CathInfo.com

Despite the comparative inadequacy of the treatment they give to the papal encyclicals, however, all the theological works dealing with this subject make it perfectly clear that all Catholics are bound seriously in conscience to accept the teaching contained in these docuмents with a true internal religious assent. It is the common teaching of the theologians who have written on this subject that the internal assent due to a great number of the doctrines proposed in the papal encyclicals is something distinct from and inferior to both the act of divine Catholic faith and the act most frequently designated as fides ecclesiastica. Most theologians hold that, while there is nothing to prevent an infallible definition of truth contained in or connected with the deposit of revelation in papal encyclicals, and while de facto it is quite probable that at least some infallible pronouncements have been made in this way, the Holy Father has not chosen to use the complete plenitude of his apostolic doctrinal authority in presenting most of the truths contained in his encyclical letters. Nevertheless they all insist that even in this portion of his ordinary magisterium the Holy Father has the right to demand, and actually has demanded, a definite and unswerving internal assent to his teaching from all Catholics.
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This authority (of the papal encyclicals) is undoubtedly great. It is, in a sense, sovereign. It is the teaching of the supreme pastor and teacher of the Church. Hence the faithful have a strict obligation to receive this teaching with an infinite respect. A man must not be content simply not to contradict it openly and in a more or less scandalous fashion. An internal mental assent is demanded. It should be received as the teaching sovereignly authorized within the Church.

 Ultimately, however, this assent is not the same as the one demanded in the formal act of faith. Strictly speaking, it is possible that this teaching (proposed in the encyclical letter) is subject to error. There are a thousand reasons to believe that it is not. It has probably never been (erroneous), and it is normally certain that it will never be. But, absolutely speaking, it could be, because God does not guarantee it as He guarantees the teaching formulated by way of definition’.
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Lercher teaches that the internal assent due to these pronouncements cannot be called certain according to the strictest philosophical meaning of the term. The assent given to such propositions is interpretative condicionatus, including the tacit condition that the teaching is accepted as true “unless the Church should at some time peremptorially define otherwise or unless the decision should be discovered to be erroneous.” Lyons and Phillips use the same approach in describing the assent Catholics are in conscience bound to give to the Church’s non-infallible teachings. Fr. Yves de la Brière speaks of the “submission and hierarchical obedience” due to these pronouncements.
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Franzelin holds that the Roman Pontiff can command all Catholics to assent to a given proposition (either directly or by condemning the contradictory statement), for either one of two different reasons. First the Holy Father can intend to define this proposition infallibly as true or as de fide. Again he can will merely to look after the security of Catholic doctrine. The  magisterium of the Church has been equipped with help from God by reason of which the first sort of teaching gives infallible truth, while the second affords infallible security. Employing the plentitude of its power, the teaching Church operates as the auctoritas infallibilitatis. Working, not to define, but merely to take those steps it deems necessary to safeguard the faith, it is the auctoritas providentiae doctrinalis. To this  auctoritas providentiae doctrinalis and to the teachings it sets forth, the faithful owe the obedience of respectful silence and of an internal mental assent according to which the proposition thus presented is accepted, not as infallibly true, but as safe, as guaranteed by that authority which is divinely commissioned to care for the Christian faith.
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Despite the divergent views about the existence of the infallible pontifical teaching in the encyclical letters, there is one point on which all theologians are manifestly in agreement. They are all convinced that all Catholics are bound in conscience to give a definite internal religious assent to those doctrines which the Holy Father teaches when he speaks to the universal Church of God on earth without employing his God-given charism of infallibility. Thus, prescinding from the question as to whether any individual encyclical or group of encyclicals may be said to contain specifically infallible teaching, all theologians are in agreement that this religious assent must be accorded the teachings which the Sovereign Pontiff includes in these docuмents. This assent is due, as Lercher has noted, until the Church might choose to modify the teaching previously presented or until proportionately serious reasons for abandoning the non-infallible teaching contained in a pontifical docuмent might appear. It goes without saying that any reason which would justify the relinquishing of a position taken in a pontifical statement would have to be very serious indeed.
[my note:  contradiction of previous Magisterium would clearly meet this condition]

 It might be definitely understood, however, that the Catholic’s duty to accept the teachings conveyed in the encyclicals even when the Holy Father does not propose such teachings as a part of his infallible magisterium is not based merely upon the dicta of the theologians. The authority which imposes this obligation is that of the Roman Pontiff himself. To the Holy Father’s responsibility of caring for the sheep of Christ’s fold, there corresponds, on the part of the Church’s membership, the basic obligation of following his directions, in doctrinal as well as disciplinary matters. In this field, God has given the Holy Father a kind of infallibility distinct from the charism of doctrinal infallibility in the strict sense. He has so constructed and ordered the Church that those who follow the directives given to the entire kingdom of God on earth will never be brought into the position of ruining themselves spiritually through this obedience. Our Lord dwells within His Church in such a way that those who obey disciplinary and doctrinal directives of this society can never find themselves displeasing God through their adherence to the teachings and the commands given to the universal Church militant. Hence there can be no valid reason to discountenance even the non-infallible teaching authority of Christ’s vicar on earth.