Does the Church provide an official definition of positive doubt and negative doubt? 

It would be helpful to have some concrete examples. (Especially from members that had some formal seminary training). 

Thank you. God bless. 

I think you're shifting again from "could be doubtful" to "is doubtful". Below are two versions of what I think is the relevant part of the Ottaviani report. They say "could be valid" and "could also not be valid" based on intention. This reads to me as saying case-by-case and not that all new Roman Masses are doubtful.

Ok, good points, but you're confusing the prayers of the new mass vs the priest's intention.  +Ottaviani said that based on the prayers alone, there is positive doubt.  This is because the new mass' consecration formula (as well as the deficiencies in the Offertory prayers) no longer make it clear the Church's/priest's intention.  So, based on the prayers alone, the new mass is positively doubtful, 100% of the time.

One could argue that for 40+ years ALL of the masses which used the translation of "for all" instead of "for many" were 100% invalid.  But I don't know enough about this; i've just heard people argue this.  I don't think their argument is extreme, based on +Benedict's correction back to "for many".  If it didn't matter (and I thought he said it did matter a lot) then there would be no reason for a correction.

The priest (if he's a priest) could supply the missing intention for the consecration.  Then the consecration would be valid.  But how would anyone know what his intention is?  How many seminarians for the last 40 years have been taught that the mass is a "remembrance", a "memorial", a "supper", a "eucharistic celebration"?  None of these ideals are sufficient for the validity of the mass, which is an actual sacrifice, the re-enactment of Calvary again.

The point is, one can NEVER know what the priest's intention is, unless you sit down with him and have an in depth interview which covers his entire theological mindset and his understanding of the mass.  Even then, what if he has a doubt against the Faith one day at mass - a temptation to not believe?  If he doubts that the consecration truly happens?  Well, then the mass would be invalid because the prayers do not supply the intention, as they do with the True Mass.

The moral of the story is that the new mass is doubtful any way you slice it.  And as I argued earlier, even if it was 100% valid, it is still illicit and immoral.  So really, the debate over validity is irrelevant.

As you probably know, Paul VI sent the report to the CDF for comment, and Ottaviani's successor at the CDF did not give it a positive review. (Paul VI supposedly also made changes to the Mass before publication that addressed some points of the Ottaviani report.) In any event, after Paul VI gave a couple audiences explaining the new Roman Mass, and the new Mass was actually published, Ottaviani is reported to have written "no one can any longer be genuinely scandalized", though the text still raises "perplexities".

Every theological issue raised by +Ottaviani, +Bacci and the other theologians about the new mass is still there.  Paul VI may have made some changes after their report, but his changes did not minimize the new theology, the protestantization of the mass, or the doubtful consecration.  

+Ottaviani was not the only theologian who wrote the report.  Even if he compromised his Faith by accepting the new mass, the objections raised in the report by the other theologians are still there.  The new mass' problems did not go away.  

Ottaviani report said "one may be allowed to doubt it", ie, it could be. If he meant "one must doubt it", that's what he would have said. Well trained theologians are careful with what exactly they write. You see that in Archbishop Lefebvre's doctrinal writing, too.

An obligatory doubt makes no sense, in this case.  1) +Ottaviani didn't have the authority nor the papal directive to issue an order that catholics "must" doubt the new mass.  This type of ruling would have to come from the pope.  2) he was studying the new mass before it was finalized (though it was in its last stages of finalization and didn't change much after this).  He's not going to issue a "final opinion" on an unfinalized liturgy.  3) His allowance that one may doubt the new mass, as an expert theologian, carries all the weight it needs to.
.
As i've said before, the issue of the validity of the new mass is irrelevant as to why you cannot attend.  Even if it was valid, +Ottaviani said that its theology was anti-Trent and protestantized.  This alone makes the liturgy illicit and immoral and highly sinful.

Liturgies can be changed as the Church pleases. If it's valid then it's valid and that's that. Calling a valid mass immoral renders you anathema according to Trent.

Paul VI violated Trent when he fabricated all the new Rites and new Mass. The Novus Ordo Missae is not binding on the faithful at all. I think it can be debated whether his publication was an official act of the Church considering he did not make any indication by a solemn pronouncement that his missal is to used. And, no reference to Quo Primum.

Liturgies can be changed as the Church pleases. 

The human/church-originated parts can; most of it cannot, since the Liturgy is of Divine creation.

If it's valid then it's valid and that's that. Calling a valid mass immoral renders you anathema according to Trent. 

Just because a consecration is valid doesn't make it moral and pleasing to God.  A priest can walk into a grocery store and perform a valid consecration on all the bread in aisle 8, but that would be HIGHLY sinful, sacrilegious and sinful (i.e. immoral).  It would also be illicit and therefore, sinful (i.e. immoral).

It is within the Pope's authority to promulgate new Masses. Trent does not and could not prevent the Pope from doing that.

The pope has the authority to revise parts of the mass which are non-essential.  Colin is correct when he said that Paul VI violated Trent (Quo Primum, to be exact, since Quo Primum was made law because of Trent.  They are inseparable).  

I suppose every parish in the world being ordered to use it, and priests being barred from saying other rites without express permission, is not enough indication that the missal is to be used?

No pope has ever ordered the new mass to be used, under penalty of sin.  The bishops ordered priests to say the new mass and lied to every catholic in the world when they said that the True Mass was outlawed.  But the popes have never said this.  In fact, in +Benedict's motu proprio, he clearly said that the True Mass was never outlawed and that it was always permitted.  Clearly, this directly contradicts your erroneous view of history.

