[Question:]{.underline} Is it true that a heretic, who does not believe in the Real Presence, can have the intention of doing what the Church does, and celebrate a valid Mass?
It is certainly true, as St. Thomas Aquinas explains, that Faith is not required of necessity in the minister for the sacraments he administers to be valid (IIIa, Q.64, a.9). In just the same way that a heretic can validly administer the sacrament of baptism (e.g. a protestant), and even the fact that he does not believe in original sin does not invalidate this sacrament, so also can a heretic celebrate a valid Mass. He does not have to intend what the Church intends, but only what the Church does, which latter is possible even when he has a gross misunderstanding of what the Church really does.
However, this being the case, the existence of heresy can certainly place a shadow of doubt over the intention of the minister giving a sacrament. Before Vatican II it was always the practice to baptize under condition any adult converts from Protestantism. There were several reasons to doubt to some degree Protestant baptisms, one of which is a defective intention of the minister. If the minister had an explicitly contrary intention, namely if he had explicitly formulated the intention of not doing what the Catholic Church has always done, then the sacrament would be invalid. It is not the fact that he does not believe in original sin that could makes the sacrament of baptism invalid, but the fact that his explicit intention is just to give an outward sign, and not to administer a sacrament that removes original sin and infuses sanctifying grace.
The same can be the case with the New Mass, and this even if the priest still believes in the Real Presence. He could have a contrary intention to that of the Church. This would be the case if his intention explicitly refuses offering a true sacrifice, the unbloody renewal of Calvary, and explicitly considers that it is to be [only]{.underline} a meal and a commemoration of the Last Supper. Such an intention would be directly contrary to the intention of doing what the Church does. We do not know how often this happens, but it is very reasonable to believe that it is a common occurrence. Consequently, there are probably many celebrations of the New Mass, by priests who are convinced of modernist theories, that are invalid.
This is one reason that we cannot have anything to do with the New Mass. However, the more universal reason is that it is insulting and injurious to Almighty God and to Our Lord Jesus Christ, even if it happens to be valid.
Answered by Father Peter Scott, SSPX.