This is a huge development, since, according to almost all theologians, a formal warning is one of the necessary steps in the deposition of a heretical Pope, since it serves to establish if the Pope is holding to a heretical doctrine with pertinacity (which is a necessary element of heresy) or if he is merely mistaken, and therefore erring in good faith.
Later in the interview, Cardinal Burke was asked: “If the Pope were to teach grave error or heresy, which lawful authority can declare this and what would be the consequences?” He did not respond to the question directly, but only said: “It is the duty in such cases, and historically it has happened, of cardinals and bishops to make clear that the Pope is teaching error and to ask him to correct it.”
But what if the Pope doesn’t correct his position? What then? Unfortunately, that question was not asked. But it is certainly one that is being pondered since this scenario is one that the Church may be facing very soon. In light of this, we will address the issue of whether the Church can judge a Pope in the case of heresy, since this act would be the next step in the process following the ecclesiastical warning.
One of the difficulties often raised against the Church judging papal heresy, is the bi-millennial doctrine, reiterated at Vatican I, that “the first see is judged by no one” (Prima sedes a nemine iudicatur). Based on this teaching, many believe that the Church cannot judge papal heresy, or declare that a Pope has fallen into heresy, since this would constitute a “judgment” against the pope, which they believe is not permitted. But this is not how the doctrine prima sedes a nemine iudicatur has traditionally been understood. As we will show in this article, an explicit exception is made in the case of a pope who is accused of heresy. This exception was part of canon law from the 12th Century until the 20th Century (before, during and after Vatican I) and has been taught by at least one pope, as well as some of the most reputable theologians and canonists for centuries.
The canon in which this exception is found is from the Decretum Gratiani, which is the first part of a collection of six legal texts that together became known as the Corpus Juris Canonici. The specific canon is Si Papa, dist 40, ch. 6, which provides:
If the Pope, being neglectful of his own salvation and that of his brethren, be found useless and remiss in his works, and, more than that, reluctant to do good (which harms himself and others even more), and nonetheless brings down with him innumerable throngs of people … Let no mortal man presumes to rebuke him for his faults, for, it being incumbent upon him to judge all, he should be judged by no one, unless he is suddenly caught deviating from the faith (nisi deprehendatur a fide devius). 
Notice that the phrase “he should be judged by no one,” which is equivalent to “the first see is judged by no one”, is followed by the exception: “unless he is suddenly caught deviating from the faith.” As we will see, Si Papa is cited regularly by the canonists and theologians who discuss the deposition of a heretical pope, and they all interpret it as permitting the Church to render a judgment against a sitting Pope, while he remains Pope.
In addition to the aforementioned canon, we also have the teaching of Pope Innocent III (d. 1216), who explicitly affirms that a Pope can be “judged by the Church” for sins against the faith. The following is from his Consecration Sermon, No. 2:
For faith is so necessary for me that, while for other sins I have only God as my judge, only for that sin which is committed against faith could I be judged by the Church.
St. Robert Bellarmine teaches the same, and cites the above quotations from Si Papa and Pope Innocent as authorities in defense of his position. He begins with the proposition:
“A Pope can be judged and deposed by the Church in the case of heresy; as is clear from Dist. 40, can. Si Papa: therefore, the Pontiff is subject to human judgment, at least in some case. I respond: there are five opinions on this matter.”
The following is his refutation of the third of the five opinions. The third opinion, which Bellarmine calls an “extreme opinion,” is that a heretical cannot be judged, and therefore a heretical Pope cannot lose his office. Bellarmine refutes this opinion by saying:
“Turrecremata in the aforementioned citation relates and refutes this opinion, and rightly so, for it is exceedingly improbable. Firstly, because that a heretical Pope can be judged is expressly held in the Canon, Si Papa, dist. 40, and with Innocent. And what is more, in the Fourth Council of Constantinople, Act 7, the acts of the Roman Council under Hadrian are recited, and in those it was contained that Pope Honorius appeared to be legally anathematized, because he had been convicted of heresy, the only reason where it is lawful for inferiors to judge superiors. Here the fact must be remarked upon that… we still cannot deny that Hadrian, with the Roman Council, and the whole Eighth Synod sensed that in the case of heresy, a Roman Pontiff can be judged.”
