http://strobertbellarmine.net/books/Concerning_A_SSPX_Dossier_on_Sedevacantism.pdf

Fr. Boulet next discusses the degrees of publicity of crimes.

3.4. Public and Notorious heresy:  It is to be understood according to the Canon Law principles. A Public crime, according to the law of the Church is not necessarily something which is done in the open and witnessed by Television cameras, as most people think.  Let me quote the famous canonist Bouscaren: “Classification as to Publicity. A crime is: 1. Public, if it is already commonly known or the circuмstances are such as to lead to the conclusion that it can and will easily become so; [...] ‘Commonly known’ (divulgatum) means known to the greater part of the inhabitants of a place or the members of a community; but this is not to be taken mathematically, but in prudent moral estimation. A crime may remain occult though known to a number of persons who are likely to keep it quiet, whereas it may be public though known to only a few who are sure to divulge it.” As the Pope is the Universal pastor of the entire Church, how can we apply such principles to the case of his heresy? According to the canonists, for an act of heresy by a Pope to be Public, the knowledge of it would either have to be either already widely spread amongst the faithful of the universal Church, being known to most of them, or at least such as that it will be in practice impossible to stop it from becoming so known and it certainly will.  Such heresy would have to be widely publicised, as well as Notorious – in order to be Public in canonical terms.  For a Pope’s heresy to be Notorious, not only would the heretical act have to be widely known of, as we have seen, but it would also have to be an act whose criminality had been legally recognised.  In other words, for the criminality of a Pope’s heresy to be legally recognised, such that his heresy would be canonically Notorious, not only would a knowledge of his heresy have to have spread widely through the Church, as we have seen above, but it would also have to have been widely recognised as a morally imputable crime.
 
a) Having quoted the Code (as translated by Bouscaren) to the effect that a crime is public “if the circuмstances are such as to lead to the conclusion that it can and will easily become [commonly known]” Fr. Boulet tells us that for this note to apply to heresy by a Pope, “the canonists” tell us that it “would have to be widely publicised, as well as
Notorious – in order to be Public in canonical terms.” Now, since no canonists are quoted or even cited in support of this claim, and since it conflicts with the definition of the term “public” given in the Code, I think we can safely leave it aside.

Here is the actual canon – 2197 – followed by the translation of Bouscaren & Ellis.

Delictum est:
1.° Publicuм, si iam divulgatum est aut talibus contigit seu versatur in adiunctis ut prudenter iudicari possit et debeat facile div ulgatum iri;

2.° Notorium notorietate iuris, post sententiam iudicis competentis quae in rem iudicatam transierit aut post confessionem delinquentis in iudicio factam ad normam can. 1750;

3.° Notorium notorietate facti, si publice notum sit et in talibus adiunctis commissum, ut
nulla tergiversatione celari nulloque iuris suffragio excusari possit;

4.° Occultum, quod non est publicuм; occultum materialiter, si lateat delictum ipsum;
occultum formaliter, si eiusdem imputabilitas.

Classification as to Publicity. A crime is:

1. Public, if it is already commonly known or the circuмstances are such as to lead to the conclusion that it can and will easily become so;

2. Notorious in law, after judgment by a competent judge which has become
res iudicata (cf. c. 1902), or after confession by the culprit in open court according to canon 1750;

3. Notorious in fact, if it is publicly known and was committed under such circuмstances that no maneuver can conceal nor any legal defense excuse it;

4. Occult, if not public; materially occult if the crime itself is hidden, formally occult if its
imputability is hidden (c. 2197). [Bouscaren and Ellis, Canon Law: A Text and Commentary, page 858]

Note that “notorious” and “public” are quite distinct, and that for something to be “public” it certainly does not need to be “notorious” or “widely publicised,” so it is not apparent why Fr. Boulet thinks what he does on this point. The remainder of his comments in this section are no more cogent – for example, he appears to conflate the two different kinds of notoriety, that of fact and of law.

b) The concept introduced by da Silveira into the definition of “notorious” – that of “the grand public” – is surely nothing more than a relic of the Revolution. He writes, “Can one understand as occult heresy that which is already known to many persons, but has still not reached the grand public, has still not become notorious and publicly divulged?” Thus he brings in the French cliché, “le grand public,” with no clear and ascertainable meaning in any law, let alone canon law. What could this mean, in this context, other than that so long the organs of the secular press treat somebody as orthodox, then he is not a public heretic?

