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Present procedure in causes of beatification and canonization
We must first distinguish causes of martyrs from those of confessors or virgins, since the method followed is not entirely identical in both cases.

The beatification of confessors
In order to secure beatification (the most important and difficult step in the process of canonization) the regular procedure is as follows:

Choosing of a vice-postulator by the postulator-general of the cause, to promote all the judicial inquiries necessary in places outside of Rome. Such inquiries are instituted by the local episcopal authority.
The preparation of the inquiries (processus) all of which are carried on by the ordinary episcopal authority. They are of three kinds: (a) Informative inquiries regard the reputation for sanctity and miracles of the servants of God, not only in general, but also in particular instances; there may be several such inquiries if the witnesses to be examined belong to different dioceses. (b) Processes de non cultu are instituted to prove that the decrees of Urban VIII regarding the prohibition of public worship of servants of God before their beatification have been obeyed; they are generally conducted by the bishop of the place where the relics of the servant of God are preserved. (c) Other inquiries are known as Processiculi diligentiarum and have for their object the writings attributed to the person whose beatification is in question; they vary in number according to the dioceses where such writings are found, or are thought likely to be found, and may not be judicially executed before an "Instruction" is obtained from the promotor of the Faith by the postulator-general and by him sent to the bishop in question.
The results of all these inquiries are sent to Rome, to the Congregation of Rites, in charge of a messenger (portitor) chosen by the judges, or by some other secure way, in case a rescript of the congregation dispenses from the obligation of sending a messenger.
They are opened, translated if necessary into Italian, a public copy is made, and a cardinal is deputed by the pope as relator or ponens of the cause, for all which steps rescripts of the congregation, confirmed by the pope, must be obtained.
The writings of the servant of God are next revised by theologians appointed by the cardinal relator himself, authorized to so act by a special rescript. Meantime, the advocate and the procurator of the cause, chosen by the postulator-general, have prepared all the docuмents that concern the introduction of the cause (positio super introductione causae). These consist of (a) a summary of the informative processes, (b) an information, (c) answers to the observations or difficulties of the promotor of the Faith sent by him to the Postulator.
This collection of docuмents (positio) is printed and distributed to the cardinals of the Congregation of Rites forty days before the date assigned for their discussion.
If nothing contrary to faith and morals is found in the writings of the servant of God, a decree is published, authorizing further action (quod in causâ procedi possit ad ulteriora), i.e., the discussion of the matter (dubium) of appointment or non-appointment of a commission for the introduction of the cause.
At the time fixed by the Congregation of Rites an ordinary meeting (congregatio) is held in which this appointment is debated by the cardinals of the aforesaid congregation and its officials, but without the vote or participation of the consultors, though this privilege is always granted them by rescript.
If in this meeting the cardinals favour the appointment of the aforesaid commission, a decree to that effect is promulgated, and the pope signs it, but, according to custom, with his baptismal name, not with that of his pontificate. Thenceforward the servant of God is judicially given the title of Venerable.
A petition is then presented asking remissorial letters for the bishops in partibus (outside of Rome), authorizing them to set on foot by Apostolic authority, the inquiry (processus) with regard to the fame of sanctity and miracles in general. This permission is granted by rescript, and such remissorial letters are prepared and sent to the bishops by the postulator-general. In case the eye-witnesses be of advanced age, other remissorial letters are usually granted for the purpose of opening a process known as "inchoative" concerning the particular virtues of miracles of the person in question. This is done in order that the proofs may not be lost (ne pereant probationes), and such inchoative process precedes that upon the miracles and virtues in general.
While the Apostolic process concerning the reputation of sanctity is under way outside of Rome, docuмents are being prepared by the procurator of the cause for the discussion de non cultu, or absence of cultus, and at the appointed time an ordinary meeting (congregatio) is held in which the matter is investigated; if it be found that the decree of Urban VIII has been complied with, another decree provides that further steps may be taken.
When the inquiry concerning the reputation of sanctity (super famâ) has arrived in Rome, it is opened (as already described in speaking of the ordinary processes, and with the same formalities in regard to rescripts), then translated into Italian, summarized, and declared valid. The docuмents super famâ in general are prepared by the advocate, and at the proper time, in an ordinary meeting of the cardinals of the Congregation of Rites, the question is discussed: whether there is evidence of a general repute for sanctity and miracles of this servant of God. If the answer is favourable, a decree embodying this result is published.
New remissorial letters are then sent to the bishops in partibus for Apostolical processes with regard to the reputation for sanctity and miracles in particular. These processes must be finished within eighteen months and when they are received in Rome are opened, as above described, and by virtue of an equal number of rescripts, by the cardinal prefect, translated into Italian, and their summary authenticated by the Chancellor of the Congregation of Rites.
The advocate of the cause next prepares the docuмents (positio) which have reference to the discussion of the validity of all the preceding processes, informative and Apostolic.
This discussion is held in the meeting called congregatio rotalis from the fact that it is only judges of the Rota who vote. If the difficulties of the promotor of the Faith are satisfactorily answered, the decree establishing the validity of the inquiries or processes is published.
