Can. 4. If B]anyone denies that for the full and perfect remission of sins
. . .
required on the part of the penitent for the integrity of the Sacrament, and for the full and perfect remission of sin,
Saint Gobban seems to be under the impression that “integrity of the sacrament” means “that without which there is no sacrament”. I think that is one likely place we might misread what Trent is saying.
“Integrity” – i.e. that which is “integral” to something – means in this context those parts which constitute a perfect whole, the fullness of the thing. This is also what the “full and perfect remission of sin” is referring to.
But, although satisfaction is INTEGRAL to the sacrament and for its perfection, it is not ESSENTIAL for its existence. Though it perfects the sacrament, it isn’t something “without which not”, i.e. it is not the “sine qua non” of the sacrament. Unlike contrition which certainly
is a “sine qua non”.
To illustrate: a man missing an arm suffers from a lack of integrity. He isn’t an integral man. He is a imperfect man. But still a man.
“Full and perfect remission of sin” doesn’t refer to the remission of eternal guilt simply. It refers to perfecting the aims of the sacrament,-- not just the primary aim of removing guilt of eternal punishment, but also the secondary aims of expiating temporal punishment and reforming the sinner. Satisfaction accomplishes this secondary effect, and absolution accomplishes the primary effect.
This is why the Catechism of Trent which I quoted earlier says:
Penance is composed of these three parts in such a way that though contrition and confession, which justify man, are alone required to constitute its essence, yet, unless accompanied by its third part, satisfaction, it necessarily remains short of its absolute perfection.