We can see that, according to Bellarmine, not only can the Church render a judgment concerning a heretical pope, but the man remains pope at least until he is judged a heretic by the Church. This is evident from the fact that he says heresy is “the only reason where it is lawful for inferiors (the Church) to judge superiors (the pope).” And “in the case of heresy, a Roman Pontiff [not a former Roman Pontiff] can be judged.” And he cites Si Papa and Innocent III (both of which explicitly mention the exception) as authorities for his position.
Bellarmine’s fellow Jesuit, Fr. Paul Layman, who was considered “one of the greatest canonists and moralists of his time,” teaches the same. In defending his position he cites the same authorities as did Bellarmine, and even quotes Bellarmine himself. Fr. Laymann also tells us who in the Church would be responsible for rendering the necessary judgment, and what would happen (or not happen) if the Church did not render a judgment, but instead deemed it more prudent to tolerate the heretical pope. We will quote Fr. Laymann at length:
It is more probable that the Supreme Pontiff, as concerns his own person, could fall into heresy, even a notorious one, by reason of which he would deserve to be deposed by the Church, or rather declared to be separated from her. … The proof of this assertion is that neither Sacred Scripture nor the tradition of the Fathers indicates that such a privilege [i.e., being preserved from heresy when not defining a doctrine] was granted by Christ to the Supreme Pontiff: therefore the privilege is not to be asserted.
The first part of the proof is shown from the fact that the promises made by Christ to St. Peter cannot be transferred to the other Supreme Pontiffs insofar as they are private persons, but only as the successor of Peter in the pastoral power of teaching, etc. The latter part is proven from the fact that it is rather the contrary that one finds in the writings of the Fathers and in decrees: not indeed as if the Roman Pontiffs were at any time heretics de facto (for one could hardly show that); but it was the persuasion that it could happen that they fall into heresy and that, therefore, if such a thing should seem to have happened, it would pertain to the other bishops to examine and give a judgment on the matter; as one can see in the Sixth Synod, Act 13; the Seventh Synod, last Act; the eight Synod, Act 7 in the epistle of [Pope] Hadrian… And in Si Papa d. 40, it is reported from Archbishop Boniface: ‘He who is to judge all men is to be judged by none, unless he be found by chance to be deviating from the Faith’. And Bellarmine himself, book 2, ch. 30, writes: ‘We cannot deny that [Pope] Hadrian with the Roman Council, and the entire 8th General Synod was of the belief that, in the case of heresy, the Roman Pontiff could be judged,’ as one can see in Melchior Cano, bk. 6, De Locis Theologicis, last chapter.
But note that, although we affirm that the Supreme Pontiff, as a private person, might become a heretic … nevertheless, for as long as he is tolerated by the Church [i.e., before the bishops rendered a judgment], and is publicly recognized as the universal pastor, he is still endowed, in fact, with the pontifical power, in such a way that all his decrees have no less force and authority than they would if he were a truly faithful, as Dominic Barnes notes well (q.1, a. 10, doubt 2, ad. 3) Suarez bk 4, on laws, ch. 7. The reason is: because it is conducive to the governing of the Church, even as, in any other well-constituted commonwealth, that the acts of a public magistrate are in force as long as he remains in office and is publicly tolerated.”
Notice, as long as the heretical Pope is being tolerated – that is, before he is judged a heretic by the bishops – he remains a true Pope, with papal authority.
The Dominican Cardinal, Tommaso de Vio Gaetani Cajetan, likewise cites the canon, Si Papa, and teaches that it permits the Church to judge a pope in the case of heresy. He also explains that the competent tribunal to render such a judgment would be a general council (an “imperfect council”):
Next that of Boniface, pope and martyr, as found in Si Papa [D. 40, c. 6], where he says, ‘Unless the pope is deviant from the faith, no mortal presumes to convict him of his faults,’ where only the crime of unbelief entails subjection to a judge by whom the pope can be judged, which is recognized to be the universal Church or the general council.
