I’m not sure what you mean by the sentance above. I think you are speaking about a different topic. “Ex cathedra” refers to the defining of a doctrine concerning faith or morals to be held by the whole church. This is a declaration of a truth already revealed by God. It is not an order by the Pope to do nor not do something. I think you are getting the power of infallibility confused with the authority of the Pope.
There is a difference between a Pope giving an order from his personal authority (such as to his assistant), and an order given by the Pope as the Head of the Catholic Church. For the latter, he has the final say. Vatican I declared that the Pope has “full and supreme power of jurisdiction over the whole church”, “not only in matters of faith and morals, but also in those which concern the discipline and government of the church”
I’m not sure what this has to do with Archbishop Lefebvre, but the declarions given by Vatican I are referring to a person who tries to change the meaning of a dogma already defined by the Church, not the Pope clarifying the meaning of a dogma, even if it be different from the meaning that was understood by a number of faithful.
Forgive me if I missread your statement, but since there was no defining of terms, I can only read into what is given. I never said that an “ex cathedra” statement ordered anybody to do anything, nor did I define what a dogma was in relation to papal authority. However, regarding binding future popes, ex cathedra statements are made by the Holy Father’s own authority and may not be changed at will, which I gather from your statement you know. However, other statements not clearly ex cathedra must be adhered to and cannot be changed by future popes without serious reason, for example:
Pope Pius XII, Humani Generis, 1950
"Nor must it be thought that what is expounded in Encyclical Letters does not of itself demand consent, since in writing such Letters the Popes do not exercise the supreme power of their Teaching Authority. For these matters are taught with the ordinary teaching authority, of which it is true to say: “He who heareth you, heareth me”;and generally what is expounded and inculcated in Encyclical Letters already for other reasons appertains to Catholic doctrine. But if the Supreme Pontiffs in their official documents purposely pass judgment on a matter up to that time under dispute, it is obvious that that matter, according to the mind and will of the Pontiffs, cannot be any longer considered a question open to discussion among theologians…Hence Our Predecessor of immortal memory, Pius IX, teaching that the most noble office of theology is to show how a doctrine defined by the Church is contained in the sources of revelation, added these words, and with very good reason: “in that sense in which it has been defined by the Church.”
Again, a pope is not free to rephrase or change the manner in which a doctrine is taught or understood, even if he has supreme authority over matters of Faith and morals, it is not in his power to change the meaning or teaching of his predecessors, for such would be an abuse of the authority his office. The Office of Holy Father may not “bind itself,” but it is bound to the Magisterium.
I think the question here is not contradicting Tradition as understood “by a number of the faithful,” but by the Popes themselves. The Holy Father may not make statements or define matters outside the way the Church has always understood them. This was the chief concern of Archbishop Lefebvre, that there appeared to be a departure from what post-Vatican II popes were saying and what those before said. (I am not saying whether he was right or wrong, only that he would not be out of hand if he was concerned by this). Vatican I also said as posted above: “Hence, too, that meaning of the sacred dogmas is ever to be maintained which has once been declared by Holy mother Church, and there must never be any abandonment of this sense under the pretext or in the name of a more profound understanding.” This applies to the Holy Father, as well as those beneath him. No man is above the law, and the Pope is not above the Magisterium of the Church, but a living part of it.
Hopefully this makes my position somewhat clearer.