44 deacons who, with 36 priests, signed this letter, as they had signed the earlier one.
Page XIII: "That strength was acknowledged when, in the summer of A.D. 325, Athanasius appeared and spoke in the Nicene Council, not as properly one of its members (which were bishops or delegates of bishops), but as one of the ecclesiastics who are present in attendance on their bishops, and were allowed to contribute to the discussions."

Nestorius
The Lives of Saints Collected from Authentic Records of Church History, 2nd ed, 1750, pg 105 on St. Cyril of Alexandria:
“Nestorius's sermons were collected into a volume, and sent to several places; and amongst the rest, to the monks of Egypt, who were put into a ferment by the abstruse questions which relate to this dispute. Upon which St. Cyril wrote to them, and advised them in general to avoid all such curious enquiries; assuring them that what he wrote was not to encourage these speculations, but to enable them to maintain the Truth. Then he declared what had been always the Belief of the Church in that point; who did not, as Nestorius would insinuate, make the Blessed Virgin Mother of the Divinity of Jesus Christ; but only asserted, that the Humanity of Jesus Christ being hypostatically united to the Divinity, the Blessed Virgin might, with the same propriety of speech, be called the Mother of God, as any other Woman is called the Mother of one, whose Soul she does not produce, without making any distinction. This letter appeared at Constantinople; and the Saints received thanks for the service he did the Church. Nestorius was not at all pleased with it; but from that moment looked on St. Cyril as his enemy, and did all in his power to ruin his credit. About this time our Saints received a letter from Pope Celestine, and several Western bishops, complaining of Nestorius's doctrine; and the Churches of the East were not wanting to express their dissatisfaction on this occasion. Encouraged by these declarations, he wrote to Nestorius, put him in mind of the scandal his sermons have given, and professed himself ready to submit to the greatest extremities, rather than betray or deny the Faith. Nestorius affected a particular softness in his reply to this letter; but did not seem inclined to change his opinion. Some other letters of the same kind passed between the 2 patriarchs; but Nestorius still remained obstinate. In the year 430, St. Cyril thought it necessary to write to the Pope, and give him the particulars of his behavior and his affair; he sent him Nestorius's sermons, and his own letters on that subject, assured him of the concurrence of all the Eastern bishops, and desired his advice concerning the safety of holding communion with Nestorius. Nestorius too wrote to the Pope, and endeavored to gain him to his party. The Pope convened a council at Rome; which, after mature examination of the question, declared in favor of St. Cyril; and ordered that Nestorius should be excommunicated, if he did not come into the sentiments of Rome and Alexandria, which appeared to be those of the whole Church. The Pope wrote seven letters of the same date; one to St. Cyril, a second to Nestorius, a third to the clergy of Constantinople, and the other for to as many of the bishops of the East, notifying the decisions of the Council, requiring Nestorius to abjure his doctrine in ten days after he should receive the said Pope's letter, under pain of being cut off from the communion of the Church; and ordering St. Cyril to act in his name, and by his Authority, in the execution of the sentence. St. Cyril would not proceed against Nestorius in a judicial manner, until he had consulted the bishops of Antioch and Jerusalem, to whom he knew the Pope had wrote upon the same subject. After that, he called a council at Alexandria; in which he drew up a profession of faith, and added to it 12 anathemas against the doctrine of Nestorius. The dispute ran so high at last, that there was no hopes left of putting an end to it, but by General Council; which was accordingly called at Ephesus, and met there in the year 431. St. Cyril presided in it; not only in right of his own See, which was the first in the East; but also as representing the Bishop of Rome, whose commission he bore. Nestorius was then at Ephesus; but depending on the favor of the court to support his conduct, did not think fit to appear in the Council, though cited three times in form. The Council then proceeded to examine what had been wrote by both sides during the contest; and after mature deliberation, unanimously condemned Nestorius's doctrine and approved of all that bore the name of St. Cyril. Upon which the former was deposed and excommunicated.”

Many Catholics today have no concept of the ordinary magisterium and mistakenly think that doctrines must be dogmatically decreed in order for us to believe them. Nothing could be further from the truth.

I've not seen that demonstrated in any recent threads. The arguments and debates continue because there is a contradiction between the infallibly defined foundational dogma of the entire Church and those who either disagree with it, reject it or otherwise mean to change the meaning of what has been infallibly defined. . . . . . because something must have been left out of the defined dogma so in vain, they strive to make it fit back in.

The point of this discussion is to show that the Church need not infallibly define anything. Do you realize the first 13 generations of Catholics lived with hardly any solemn decrees? They all relied on the ordinary magisterium to know what was Catholic truth and what was not, and that includes the teaching on baptism. You feel there is a contradiction, but it is your understanding that is wrong.

The Syllabus of Errors
The obligation by which Catholic teachers and authors are strictly bound is confined to those things only which are proposed to universal belief as dogmas of faith by the infallible judgment of the Church. - Condemned

I fail to see why you posted this quote from the Syllabus of Errors and what it has to do with this discussion?

What we have all witnessed in recent threads though is error:
Good hopes at least must be entertained of the eternal salvation of all those who in no way belong to the True Church of Christ. - Condemned

Again, because your understanding is off, it's no doubt you would post this quote. Pope Pius X himself stated It's possible to belong to the soul of the church without belonging to the body. Don't understand this (or refuse to believe it), then it's no surprise you would post a quote like this.

Did any of those Catholics believe that the Throne of Peter could be vacant for 50 or more years?  What does the Ordinary Magisterium say about that?

There are vacancies between each and every Pope, Jehanne, whether hours, days, weeks or years. As you may have noticed in the other discussion called "interregnums", there have been many times throughout the history of the Church where there was no Pope for years. In total, these Interregnums add up to about 10 years without a Pope. Do you acknowledge this? So we know it's possible there can be no Pope for years, because it's happened previously. How many years maximum can an interregnum be? A maximum has never been specified by the Church.

Quote from: Jehanne

Did any of those Catholics believe that the Throne of Peter could be vacant for 50 or more years?  What does the Ordinary Magisterium say about that?

I know we are getting off-topic here, but I thought I would also provide you this quote, Jehanne. From the Catholic Encyclopedia, in the article "election of Popes", it states:

"Between the death of Clement IV (1268) and the coronation of Gregory X (1272) an interregnum of nearly three years intervened. To prevent a repetition of so great a misfortune the pope in the Council of Lyons (1179) issued the Decree "Ubi periculum""

Notice the Church only refers to such a long interregnum as a "misfortune".

SB13,

How does the Church recover from a 50+ year interregnum?  In the Holy Sacrifice of the Mass, whom does the celebrant pray for?  Doesn't it bother you that some priests (such as the SSPV, CMRI, etc.,) are altering the Canon of the Mass by omitting the Holy Father and local ordinary?  What would centuries of Catholics say to that?!