Meanwhile all necessary preparation is made for the discussion of the question (dubium): Is there evidence that the venerable servant of God practiced virtues both theological and cardinal, and in an heroic degree? (An constet de virtutibus Ven. servi Dei, tam theologicis quam cardinalibus, in heroico gradu?) In the causes of confessors this step is of primary importance. The point is discussed in three meetings or congregations called respectively, ante-preparatory, preparatory, and general. The first of these meetings is held in the palace of the cardinal relator (reporter) of the cause, and in it only consultors of the Congregation of Sacred Rites, and with their chairman, or prefect, presiding, the third is also held in the Vatican, and at it the pope presides, and both cardinals and consultors vote. For each of these congregations the advocate of the cause prepares and prints official reports (positiones), called respectively report, new report, final report, concerning the virtues, etc., — positio, positio nova, positio novissima, super virtutibus. In each case, before proceeding to the subsequent meeting, a majority of the consultors must decide that the difficulties of the promotor of the Faith have been satisfactorily solved.
When the Congregation of Rites in the above described general meeting has decided favourably, the pope is asked is asked to sign the solemn decree which asserts that there exists evidence of the heroic virtues of the servant of God. This decree is not published until after the pope, having commended the matter to God in prayer, gives a final consent and confirms by his supreme sentence the decision of the congregation.
The miracles now remain to be proved, of which two of the first class are required in case the practice of virtues in the heroic degree has been proved, in both ordinary and Apostolic inquiries or processes by eyewitnesses — three, if the eyewitnesses were found only in the ordinary processes; four, if the virtues were proven only by hearsay (de auditu) witnesses. If the miracles have been sufficiently proven in the Apostolic processes (super virtutibus) already declared valid, steps are taken at once to prepare the docuмents with regard to miracles (super miraculis). If in the Apostolic processes only general mention has been made of the miracles, new Apostolic processes must be opened, and conducted after the manner already described for proving the practice of virtues in an heroic degree.
The discussion of the particular miracles proceeds in exactly the same way and in the same order as that of the virtues. If the decisions be favourable, the general meeting of the congregation is followed by a decree, confirmed by the pope, in which it is announced that there is proof of miracles. It must be noted here that in the positio for the ante-preparatory congregation there are required, and are printed, opinions of two physicians, one of whom has been chosen by the postulator, the other by the Congregation of Rites. Of the three reports (positiones) above mentioned, and which are now also required, the first is prepared in the usual way; the second consists of an exposition of the heroic virtues of the servant of God, an information, and a reply to later observations of the promotor of the Faith; the last consists only of an answer to his final observations.
When the miracles have been proved, another meeting of the Congregation of Rites is held in which it is debated once, and only once, whether or not, given the approbation of the virtues and miracles, it is safe to proceed with the solemnities of beatification. If a majority of the consultors be favourable, a decree to this effect is issued by the pope, and at the time appointed by him the solemn beatification of the servant of God takes place in the Vatican Basilica, on which occasion a pontifical Brief is issued permitting the public cultus and veneration of the beatified person now known as Blessed (Beatus).
The beatification of martyrs
The causes of martyrs are conducted in the same way as those of confessors as far as the informative processes and those de non cultu and ad introductionem causae are concerned. But when once the commission of introduction has been appointed they advance much more rapidly.
No remissorial letters are granted for Apostolic processes concerning the general reputation for martyrdom and miracles; the letters sent call for an immediate investigation into the fact of martyrdom, its motive, and the particular miracles alleged. There is no longer a discussion of the general reputation for martyrdom or miracles.
The miracles are not discussed, as formerly, in separate meetings, but in the same meetings that deal with the fact and the motive of the martyrdom.
The miracles (signa) required are not those of the first class; those of the second class suffice, nor is their number determined. On some occasions the decision as to miracles has been entirely dispensed with.
The discussion as to martyrdoms and miracles, formerly held in three meetings or congregations, viz. the ante-preparatory, preparatory, and general, is now usually conducted, through a dispensation to be had in each instance from the sovereign pontiff, in a single congregation known as particularis, or special. It consists of six or seven cardinals of the Congregation of Rites and four or five prelates especially deputed by the pope. There is but one positio prepared in the usual way; if there be an affirmative majority a decree is issued concerning the proof of martyrdom, the cause of martyrdom, and miracles. (Constare de Martyrio, causâ Martyrii et signis.)
The final stage is a discussion of the security (super tuto) with which advance to beatification may be made, as in the case of confessors; the solemn beatification then follows.
This procedure is followed in all cases of formal beatification in causes of both confessors and martyrs proposed in the ordinary way (per viam non cultus). Those proposed as coming under the definition of cases excepted (casus excepti) by Urban VIII are treated in another way. In such cases it must be proved that an immemorial public veneration (at least for 100 years before the promulgation, in 1640, of the decrees of Urban VIII) has been paid the servant of God, whether confessor or martyr. Such cause is proposed under the title of "confirmation of veneration" (de confirmatione cultus); it is dealt with in an ordinary meeting of the Congregation of Rites. When the difficulties of the promotor of the Faith have been satisfied, a pontifical decree confirming the cultus is promulgated. Beatification of this kind is called equivalent or virtual.

