On the topic of how many shall be saved, from a Catholic view, Fr. Lasance in the early 1900s comments on this topic in "My Prayer Book", p. 55: https://archive.org/details/MyPrayerBookHappinessInGoodness/page/55/mode/2up
Attempt at Summary
The heresy of Jansenism in the 1600s tended towards a strict view of salvation that only a few would be saved. Over the centuries we are now tending towards the other condemned view of "universal salvation", or that all will be saved no matter what. A common opinion of theologians is that "few" will be saved, but we know not how many.
Fr. Lasance mentions that Catholics are permitted to believe that a majority of Catholics will be saved, or the majority of mankind; Catholics have not authoritively stated we must believe this number or that number will be saved.
People are simply encouraged to strive to be among the few; if only a few are saved, then hopefully they are among that number, and if many are saved, then they should also be among that number:
> If you want to be certain of being in the number of the Elect, strive to be one of the few, not one of the many. And if you would be quite sure of your salvation, strive to be among the fewest of the few. -St. Anselm
> Strive to enter by the narrow gate; for many, I say to you, shall seek to enter, and shall not be able. Luke 13:24
Feeneyism and "Universal Baptism of Desire"
Now today there is a “strict” error Catholics have had to deal with dubbed “Feeneyism”, or the view that only the water baptized may be saved. Catholics have acknowledged that one may be “baptized by shedding their blood” or “baptized by virtue of desiring baptism”. There are many examples of martyrs who were not baptized by water, but “by their blood”, who are considered to be saints, or among the saved.
I think this error of “Feeneyism” came about in reaction to an opposite error of “universal salvation by baptism of desire”, or modernists arguing “everyone has an implicit desire for baptism, whether they know it or not”. In effect they were arguing that almost everyone will be baptized, simply because they have an unknown desire for baptism, and therefore will be saved.
This seems to plainly conflict with people who are aware of a need to be baptized by water, but who for whatever reason do not go and receive baptism, nor make any attempt to do so; the counter-argument would be here that there are at least some people who have had a desire for baptism they haven’t acted on or have opposed, which would be considered to be “morally imputable”.
In any event, I think these are twin erroneous tendencies, with “Feeneyism” taking a strict incorrect approach, with the “universal baptism of desire” approach, which is unnamed, having an incorrect “broad” view of things, and with Catholics taking a “moderate” position that some may be “baptized by blood or desire” and be saved.
(I have heard some young people have become attracted to the idea of “Feeneyism” as a “strict” reaction to some “broad” erroneous attitudes today)
Have you encountered "feeneyism" or an opposite idea of "universal baptism of desire", or do you have any more to elaborate about on the topics?
matter (water), form (must make the sign of the cross with the water with the words "I baptize you in the name of the Father, Son, and Holy Ghost"), and intent (to intend to baptize a person as the Church intends people do).
Some other rules of thumb are noted on this topic:
Catholic encyclopedia on "Baptism" (early 1900s) https://www.newadvent.org/cathen/02258b.htm:
> The Fathers and theologians frequently divide baptism into three kinds: the baptism of water (aquæ or fluminis), the baptism of desire (flaminis), and the baptism of blood (sanguinis). However, only the first is a real sacrament. The latter two are denominated baptism only analogically, inasmuch as they supply the principal effect of baptism, namely, the grace which remits sins. It is the teaching of the Catholic Church that when the baptism of water becomes a physical or moral impossibility, eternal life may be obtained by the baptism of desire or the baptism of blood.
This issue also pops up a bit due to the teaching on limbo, that the souls of the unbaptized infants may go to limbo, or otherwise "good" unbaptized people:
"Limbo" entry https://www.newadvent.org/cathen/09256a.htm:
> In theological usage the name is applied to (a) the temporary place or state of the souls of the just who, although purified from sin, were excluded from the beatific vision until Christ's triumphant ascension into Heaven (the "limbus patrum"); or (b) to the permanent place or state of those unbaptized children and others who, dying without grievous personal sin, are excluded from the beatific vision on account of original sin alone (the "limbus infantium" or "puerorum").
edit: http://infogalactic.com/info/Feeneyism