I disagree, and so does St. Thomas.  It's based on the objective and externally-manifested (albeit internal) intention of the minister.  So if the priest performs the Catholic Rite as prescribed, he has the intention to do WHAT the Church DOES ...

A priest who forms a contrary internal intention does not confect the sacrament, despite the performance of the external rite.

Generally speaking, we are morally certain that a priest who performs a sacramental rite (e.g., TLM or NOM) possesses sufficient intention, because there can only be positive doubt regarding a contrary intention if it is manifested somehow in the external forum.

But this is not the case in Fr. Scott's argument:

He is not concerned about what is being externally manifested, but in what is NOT being externally manifested.

By definition, this can only produce a negative doubt, since, there being no external manifestation of a contrary intention, the consideration pertains to the internal forum (which is unknowable without such external manifestation).

In short, the requisite intention, which is nearly automatic (and not on the basis of the form of the rite, but on the basis of a sane priest performing a sacramental rite obviously aware of doing what the Church does) is so difficult to lose, that doubting its presence without any manifestation of having formed a contrary intention, is practically inadmissible.

Here, once again, is Fortesque:

“People who are not theologians never seem to understand how little intention is wanted for a sacrament… The ‘implicit intention of doing what Christ instituted’ means so vague and small a thing that one can hardly help having it — unless one deliberately excludes it. At the time when everyone was talking about Anglican orders, numbers of Catholics confused intention with faith. Faith is not wanted. It is heresy to say that it is. (This was the error of St Cyprian and Firmilian against which Pope Stephen I [254–257] protested.) A man may have utterly wrong, heretical and blasphemous views about a sacrament and yet confer or receive it quite validly.”

-Adrian Fortescue: The Greek Fathers

Highly debatable, and even the Satanists know this, so Satanic Masses use stolen consecrated Hosts.

Your point is valid if we’re talking about a satanic priest who was never a real priest.  In the case of a former valid priest-turned-satanist, then the consecration would be valid, and there are historical cases of this.  

The point is that when comparing the external intentions of the TLM vs the NOM, one is comparing apples-oranges.  Cardinal Ottaviani, and his fellow theologians (of which you are not one) said that the external intention of the NOM is corrupted and cannot be trusted as a visible display of the sacramental intention, due to the changes in the prayers, which affect the mass’ overall purpose and also the priest's intention.  

External intention?

Please quote the passage.

Internal intention is what is requisite for a valid intention.

The only bearing an external intention can have in the matter, is if it is a contrary external intention.

PS: I like how you are trying to make it seem as though Cardinal Ottaviani wrote the "Brief Critical Study."  

PPS: The Ottaviani Intervention wasa written before the NOM was officially promulgated.  Once that happened, here is what Ottaviani had to say:

“I have REJOICED PROFOUNDLY to read the Discourse by the Holy Father on the question of the new Ordo Missae, and ESPECIALLY THE DOCTRINAL PRECISIONS CONTAINED IN HIS DISCOURSES at the public Audiences of November 19 and 26, after which I believe, NO ONE CAN ANY LONGER BE GENUINELY SCANDALIZED. As for the rest, a prudent and intelligent catechesis must be undertaken to solve some legitimate perplexities which the text is capable of arousing. In this sense I wish your ‘Doctrinal Note’ [on the Pauline Rite Mass] and the activity of the Militia Sanctae Mariae WIDE DIFFUSION AND SUCCESS.” (Whitehead, 129, Letter from his eminence Alfredo Cardinal Ottaviani to Dom Gerard Lafond, O.S.B., in Docuмentation Catholique, #67, 1970, pages 215-216 and 343) 

Cardinal Ottaviani published later yet another very relevant public statement in which he said: “The Beauty of the Church is equally resplendent in the variety of the liturgical rites which enrich her divine cult-when they are legitimate and conform to the faith. Precisely the LEGITIMACY OF THEIR ORIGIN PROTECTS AND GUARDS THEM AGAINST INFILTRATION OF ERRORS. . . .The PURITY AND UNITY OF THE FAITH is in this manner also UPHELD BY THE SUPREME MAGISTERIUM OF THE POPE THROUGH THE LITURGICAL LAWS.”(In Cruzado Espanol, May 25, 1970)