The problem here is that what the canons have in view is an objective rule for classifying the nature of a crime, not a subjective measure determined by how many people actually notice the crime.  Several considerations illustrate this.

i) It assists to remember that divulgatum and publice are distinct terms, the first of which means “commonly known” whilst the second is a technical term defined in the Code. Much confusion is generated by those who equate the terms so that publice loses its objective character and depends instead upon the dispositions of the editors of the press and the interest of the populace.

ii) The Code tells us that something is “public” even if it is not known by many, but only that “the circuмstances are such as to lead to the conclusion that it can and will easily become” commonly known. That is, such a crime is already public even though hardly anybody knows about it. An analogy may assist. Consider, instead of the concept of “publicity,” the notion of “danger.” Something may be dangerous even though no actual harm occurs in a given case. It is true that in assessing degrees of danger we would properly take into account actual harm which has occurred in cases, and so if great harm had frequently occurred in a given set of circuмstances, we would certainly classify those circuмstances as “dangerous.” But having introduced this consideration of actual harm, we would upset the entire concept of “danger” as distinct from “harm” if we were subsequently to measure danger in actual cases only by virtue of the harm which arose in each of those cases. Thus all would see the absurdity of a claim that a man driving through crowded streets at very high speed could only be described as acting dangerously if somebody gets hurt on that occasion. The classification arises from a consideration of actual harm in past cases; the usefulness of the classification is precisely in its applicability to cases in which actual harm has not yet been caused. But, of course, we would classify as “dangerous” any actual circuмstances which subsequently did result in actual harm. The point is that we would certainly not consider it reasonable to deny the tag “dangerous” to a concrete case merely on the grounds that actual harm was avoided.  

Likewise degrees of publicity of crimes are generic classifications built up based on cases – but to argue that something is not “public” merely because the common man has not yet heard about it is to submit to the arbitrary rule of the mass media instead of abiding by the rules of reason.
 
Hence Bouscaren & Ellis explain, ‘Commonly known’ (divulgatum) means known to the greater part of the inhabit ants of a place or the members of a community; but this is not to be taken mathematically, but in prudent moral estimation. A crime may remain occult though known to a number of persons who are likely to keep it quiet, whereas it may be public though known to only a few who are sure to divulge it. It may be public in one place and occult in another, or may become occult even in the same place after a lapse of years." [Bouscaren and Ellis, Canon Law: A Text and Commentary, page 858]

iii) Notoriety chiefly relates to guilt, not to the element of divulgation. The Canonist
Augustine explains, “It is this element of inexcusability or of knowledge of the criminal character of the deed that appears to distinguish a public from a notorious crime. For the text manifestly lays stress on divulgation with regard to public crimes and emphasizes the criminal character as known and inexcusable.” [Augustine, A Commentary on Canon Law, volume 8, page 17]

iv) This is also made clear by Woywod, who employs “publicly known” as an equivalent term to “public.” He writes, “The distinction between occult and public offenses is explained in general terms by the Code. Canonists have given more specific rules by which one may judge whether an offense is to be considered publicly known. In the first place, the number of people who were witnesses to an offense and the number of inhabitants of the place where the offense was committed, must be taken into consideration to determine whether an offense may be said to be public. It is maintained by many canonists that at least six persons in a small town or community must know of the offense before it can be called public, and more persons in proportion to the greater number of inhabitants before it can be called public in larger places. However, canonists consider, not only the relative number in determining whether an offense is occult or public, but also the character of the perhaps few persons who witnessed the commission of the offense – whether they are reserved and taciturn or talkative and eager to make known what they have witnessed. The Code calls an offense public when knowledge of it has been spread among the people (divulgatum), or when it was committed under circuмstances which make it practically impossible to keep the offense secret.” [A Practical Commentary on the Code of Canon Law, Woywod Smith, volume 2, p. 403]
It should be sufficiently clear that in the language of canon law the term “notorious” is a technical term with a very specific definition, and the way in which we use the same term in common discourse is quite different. Sometimes these matters appear to be approached with a lack of discipline which causes technical terms to be understood in their everyday sense, which of course can be and often is fatal to a proper understanding of them (cf. CIC18). This certainly appears to be true of da Silveira when he enters into this question of the degrees of publicity.

v) Summarising these points, we see that something may be notorious with a notoriety of fact if it is known to few, but talkative, persons, and was committed under such circuмstances as to be inexcusable. That is, if it meets the definition of “publice” and also could not be excused by any legal defence.

I am not here arguing that Paul VI, John Paul II, or Benedict XVI have all been notorious heretics in the legal sense, although that case could be made. I think it may easily be demonstrated that all three of these men have been public heretics, and that suffices.