Further, in all the negotiations between new-rome and the sspx, new-rome has NEVER said that the new mass is obligatory.

Old laws of the Church do not have to be mentioned by name to be superseded either. 

Yes they do.  Every revision made to the Quo Primum missal since the 1570s has included a reference to Quo Primum and a specific mention of the previous missal being revised.  John XXIII did just that in 1962.  When you have established law, you must mention existing laws to overrule them.  But Paul VI was creating a new missal, unrelated to Quo Primum (which is why it's illegal) that's why he didn't revise John XXIII's missal.

Fabricated? It is within the Pope's authority to promulgate new Masses. Trent does not and could not prevent the Pope from doing that.

And the rest of your post is just legalism at its finest. You cannot honestly argue that the Pope promulgating a new rite is not an official act of the Church. I suppose every parish in the world being ordered to use it, and priests being barred from saying other rites without express permission, is not enough indication that the missal is to be used?

Old laws of the Church do not have to be mentioned by name to be superseded either.

Yes, the new Mass is a fabrication. Ratzinger, in 1986 wrote,

"The new Missal was published as if it were a book put together by professors, not a phase in a continual growth.  Such a thing has never happened before.  It is absolutely contrary to the laws of liturgical growth."

Session VII CANON XIII.

-If any one saith, that the received and approved rites of the Catholic Church... or be changed, by any pastor of the churches, into other new ones; let him be anathema.

The word for "any" is quemcunque which can be translated to "whomsoever" or "whatever". Is the Pope not a pastor of the Church?

Quo Primum 

"At no time in the future can a priest, whether secular or order priest, ever be forced to use any other way of saying Mass...  by virtue of our Apostolic authority that we decree and prescribe that this present order and decree of ours is to last in perpetuity, and never at a future date can it be revoked or amended legally. . . . “And if, nevertheless, anyone would dare attempt any action contrary to this order of ours, handed down for all times, let him know that he has incurred the wrath of Almighty God, and of the Blessed Apostles Peter and Paul.”

JUAN CARDINAL DE TORQUEMADA [IOANNES DE TURRECREMATA], O.P. (1388-1468)
(UNCLE OF THE GRAND INQUISITOR)
OFFICIALLY DESIGNATED THEOLOGIAN OF THE COUNCIL OF BASEL/FLORENCE
GIVEN BY POPE EUGENE IV THE TITLE OF "DEFENDER OF THE FAITH"

        "Although it clearly follows from the circuмstances that the Pope  
can err at times, and command things which must not be done, that we are  
not to be simply obedient to him in all things, that does not show that  
he must not be obeyed by all when his commands are good.  To know in  
what cases he is to be obeyed and in what not,... it is said in the Acts  
of the Apostles:  'One ought to obey God rather than man'; therefore,  
were the Pope to command anything against Holy Scripture, or the  
articles of faith, or the truth of the Sacraments, or the commands of  
the natural or divine law, he ought not to be obeyed, but in such  
commands, to be passed over (despiciendus)...."  (Summa de Ecclesia
[1489], founded upon the doctrine formulated and defined by the Council
of Florence and defined by Pope Eugenius IV and Pope Pius IV)
      
    
        "By disobedience, the Pope can separate himself from Christ
despite the fact that he is head of the Church, for above all, the unity
of the Church is dependent upon its relationship with Christ.  The Pope
can separate himself from Christ either by disobeying the law of Christ,
or by commanding something that is against the divine or natural law.  
by doing so, the Pope separates himself from the body of the Church
because this body is itself linked to Christ by obedience.  In
this way, the Pope would, without doubt, fall into schism....
        "He would do that if he did not observe that which the Universal
Church observes in basing herself on the Tradition of the Apostles, or
if he did not observe that which has been ordained for the whole world
by the universal councils or by the authority of the Apostolic See.  
Especially is this true with regard to the divine liturgy, as, for
example, if he did not wish personally to follow the universal
customs and rites of the Church.  This same holds true for other aspects
of the liturgy in a very general fashion, as would be the case of one
unwilling to celebrate with priestly vestments, or in consecrated
places, or with candles, or if he refused to make the sign of the cross
as other priests do, or other similar things which, in a general way,
relate to perpetual usage in conformity with the Canons.
        "By thus separating himself apart, and with obstinacy, from the
observance of the universal customs and rites of the Church, the Pope
could fall into schism.  The conclusion is sound and the premises are
not in doubt, since just as the Pope can fall into heresy, so also he
can disobey and transgress with obstinacy that which has been
established for the common order of the Church.  Thus it is that [Pope]
Innocent [III] states (De Consuetudine) that it is necessary to obey a
Pope in all things as long as he does not himself go against the
universal customs of the Church, but should he go against the universal
customs of the church, he ought not to be obeyed...."  
(Summa de Ecclesia [1489])

[/pre]

Clearly we see that even the Pope does not have the right to do whatever he pleases in regards to the sacred liturgy. It is YOUR idea that the Pope has the right to construct an entirely new rite of Mass, not the Church's.

Blessed Pope Pius IX, when requested to add the name of St. Joseph to the Canon, replied: “I am only the Pope. What power have I to touch the Canon?”

Forlorn,
I don't even know why you're on this site.  You're clearly not a Traditional Catholic.  Why don't you go hang out on Fisheaters or some other novus ordo site?

I don't attend Novus Ordo Masses at all, I go to the SSPX(no Resistance masses available). Maybe if you'd actually read what I say instead of just imagining whatever you want to read instead(like your nonsensical rant about me defending Indults when I NEVER even MENTIONED them), you'd understand.