Speaking of traditional rites (not V2 rites), I don’t see how if someone follow the matter/form of baptism, then it’s not 100% valid.  There must be some details related to that Holy Office condemnation that are missing.  The private intention of the person performing the baptism is irrelevant.  If it matters, then no baptism is certain.  

Struthio's 1690 quote, if accepted, would only require allowing some case where intention prevents baptism despite correct matter and form.

Lets say we have a theatrical play about the early church in which the actor playing St. Peter says the words of baptism while throwing some water on other actors. Matter and form appear correct. However, the intention is for a performance, not a sacrament. iIn this case that intention is clear, so we or the Church can make a judgment.

From your link.  Pages 176-177.  https://archive.org/details/sacraments01pohluoft/page/n185/mode/2up
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Reflex intention = A priest has the explicit desire to cleanse the child from Original Sin and bestow grace.  A reflex intention is not required for a valid sacrament.  This is your thesis and Pohle disagrees with you.

My thesis? You're joking! Could you please quote "my thesis" from my posts, where I talk about a reflex intention!!? You can't because I didn't!

You're deviating. Please go ahead and refute Pohle's proof of Thesis II on page 183 (book not pdf).

If you read further, the condemnation was due to a guy who was saying that following the rite was all that mattered.

Yes, indeed. That's the case. And Ladislaus and Ibranyi say the same. And you did, too (quote below, the last one of this post)!

The example given of why intention matters are a priest who gives absolution to a penitent while laughing. He did not perform the sacrament "seriously" so his intention is in doubt.  But in cases where the priest is orthodox, such concerns don't exist.

You better read on. There's more.

If your entire point of this thread is to say that we only have "moral certainty" and not 100% certainty, then I agree.  But why focus on such a topic?  Does it help your faith?  Seems to me that such thoughts, especially in our times of crisis, are dangerous.

My point is the condemnation of the Holy Office of Alexander VIII.

You said less than two hours ago:

Speaking of traditional rites (not V2 rites), I don’t see how if someone follow the matter/form of baptism, then it’s not 100% valid.

Do you now, after having read some of Pohle, retract this statement? Do you desist from being "a guy who was saying that following the rite was all that mattered"?

I get what you’re saying but “following the rite” is sufficient in most cases and in others it’s not. On the pages I quoted, Pohle says a direct intention is sufficient.  The condemnation is mentioned a few pages later and it has to do with EXTERNAL evidence that the person doesn’t intend to do “what the church does” (ie a priest giving absolution while laughing). .
So you can say that an intention is presumed if one follows the rite but you can also say that...in certain cases, due to external evidence...that a lack of intention isn’t presumed and can affect validity.  
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Context matters.  The condemnation was for a very specific circuмstance.  Generally speaking, if you know the priest is orthodox and he performs the sacrament with reverence, and according to the rite, everything is fine.  To your point, it’s only morally certain but that’s a pretty high standard.

Do you accept the condemnation of the Holy Office of Alexander VIII, and do you not reject it like Ladislaus and Ibranyi explicitly do?

True. But there is doubt with respect to the intention of clerics of the Antichrist NO sect, as well as based on the fact that most of them hate their own books and rites and use home made prayers and formulae.

How can anyone without having a special revelation know the intention of anyone? 

Well if the private intention of the minister can make sacraments done by the books invalid, then nobody can ever know if they were even baptized or ever recieved the true Body of Christ or was really forgiven in confession. Also, then Lefebvre was never a priest and most of us are not receiving the true sacraments and a very large number of people throughout history were not receiving the sacraments due to unbelieving priests and infiltrators. Would Christ set up the sacraments in such a way where they could so easily be invalidated without anyone ever knowing?

That's right, which is why as long as the proper formula is used, the sacrament is administered and the baptism is valid -  of this we are certain because the sacraments are the outward sign. Outward sign = the only way we know.

When it comes to this most essential of all the sacraments, Our Lord did not leave it's validity to the mercy of the private intentions of the minister, the Church purposely removed that ingredient for the sake of the sacrament so as to always remove all doubt.

If the proper formula is used, it's 100% valid.
   

Well if the private intention of the minister can make sacraments done by the books invalid, then nobody can ever know if they were even baptized or ever recieved the true Body of Christ or was really forgiven in confession. Also, then Lefebvre was never a priest and most of us are not receiving the true sacraments and a very large number of people throughout history were not receiving the sacraments due to unbelieving priests and infiltrators. Would Christ set up the sacraments in such a way where they could so easily be invalidated without anyone ever knowing?

As Rev. De Salvo states, no one can have absolute certainty that any particular sacrament is valid.

"It's true that without a special revelation no one can have absolute certainty that he has received a sacrament or that he is in the state of grace, but his assurance on this subject may approach so nearly to this absolute certainty as to make any misgiving on the part of the recipient foolish and vain.” (p.x)

--- De Salvo, Rev. Raphael, O.S.B., S.T.L. The Dogmatic Theology on the Intention of the Minister in the Confection of the Sacraments. 1949. 


Though we cannot have absolute certainty about the validity of any particular sacrament, we can be sufficiently certain, as Cardinal Billot states.

“…whenever there is no appearance of simulation on the part of the minister, the validity of the sacrament is sufficiently certain.” (p.201)

--- Billot, Cardinal Louis, S.J. De Ecclesiae Sacramentis. Commentarius in Tertiam Partem S. Thomae. Vol.1, 5th Ed. 1914. 


Apart from special revelation, we can never have absolute certainty about the validity of a sacrament, but when it is performed with the proper matter and form, and with no appearance of simulation, we have moral certainty of its validity. This moral certainty is what Cardinal Billot previously described as being “sufficiently certain.” Moral certainty is not the certainty of faith, for we cannot have the certainty of faith that any particular sacrament is valid; but moral certainty is all we need.

“It is true that we cannot be certain with the certainty of faith, — that is, with the certainty with which we believe the being of God or the articles of the creed, — that this or that priest has been validly ordained, or this or that Sacrament has been validly administered; but we are certain, with the certainty of faith, that priests and Sacraments are Christ’s institution; and moreover we may be morally certain that in any indefinite number of instances there was an intention to do what the Church does; and these two certainties are enough for all practical purposes.” (p.28)

--- Brotherhood of St. Vincent of Paul. “The Intention of the Minister Necessary, etc.” The Clifton Tracts, Vol.III. 1865. 


This moral certainty, therefore, is sufficient for acting prudently and without anxieties.

“Concerning the validity of the sacraments one can have moral certitude, which suffices for acting prudently, and for dispelling anxieties of spirit. Thus Leo XIII: "When someone seriously and according to the ritual adheres to the due matter and form for confecting and conferring a sacrament, from this fact [considered according to the common manner in which men act] it may be inferred that he undoubtedly intends (with an internal intention) to do what the Church does."[Apostolicae Curae]” (n.479, rep. to obj. 2)

--- Hervé, Msgr. Jean Marie. Manuale Theologiae Domaticae, Vol. III. 1929.