John of St. Thomas, who is recognized as one of the greatest Thomists the Church has produced, and who was known, even in his own day as “the second Thomas,” cites Si Papa and explicitly states that this canon provides exception to the doctrine that the pope is judged by no one:
Concerning the case of heresy, theologians and Canon lawyers have disputed very much [about precisely how the Pontificate is lost]. It is not necessary to delve into this question now. However, there is an agreement among the Doctors on the fact that the Pope may be deposed in case of heresy. (…)
A specific text is found in the Decree of Gratian, Distinction 40, chapter ‘Si Papa,’ where it is said: ‘On earth, no mortal should presume to reproach the Pontiff for any fault, because he who has to judge others, should not be judged by anyone, unless he is found deviating from the Faith’ (Pars I, D 40, c. 6). This exception obviously means that in case of heresy, a judgment could be made about the Pope.
The same thing is confirmed by the letter of Pope Hadrian, reported in the Eighth General Council [IV Constantinople, 869- 870], in the 7th session, where it is said that the Roman Pontiff is judged by no one, but the anathema was made by the Orientals against Honorius, because he was accused of heresy, the only cause for which it is lawful for inferiors to resist their superiors. Also, Pope St. Clement says in his first epistle that St. Peter taught that a heretical Pope must be deposed.
Next we have Francisco Suarez, who also teaches that heresy is the exception to the general rule that “the pope is judged by no one”. He wrote:
If you ask what gives us certainty that, by Divine Law, a Pontiff is deposed as soon as a sentence is pronounced by the Church: I respond, in the first place, that I have already produced the testimony of [Pope] Clement, which is from the mouth of Peter; in the second place … it is the common consensus of the Church and the Pontiffs. (… ) I say fourthly: outside of the case of heresy, a true and undoubted Pontiff, even if he be extremely wicked, cannot be deprived of his dignity. (…) Therefore all the Pontiffs cited above, while affirming that the Church can pass judgment on the Supreme Pontiff in the case of heresy, deny absolutely that she can pass judgment on him outside of that case; and it is in this sense that the often say that the Pope is judged by no one.
It should be noted, however, as Suarez explains in the following citation, that even in the case of heresy the Church is not superior to the Pope (this is the error of Conciliarism). Rather, the Church merely judges and declares his crime, at which time Christ Himself authoritatively deposes the pope. The crime of heresy judged by the Church is the dispositive cause for the loss of office; Christ Himself is the efficient cause, since only Christ can authoritatively sever the bond uniting the man to the papal office, just as Christ alone possesses the authority to make the man pope, by joining the him to the office, following the election. Suarez explains:
Therefore, others [e.g., Azorius] affirm the Church is superior to the Pope in the case of heresy, but this is difficult to say. For Christ the Lord constituted the Pope as supreme judge absolutely; even the canons indifferently and generally affirm this; and at length the Church does not validly exercise any act of jurisdiction against the Pope; nor is the power conferred to him by election, rather [the Church] merely designates a person upon whom Christ confers the power by himself; Therefore on deposing a heretical Pope, the Church would not act as superior to him, but juridically and by the consent of Christ she would declare him a heretic and therefore unworthy of Pontifical honors; he would then ipso facto and immediately be deposed by Christ…
In the above citation, Suarez is drawing a parallel between how a man becomes pope, following the Church’s judgment (the election), and how a heretical pope loses his office, which also follows the Church’s judgment. During a papal election, a man is chosen by the human judgment of the proper authorities. If he accepts the office, Christ joins the man to the Pontificate, thereby making him pope. This act of Christ, following the double consent (the consent of the Church and the consent of the one elected), is similar to how God joins husband and wife in matrimony following their double-consent (“I do”). In the loss of office for heresy, there is also a double-consent: the will of the pope is demonstrated when he pertinaciously holds to heresy (in the face of an ecclesiastical warning) and the consent of the Church is expressed in willing his deposition. Following this double-consent, Christ severs the bond uniting him to the papacy, just as he joined the man to the papacy following double-consent expressed in the election and acceptance.