1) On a case by case basis, there may or may not be positive doubt as regards the validity of the NOM: But as a matter of principle, one cannot conclude they are all per se doubtful, because:

The good Archbishop Lefebvre, God rest his soul, would disagree with you:
- "And we have the precise conviction that this new rite of Mass expresses a new faith, a faith which is not ours, a faith which is not the Catholic Faith.This New Mass is a symbol, is an expression, is an image of a new faith, of a Modernist faith… Now it is evident that the new rite, if I may say so, supposes another conception of the Catholic religion - another religion.” (Sermon, June 29, 1976)

-“I will never celebrate the Mass according to the new rite, even under threat of ecclesiastical penalties and I will never advise anyone positively to participate actively in such a Mass." (Conference April 11, 1990) 

-“The current Pope and bishops no longer hand down Our Lord Jesus Christ, but rather a sentimental, superficial, charismatic religiosity through which, as a general rule, the true grace of the Holy Ghost no longer passes. This new religion is not the Catholic religion; it is sterile, incapable of sanctifying society and the family.” (Spiritual Journey, p. ix)

-“It is the new Mass in itself. It is not the priest who is saying it. It is not because he says it piously or anything that the new rite changes. It doesn’t change anything in the rite of the Mass. It is obvious that this new rite is a rite that has been made only to draw us closer to the Protestants. That is clear! (April 11, 1990)

-“This Mass is poisoned, it is bad and it leads to the loss of faith little by little. We are clearly obliged to reject it.” (The Mass of All Times, p. 353)

-“It must be understood immediately that we do not hold to the absurd idea that if the New Mass is valid, we are free to assist at it. The Church has always forbidden the faithful to assist at the Masses of heretics and schismatics even when they are valid. It is clear that no one can assist at sacrilegious Masses or at Masses which endanger our faith.…All these innovations are authorized. One can fairly say without exaggeration that most of these [new] Masses are sacrilegious acts which pervert the Faith by diminishing it. The de-sacralization is such that these Masses risk the loss of their supernatural character, their mysterium fidei; they would then be no more than acts of natural religion. These New Masses are not only incapable of fulfilling our Sunday obligation, but are such that we must apply to them the canonical rules which the Church customarily applies to communicatio in sacris with Orthodox Churches and Protestant sects.” (The New Mass and the Pope, November, 8, 1979)

-“… this [new] rite is bad! Is bad, is bad. And the reason why this rite is bad in itself, is because it is poisoned. It is a poisoned rite! Mr. Salleron says it very well, here: "It is not a choice between two rites that could be good. It is a choice between a Catholic Rite and a rite that is practically a neighbor to Protestantism,” and thus, which attacks our Faith, the Catholic Faith! So, it is out of the question to encourage people to go to Mass in the new rite, because slowly, even without realizing it, they end up ecuмenist! It’s strange, but it's like that. It is a fact. Then, ask them questions on ecuмenism, on what they think of the relations with other religions and you will see! They are all ecuмenist. For the priest himself, the fact of saying this mass and celebrating it in a constant manner, even without thinking about anything, about its origin, or why it was made, turns him and the people who assist at it ecuмenist.” (Conference, April 11, 1990)

-"This union which liberal Catholics want between the Church and the Revolution is an adulterous union — adulterous. This adulterous union can only beget bastards. Where are these bastards? They are [the new] rites. The [new] rite of Mass is a bastard rite. The sacraments are bastard sacraments.We no longer know whether they are sacraments that give grace. We no longer know if this Mass gives us the Body and the Blood of Our Lord Jesus Christ. ... The priests emerging from the seminaries are bastard priests." (Homily preached at Lille, August29, 1976)

-“The radical and extensive changes made in the Roman Rite of the Holy Sacrifice of the Mass and their resemblance to the modifications made by Luther oblige Catholics who remain loyal to their faith to question the validity of this new rite.”(Écône, February 2, 1977)

-“Your perplexity takes perhaps the following form: may I assist at a sacrilegious Mass which is nevertheless valid, in the absence of any other, in order to satisfy my Sunday obligation? The answer is simple: these Masses cannot be the object of an obligation; we must moreover apply to them the rules of moral theology and Canon Law as regards the participation or the attendance at an action which endangers the faith or may be sacrilegious. The New Mass, even when said with piety and respect for the liturgical rules, is subject to the same reservations since it is impregnated with the spirit of Protestantism. It bears within it a poison harmful to the faith.” (An Open Letter to Confused Catholics, Ch. 4)

