CathInfo.com

Paul VI said that? Do you have a reference for me please Dusty?
Was it an infallible declaration?

Unless he explicitly referenced his intention to engage infallibility, then it is not.

Well, that is in fact the meaning of Sacramentum Ordinis:

Sacramentum Ordinis - Papal Encyclicals

in the Episcopal Ordination or Consecration, the matter is the imposition of hands which is done by the Bishop consecrator. The form consists of the words of the “Preface,” of which the following are essential and therefore required for validity:

Just because the said words are essential, does not mean that the whole preface is not part of the form. It is, according to this docuмent. And of course, those 'essential words' are different in the other rites. Sacramentum Ordinis lays down the principles:

3. All agree that the Sacraments of the New Law, as sensible signs which produce invisible grace, must both signify the grace which they produce and produce the grace which they signify. Now the effects which must be produced and hence also signified by Sacred Ordination to the Diaconate, the Priesthood, and the Episcopacy, namely power and grace, in all the rites of various times and places in the universal Church, are found to be sufficiently signified by the imposition of hands and the words which determine it.

Don't misunderstand, I'm not arguing in favour of the new rite's validity. It's disputed, and I believe the only way that dispute can be resolved definitively is by the Magisterium which is on strike at the moment! However, I do consider it rash to definitively declare it certainly invalid when there are theological opinions to the contrary.

PV, we don't need to declare it "certainly invalid." The standard in the moral theology manuals is much lower. All one needs is enough evidence for possible invalidity to introduce a "positive doubt." Callan and McHugh state that a "tutiorist" stance must be taken when "there is question of the validity or invalidity of a Sacrament, for the virtue of religion requires that the Sacraments be administered with fidelity, and be not exposed to the peril of nullity."

What you and Dusty have brought up in Sacramentum Ordinis is evidence enough for "positive doubt." But there is enough evidence, I believe, for moral certainty in the matter.
  
Pull up Sacramentum Ordinis in Latin in one window and in the official English translation in another window. Notice how the words "validitatem" and "valorum" are used precisely (in the Latin) to mean different things. But in the English translation both of those different Latin words are translated as the same word, "validity."

Also, look at the use of the words referring to "essence" and "substance." These are technical theological terms. In Aquinas, these words refer to very different cognitive and ontological topoi. Any "substance" consists of "matter" and "form" as the genetic components of that "substance." A "substance" cannot "exist" unless there is FIRST a coalescence of matter and form. So a Sacrament (as a particular instance of the Eucharist, for example) cannot "exist" without the presence of BOTH matter and form. The "substance" refers to a particular reality, the thing itself.

An "essence" is very different. The "essence" of a thing is a mental abstraction of properties from already existing things possessing that "essence." The essence is determined by empirical examination of already existing realities (that is, things already built up by the coalescence of matter and form). Another name for "essence" in Thomism is quiddity, or the "whatness" of the thing.  An "essence" is conceptual in nature, a construct of the mind, it is not "the thing itself." 

So, only the "substance" of the Sacrament pertains to its "validity." This is Thomism. And it is the basis of the quote from Trent in paragraph 1 of SO, that the "substance of the Sacraments" cannot be changed. Note, however, that in SO paragraph 5, each quoted phrase mentioned is introduced as being "essentialia ideoque ad valorem requisita [essential and therefore required for value]." Nothing in the Latin text, in that section, refers to "substance" or "validity." What???? This should set off alarm bells.


So what is going on in paragraph 5? "Essences," using the precise Thomistic theological terminology, are not related to "validity," but instead, they can add "value" to help us understand the Sacrament better, in this case, the Sacrament of Orders. Why do they "add value?" Because they define the "whatness," or the quiddity, of the particular Order referenced. In other words, something "essential" is helpful to know, but it is not a constituent of "validity." Only the matter and form are constituents related to "validity" of a Sacrament, which is a "substance," an ontological reality. In the case of the Sacrament of Orders, the ontological reality is the indelible character imprinted on the soul of the recipient of the Sacrament.

So the "essential" words that are quoted in SO paragraph 5 are not required for "validity." They are simply the most important (highest value) words in the Preface. The ENTIRE PREFACE is required for "validity" because the ENTIRE PREFACE (and no less) is "the form." To apply the same idea to another Sacrament, would be like saying the following: "I baptize thee, in the name of the Father, and of the Son, and of the Holy Spirit is the form of baptism, of which the word 'baptize' is essential and therefore required for value." In other words, don't use a word like "wash" or "cleanse" or whatever instead of "baptize" because the specific word "baptize" reflects something "essential" in that Sacrament. That particular word helps us understand Baptism in a definitive way.

Bottomline: Pius XII stated that "the form" of each Order is the ENTIRE Preface (for each level of Order). It is reductionism leading to invalidity to restrict the required words of "the form" to only the quoted words that are "essential and therefore required for value."