Bellarmine teaches the same in De Romano Pontifice, in his refutation of the “second opinion.” The second opinion, which Bellarmine also refers to as “an extreme,” maintains that a heretical Pope will lose his office for violating Divine law by committing the sin of heresy, without requiring an antecedent (prior) judgment of the Church. Bellarmine refutes this opinion by arguing that just as God does not join a man to the papacy without human judgment (that of the electors), neither will Christ depose a heretical pope accept “through men” (the proper authorities) who first judge him. This citation once again confirms that Bellarmine held that a sitting can be judged by the Church, and that he will not lose his office until such a judgment is rendered:
Jurisdiction is certainly given to the Pontiff by God, but with the agreement of men [who elect him], as is obvious; because this man, who beforehand was not Pope, has from men that he would begin to be Pope; therefore, he is not removed by God unless it is through men. But an occult heretic cannot be judged by men, nor would such wish to relinquish that power by his own will.
We can see how mistaken those are who interpret Bellarmine as having taught that God will secretly depose a Pope without him first being judged by the Church, and that it is up to each individual to determine for themselves if the loss of office has taken place. John of St. Thomas correctly interprets Bellarmine as teaching that Christ deposes the pope after he is judge a heretic by the Church. He wrote:
It cannot be held that the Pope, by the very fact of being a heretic, would cease to be pope antecedently to a declaration of the Church. (…) What is truly a matter of debate is whether the Pope, after he is declared by the Church to be a heretic, is deposed ipso facto by Christ the Lord, or if the Church ought to depose him. In any case, as long as the Church has not issued a juridical declaration, he must always be considered the Pope.
A little later, when commenting on Bellarmine’s opinion, John of St. Thomas wrote:
Bellarmine and Suarez are of the opinion that, by the very fact that the Pope is a manifest heretic and declared to be incorrigible, he is deposed by Christ our Lord without any intermediary, and not by any authority of the Church. 
Next we have the teaching of Fr. Matthias of Corona, S.T.D, who also explains that a pope can only be judged and deposed for heresy or schism, but not for lesser crimes.
A Pontiff, lapsed into heresy, can be most justly deposed. Thus Duvallius, above in q. 10. The reason is, that it is not credible that Christ wants to retain him as Vicar of His Church, who pertinaciously segregates himself whole from Her, since Christ has especially commanded Her to hear His Voice, as a faithful people, and to comply with Him, just as sheep hear the voice of their shepherd. John 10:3: ‘The sheep hear His Voice and they follow Him’. Verse 4: ‘The sheep follow Him.’ But far be it, only, that the Church should hear a Pontiff lapsed into heresy, She who rather is bound to stop up Her own ears against his violent speech, lest She be infected by the venom of his doctrine, and his casting-out and new election ought to be urged by the assembly of the Sacred Cardinals. … if he remains there, after having been judicially denounced as a heretic, he is to be immediately dispossessed of the Pontificate, if his heresy is external and manifest through the evidence of fact [judged by the Church], and/or the declaration of a Council. … Second, no Pope has been deposed or judged, except on account of heresy and/or schism”
Notice again that a sitting pope is only removed from office after being “juridically denounced as a heretic.”  We also see that heresy is presented as a case in which it is licit for the Church to judge a pope. And for those who mistakenly believes the famous axiom “the first see is judged by no one” only originated at the First Vatican Council, and that therefore after Vatican I no theologian or canonist has taught that the Church can judge a pope in the case of heresy, we will provide a citation from a book that was published two decades after the close of the Council. And we should also note that following its initial publication, the book was meticulously reviewed by two canonists in Rome. In their lengthy reports, which were included at the beginning of the later editions, we find five or six inaccuracies that required revision, but the following citation was not one of them. What this shows is that the following teaching (which is consistent with what the theologians can canonists have taught for centuries), is in no way contrary to anything taught at Vatican I. The following citation is taken from Elements of Ecclesiastical Law, by Reverend S. B. Smith, D.D. 9th edition, published in 1893:
“Question: Is a Pope who falls into heresy deprived,ipso jure,of the Pontificate?