The canonization of confessors or martyrs
The canonization of confessors or martyrs may be taken up as soon as two miracles are reported to have been worked at their intercession, after the pontifical permission of public veneration as described above. At this stage it is only required that the two miracles worked after the permission awarding a public cultus be discussed in three meetings of the congregation. The discussion proceeds in the ordinary way; if the miracles be confirmed another meeting (super tuto) is held. The pope then issues a Bull of Canonization in which he not only permits, but commands, the public cultus, or veneration, of the saint.

It is with the utmost possible brevity that I have described the elements of a process of beatification or canonization. It may be easily conjectured that considerable time must elapse before any cause of beatification or canonization can be conducted, from the first steps of the information, inquiry, or process, to the issuing of the decree super tuto. According to the constitution of this Congregation, more than one important discussion (dubia majora) cannot be proposed at the same time. It must be remembered

that the same cardinals and consultors must vote in all discussions;
that there is but one promotor of the Faith and one sub-promotor, who alone have charge of all observations to be made with regard to the dubia;
that these cardinals and consultors have to treat questions of ritual as well as processes of canonization and beatification.
To execute all this business there is but one weekly meeting (congressus), a kind of minor congregation in which only the cardinal prefect and the major officials vote; in it less important and practical questions are settled regarding rites as well as causes, and answers are given, and rescripts which the pope afterwards verbally approves. The other meetings of the congregation (ordinary, rotal, and "upon virtues and miracles") may be as few as sixteen in the course of the year. Some other cause must therefore be found for the slow progress of causes of beatification or canonization than a lack of good will or activity on the part of the Congregation of Rites.

Would the anti-Popes be beatified and canonized under this procedure?