-“The current problem of the Mass is an extremely serious problem for the Holy Church. I believe that if the dioceses and seminaries and works that are currently done are struck with sterility, it is because the recent deviations drew upon us the divine curse. All the efforts that are made to hang on to what is being lost, to reorganize, reconstruct, rebuild, all that is struck with sterility, because we no longer have the true source of holiness which is the Holy Sacrifice of the Mass. Profaned as it is, it no longer gives grace, it no longer makes grace pass.” (Archbishop Lefebvre, August 1972, priestly retreat)

-“We must not forget that the conciliar reforms of the liturgy, the reforms of the Bible, the changes in the internal structure of the Church, of the constitution of the Church—all these things are a result of the ecuмenical spirit. That is clear, since Protestants were present for the changes in the Mass—six Protestant ministers were photographed with Pope Paul VI who thanked them for having come to participate in the liturgical commission, which transformed our Catholic Mass!Everything was done in this ecuмenical spirit: liturgical reforms, catechetical reforms, an ecuмenical Bible—which is sold in the bookstore at the Vatican. There was then, a considerable Protestant influence.” (Conference in Germany, October 29, 1984)

-“…if they are going to the New Mass—slowly, slowly they change their mind and become, slowly, slowly Protestant. It is very dangerous to go to the New Mass regularly, each week, because the New Mass is not some accidental change, but it is a whole orientation, a new definition of the Mass. It has not the same definition as the True Mass.” (Interview, St. Michael’s Mission, Atlanta, April 27, 1986)

“… So, if someone asks me: “I only have Mass of St. Pius V once a month. So what should I do on the other Sundays? Should I go to the New Mass if I do not have the Mass of St. Pius V? ...
I reply: Just because something is poisoned, obviously it is not going to poison you if you go on the odd occasion, but to go regularly on Sunday like that, little by little the notions will be lost, the dogmas will diminish. They will become accustomed to this ambiance which is no longer Catholic and they will very slowly lose the Faith in the Real Presence, lose the Faith in the Holy Sacrifice of the Mass, and have a spirituality, since the prayers are changed and they have modified everything, in the sense of another spirituality. It is a new conception of Christian spirituality. There is no longer any ascetical effort, no longer a combat against sin, no longer a spiritual combat. There is a great need to combat against our own tendencies, against our faults, against everything which leads us to sin. So I would say to them: Listen, I cannot advise you to go to something which is evil. Myself, I would not go because I would not want to take in this atmosphere. I cannot. It is stronger than me. I cannot go. I would not go. So I advise you not to go." (Spiritual Conference at Econe, June 25, 1981)

“The consequences of this state of mind or spirit spread within the Church, inside the Church, are deplorable, and are ruining and sapping the spiritual vitality of the Church. In conscience, all we can do is turn priests and faithful away from using the Novus Ordo Missae if we wish that the complete and whole Catholic Faith remains still living.” (Letter to John Paul II, April 5, 1983 - Archbishop Lefebvre, Conference #1, St. Thomas Aquinas Seminary, April 24, 1983)

“…that the evil in the New Mass is truly intrinsic, in the text … and not only something purely extrinsic, [in the abuses], this is certain. Precisely by this general effect which diminishes the proclamation of our faith, this diminution is present everywhere, in the words and in the actions. They wanted to be ecuмenical to such a point, to bring themselves closer to the Protestants in order to pray with them, that in the end they no longer affirm the Faith. And that is very grave. This diminution is excessively grave for our faith, how can it be otherwise? … Really, in conscience, I cannot advise anyone to attend this Mass, it is not possible.” (Conference at Econe, June 24, 1981)

The good Archbishop Lefebvre, God rest his soul, would disagree with you:
- "And we have the precise conviction that this new rite of Mass expresses a new faith, a faith which is not ours, a faith which is not the Catholic Faith.This New Mass is a symbol, is an expression, is an image of a new faith, of a Modernist faith… Now it is evident that the new rite, if I may say so, supposes another conception of the Catholic religion - another religion.” (Sermon, June 29, 1976)