"Answer: There are two opinions: one holds that he is by virtue of divine appointment, divestedipso facto, of the Pontificate; the other, that he is,jure divino,only removable.Both opinions agree that he must at least be declared guilty of heresy by the Church- i.e., by an ecumenical council or the College of Cardinals.”
The two opinions alluded to by Reverend Smith can be classified as the Jesuit Opinion (defended by Suarez and Bellarmine) and the Dominican Opinion (defended by Cajetan and John of St. Thomas). As Smith notes, and as John of St. Thomas confirmed in the earlier citation, both opinions agree that a heretical Pope must at least be judged guilty of heresy by the Church, before any ipso facto loss of office occurs (Jesuit Opinion), or before the Church can “depose” a Pope (Dominican Opinion).
In light of what we have seen, should Pope Francis show himself pertinacious in holding to a heretical doctrine following an ecclesiastical warning (or two), the famous axiom “the first see is judged by no one” would not prevent the proper authorities from taking the necessary steps to establish the crime of heresy, which would likely be followed, quite quickly, by his fall from the Papal office. However these events play out, we are living through some very historic times.
 Si Papa, dist 40, ch 6; Latin found in Brian Tierney, The Crisis of Church and State (Englewood Cliffs, New Jersey: Prentice-Hall, 1964), p. 124.
 There is a nuance in the notion of judging the Pope. The Church judges the matter (the doctrine) and then performs the necessary functions to establish that he is pertinacious, thereby “demonstrating that he has already been judged.” For more on this nuance, see: Salza & Siscoe, True or False Pope, 1st ed. (Winona Minnesota, St. Thomas Aquinas Seminary, 2016) pp. 258-260.
 Serm. Consecrat. Pontif. Rom., P. L. CCXVII, col. 656.
 Bellarmine, De Romano Pontifice, bk. 2, ch. 30
 Catholic Encyclopedia, 1913, Vol. IX (Fr. Paul Laymann), p 95
 Laymann, Theol. Mor., bk. 2, tract 1, ch. 7, p. 153 (emphasis added).
 Cajetan, De Comparatione Auctoritatis Papae et Concilii, English Translation in Conciliarism & Papalism, by Burns & Izbicki (New York: Cambridge University Press, 1997), p. 103.
 Cursus Theologici II-II De Auctoritate Summi Pontificis, Disp. II, Art. III, De Depositione Papae, p. 133 (emphasis added); translated by Albert Doskey.
 Saurez, Tractatus De Fide, Disp. 10, Sect. 6, n. 10, p. 318.
 Bellarmine, De Romano Pontifice, ch. 30.
 John of St. Thomas, Cursus Theologicus, Tome 6. Questions 1-7 on Faith. Disputation 8., Article 2
 Ecclesia Sancta A Potestate Et Dignitate, S.R.E. Cardinalium, Legatorum Apostolicorum, &C, (1677) R. P. Matthiae a Corona Leod. Carm. S. Th. Doctr. Paris, tract I, caput XXI, p. 80. Translated by Brother Alexis Bugnolo
 Some theologians maintain that the fall from the office would occur after the Church established the crime, but before the declaratory sentence of the crime was issued. This opinion is intended to void any possibility of the Church inappropriately judging the Pope. The more common opinion, however, is that the Church is not only able to establish the crime of incorrigible heresy, but is also able to issue a declaratory sentence, since such a sentence does not involve coercion or punishment. Regarding this point, Cajetan wrote: “Because neither God nor nature fails in necessary things, the same authority extends to all pre-conditions [for a Pope to be deposed]. I do not require any of them as requiring coercive power over Pope Peter; it is sufficient for the powers to be
declaratory, admonitory and the like. The judgment, being based [on] … the evident fact or open profession of incorrigible heresy… which happens without being coerced” (Cajetan, De Comparatione Auctoritatis Papae et Concilii, ch. XXI).
 Elements of Ecclesiastical Law, Rev. SB Smith DD (Benzinger Br., New York, 1893), 9th ed., p 240.