Your arguments are not with me - they are with Ott who quotes the majority opinion, Bellarmine who states no-one can know with the certainty of faith anyone's intention.

Problem here is with the notion of "interior" intention.  Interior/internal only speaks to the fact that it's internal, an act of the mind and will, vs. just physical activity.

What's at issue is not whether it must be interior or internal, but what the OBJECT of that intention must be.

Again, the object of said "internal" intention must be simply to DO that which the Church DOES.  One need not intend the same thing the Church intends by doing that action.  So what's under discussion is the OBJECT of said internal intention.  If one must intend what the Church intends, then pagans could never validly baptize.  But if one merely intends to DO that which the Church DOES, then anyone can validly baptized.

And notice the language of Trent; one must intend to DO that which the Church DOES.  No mention of someone having to intend what the Church intends.

Let me give you an example of where the interior intention is lacking.  Let's say you have a priest who's just practicing offering Mass (for whatever reason).  Perhaps it's because he's been just conditionally ordained from the Novus Ordo but doesn't yet know how to offer the Tridentine Mass.  He does everything including saying the words of consecration.  But his intention is just to "practice".  In that case there's no intention to perform the action that the Church performs.  This would not be valid.  So the mere external action of saying the words does not suffice to validly confect the Sacrament.

But, on the contrary, if you have a rogue priest (say, some Communist infiltrator) who goes up there and says Mass for the parish.  In his mind, he's saying "I do not intend to consecrate."  This matters not.  By going there and publicly offering the Mass, he intends to DO what the Church does, to PERFORM the actions that the Church performs in order to validly offer the Mass.  That act of the intellect & will (internal actions) suffices to make the Mass valid, despite him intending NOT to do that which the Church INTENDS by the Mass.

That's why, regardless of what rogue infiltrators might be in the Church, God will safeguard the validity of the Sacraments for the faithful.  God doesn't withhold the Sacraments from the faithful due to such rogue elements.

Anthony Gavin, a Catholic priest of Saragossa, describes the confession of a brother priest on his deathbed, whose name he conceals, and who says: "The necessary intention of a priest in the administration of baptism and consecration (of the wafer) without which the sacraments are of no effect, I confess I had it not on several occasions, as you may see in the parish books; and observe that the baptism was invalid of every person whose name is there marked with a star, for in such cases I had no intention. And for this I can give no other reason than my malice and wickedness. Many of them are dead, for which I am heartily sorry. As for the times I have consecrated (the wafer) without intention we must leave it to God's mercy, for the wrong done by it to the souls of my parishoners, and those in purgatory cannot be helped." [Master Key to Popery, 1833 Cincinnati, p. 35] (…) Gavin, on examining the parish books, found one hundred and fifty-two names marked with a star, and of the persons enrolled in this ill-starred register eighty six were dead. Gavin was greatly troubled about these persons, knowing that it is the decided opinion of the Church that "The intention of the priest is absolutely necessary to the validity of a sacrament, without which there is no sacrament at all." By the advice of his brother priests he communicated the case to the bishop, who summoned the persons still living, who through the absence of intention in the defunct priest, were not baptized when they passed through all the forms of baptism, and bringing them into his own chamber separately, he baptized them; enjoining the strictest secrecy under the heaviest penalties upon each. [Master Key to Popery, 1833 Cincinnati, p. 38]

Quote from: curioustrad

And now a word from the Novus Ordo: Source

The point here is that they also err on the side of caution !

Nonsense,  Based on your principles, alleging that one must intend as the Church intends, pagans could never validly baptize.  Consequently, there's no need for a "conditional" baptism after the fact.

Pope Alexander VIII, in 1690, rejected the following proposition: Valet Baptismus collatus a ministro, qui omnem ritum externum formamque baptizandi observat, intus vero in corde suo apud se resolvit: non intendo, quod facit Ecclesia. (A Baptism is valid which is conferred by a minister who observes all the external rite and the form of baptising but who says in his heart" I do not intend to do what the Church does") D 1318.

I will take a standard Catholic theologian any day.

Quote from: curioustrad

I will take a standard Catholic theologian any day.

Yeah, yeah, the same crap we always here when someone can't actually argue the point.  We're arguing about which theologian(s) are right.  So if you don't want to argue, then shut up and get off the thread.  It's been duly noted what one or another theologian thinks of the subject.  So rather than posting this tired refrain on every post, either join the substance of the argument or get off the thread.  You're annoying and wasting everyone's time.

As I studied logic "ad hominem" attacks were always the proof that the one disputing had the weaker case. I have shown authority after authority - your argument is with them not with me. If you reject their authority, then you are right: cuм negante principia nequit disputare.

Quote from: curioustrad

No the question is in the "intention", not in failing to perform the ritual. Read the Catholic Encyclopedia article and follow their logic not mine.

Again, you keep collapsing your position into "intention".  What's at issue is what the OBJECT the intention needs to be.

"I intend to perform a Sacrament that remits Original Sin and puts the soul into a state of sanctifying grace." [your position]

OR

"I intend to perform this ceremony that the Catholic Church does." [my position]

Unless the object of the intention is as I argue, pagans could NEVER validly baptize.

Based on BOTH our positions, the intention of a Prot would be questionable.