-“I will never celebrate the Mass according to the new rite, even under threat of ecclesiastical penalties and I will never advise anyone positively to participate actively in such a Mass." (Conference April 11, 1990)

-“The current Pope and bishops no longer hand down Our Lord Jesus Christ, but rather a sentimental, superficial, charismatic religiosity through which, as a general rule, the true grace of the Holy Ghost no longer passes. This new religion is not the Catholic religion; it is sterile, incapable of sanctifying society and the family.” (Spiritual Journey, p. ix)

-“It is the new Mass in itself. It is not the priest who is saying it. It is not because he says it piously or anything that the new rite changes. It doesn’t change anything in the rite of the Mass. It is obvious that this new rite is a rite that has been made only to draw us closer to the Protestants. That is clear! (April 11, 1990)

-“This Mass is poisoned, it is bad and it leads to the loss of faith little by little. We are clearly obliged to reject it.” (The Mass of All Times, p. 353)

-“It must be understood immediately that we do not hold to the absurd idea that if the New Mass is valid, we are free to assist at it. The Church has always forbidden the faithful to assist at the Masses of heretics and schismatics even when they are valid. It is clear that no one can assist at sacrilegious Masses or at Masses which endanger our faith.…All these innovations are authorized. One can fairly say without exaggeration that most of these [new] Masses are sacrilegious acts which pervert the Faith by diminishing it. The de-sacralization is such that these Masses risk the loss of their supernatural character, their mysterium fidei; they would then be no more than acts of natural religion. These New Masses are not only incapable of fulfilling our Sunday obligation, but are such that we must apply to them the canonical rules which the Church customarily applies to communicatio in sacris with Orthodox Churches and Protestant sects.” (The New Mass and the Pope, November, 8, 1979)

-“… this [new] rite is bad! Is bad, is bad. And the reason why this rite is bad in itself, is because it is poisoned. It is a poisoned rite! Mr. Salleron says it very well, here: "It is not a choice between two rites that could be good. It is a choice between a Catholic Rite and a rite that is practically a neighbor to Protestantism,” and thus, which attacks our Faith, the Catholic Faith! So, it is out of the question to encourage people to go to Mass in the new rite, because slowly, even without realizing it, they end up ecuмenist! It’s strange, but it's like that. It is a fact. Then, ask them questions on ecuмenism, on what they think of the relations with other religions and you will see! They are all ecuмenist. For the priest himself, the fact of saying this mass and celebrating it in a constant manner, even without thinking about anything, about its origin, or why it was made, turns him and the people who assist at it ecuмenist.” (Conference, April 11, 1990)

-"This union which liberal Catholics want between the Church and the Revolution is an adulterous union — adulterous. This adulterous union can only beget bastards. Where are these bastards? They are [the new] rites. The [new] rite of Mass is a bastard rite. The sacraments are bastard sacraments.We no longer know whether they are sacraments that give grace. We no longer know if this Mass gives us the Body and the Blood of Our Lord Jesus Christ. ... The priests emerging from the seminaries are bastard priests." (Homily preached at Lille, August29, 1976)

-“The radical and extensive changes made in the Roman Rite of the Holy Sacrifice of the Mass and their resemblance to the modifications made by Luther oblige Catholics who remain loyal to their faith to question the validity of this new rite.”(Écône, February 2, 1977)

-“Your perplexity takes perhaps the following form: may I assist at a sacrilegious Mass which is nevertheless valid, in the absence of any other, in order to satisfy my Sunday obligation? The answer is simple: these Masses cannot be the object of an obligation; we must moreover apply to them the rules of moral theology and Canon Law as regards the participation or the attendance at an action which endangers the faith or may be sacrilegious. The New Mass, even when said with piety and respect for the liturgical rules, is subject to the same reservations since it is impregnated with the spirit of Protestantism. It bears within it a poison harmful to the faith.” (An Open Letter to Confused Catholics, Ch. 4)

-“The current problem of the Mass is an extremely serious problem for the Holy Church. I believe that if the dioceses and seminaries and works that are currently done are struck with sterility, it is because the recent deviations drew upon us the divine curse. All the efforts that are made to hang on to what is being lost, to reorganize, reconstruct, rebuild, all that is struck with sterility, because we no longer have the true source of holiness which is the Holy Sacrifice of the Mass. Profaned as it is, it no longer gives grace, it no longer makes grace pass.” (Archbishop Lefebvre, August 1972, priestly retreat)

-“We must not forget that the conciliar reforms of the liturgy, the reforms of the Bible, the changes in the internal structure of the Church, of the constitution of the Church—all these things are a result of the ecuмenical spirit. That is clear, since Protestants were present for the changes in the Mass—six Protestant ministers were photographed with Pope Paul VI who thanked them for having come to participate in the liturgical commission, which transformed our Catholic Mass!Everything was done in this ecuмenical spirit: liturgical reforms, catechetical reforms, an ecuмenical Bible—which is sold in the bookstore at the Vatican. There was then, a considerable Protestant influence.” (Conference in Germany, October 29, 1984)

-“…if they are going to the New Mass—slowly, slowly they change their mind and become, slowly, slowly Protestant. It is very dangerous to go to the New Mass regularly, each week, because the New Mass is not some accidental change, but it is a whole orientation, a new definition of the Mass. It has not the same definition as the True Mass.” (Interview, St. Michael’s Mission, Atlanta, April 27, 1986)

“… So, if someone asks me: “I only have Mass of St. Pius V once a month. So what should I do on the other Sundays? Should I go to the New Mass if I do not have the Mass of St. Pius V? ...
I reply: Just because something is poisoned, obviously it is not going to poison you if you go on the odd occasion, but to go regularly on Sunday like that, little by little the notions will be lost, the dogmas will diminish. They will become accustomed to this ambiance which is no longer Catholic and they will very slowly lose the Faith in the Real Presence, lose the Faith in the Holy Sacrifice of the Mass, and have a spirituality, since the prayers are changed and they have modified everything, in the sense of another spirituality. It is a new conception of Christian spirituality. There is no longer any ascetical effort, no longer a combat against sin, no longer a spiritual combat. There is a great need to combat against our own tendencies, against our faults, against everything which leads us to sin. So I would say to them: Listen, I cannot advise you to go to something which is evil. Myself, I would not go because I would not want to take in this atmosphere. I cannot. It is stronger than me. I cannot go. I would not go. So I advise you not to go." (Spiritual Conference at Econe, June 25, 1981)

“The consequences of this state of mind or spirit spread within the Church, inside the Church, are deplorable, and are ruining and sapping the spiritual vitality of the Church. In conscience, all we can do is turn priests and faithful away from using the Novus Ordo Missae if we wish that the complete and whole Catholic Faith remains still living.” (Letter to John Paul II, April 5, 1983 - Archbishop Lefebvre, Conference #1, St. Thomas Aquinas Seminary, April 24, 1983)

“…that the evil in the New Mass is truly intrinsic, in the text … and not only something purely extrinsic, [in the abuses], this is certain. Precisely by this general effect which diminishes the proclamation of our faith, this diminution is present everywhere, in the words and in the actions. They wanted to be ecuмenical to such a point, to bring themselves closer to the Protestants in order to pray with them, that in the end they no longer affirm the Faith. And that is very grave. This diminution is excessively grave for our faith, how can it be otherwise? … Really, in conscience, I cannot advise anyone to attend this Mass, it is not possible.” (Conference at Econe, June 24, 1981)

Tx:

You like to quote mine?

Excellent!

Please find me one of the Archbishop saying something along the lines of, "Even in the face of a certainly validly ordained minister, with proper intention, valid form and matter, the conciliar sacraments are nonetheless all doubtful."

You won't be able to.

Tx:

You like to quote mine?

Excellent!

Please find me one of the Archbishop saying something along the lines of, "Even in the face of a certainly validly ordained minister, with proper intention, valid form and matter, the conciliar sacraments are nonetheless all doubtful."

You won't be able to.

See my previous post.  He's basing the doubt not on intention but on modifications to the rite.

Tx:

You like to quote mine?

Excellent!

Please find me one of the Archbishop saying something along the lines of, "Even in the face of a certainly validly ordained minister, with proper intention, valid form and matter, the conciliar sacraments are nonetheless all doubtful."

You won't be able to.

Matter, form and intent don't matter if the NO mass is not Catholic. 
.
"And we have the precise conviction that this new rite of Mass expresses a new faith, a faith which is not ours, a faith which is not the Catholic Faith."