I’m curious, by what means is a doctrine declared infallible, or unchangable, or dogmatic, in the Church today and what are some relatively modern (post 16th Century) examples of this practice?
I don’t beleive the Orthodox have declared anything infailable since well before the schism.
We teach and define that it is a dogma Divinely revealed that the Roman pontiff when he speaks ex cathedra, that is when in discharge of the office of pastor and doctor of all Christians, by virtue of his supreme Apostolic authority, he defines a doctrine regarding faith or morals to be held by the universal Church, by the Divine assistance promised to him in Blessed Peter, is possessed of that infallibility with which the Divine Redeemer willed that his Church should be endowed in defining doctrine regarding faith or morals, and that therefore such definitions of the Roman pontiff are of themselves and not from the consent of the Church irreformable.
So then, should anyone, which God forbid, have the temerity to reject this definition of ours: let him be anathema.
The aforesaid dogmatic constitution then goes on in chapter 4 to define the conditions for papal infallibility:
* we teach and define as a divinely revealed dogma that o when the Roman pontiff speaks EX CATHEDRA, + that is, when, 1. in the exercise of his office as shepherd and teacher of all Christians, 2. in virtue of his supreme apostolic authority, 3. he defines a doctrine concerning faith or morals to be held by the whole church, o he possesses, + by the divine assistance promised to him in blessed Peter, o that infallibility which the divine Redeemer willed his church to enjoy in defining doctrine concerning faith or morals. o Therefore, such definitions of the Roman pontiff are of themselves, and not by the consent of the church, irreformable. So then, should anyone, which God forbid, have the temerity to reject this definition of ours: let him be anathema.
In other words the conditions for infallibility are:
1)The Roman Pontiff (Pope) must invoke it
2)Speak Ex Cathedra (as defined in Pastor Aeternus above)
3)He MUST give a definition (i.e. He must define)
4)The doctrine defined must concern faith or morals
5)Must be intended to be binding upon the whole Church
An Ecumenical council may exercise infallibility only through the Pope's infallibility and never separate from him. Only the pope's promulgation of an ecumenical council can give the charism of infallibility as defined in Vatican I. Also, It is VERY, VERY important to note that in order for a teaching of the Pope or an Ecumenical Council to be considered infallible, it must make it explicit that the teaching is to be considered infallible, definitive, and binding upon the church. There is not any exact phrasing prescribed to do this, but it is usually indicated by one or sometimes both of the following phrases: (1) a formula indicating that this teaching is definitive (such as "We declare, decree and define..."), or (2) an anathema stating that anyone who deliberately dissents is outside the Catholic Church.
The Church may also contradict a previous teaching of the church, as long as the teaching was not taught infallibly. If this happens the infallible teaching voids the fallible one.
The charism of infallibility is used rather rarely. It may be invoked by the pope alone, but it is often exercised by the pope in conjunction with the college of Bishops when meeting in Ecumenical Councils. (According to Vatican I, Ecumenical councils are only infallible when the pope is in agreement with the decrees). Vatican II is a bit peculiar because it does not make the explicit dogmatic definitions which are required for infallibility according to Vatican I. Thus there is often a lot of debate whether or not certain teachings of Vatican II are infallible or merely pastoral recommendations. (The arguments for this are quite strong). This is exacerbated by the fact that Pope Paul VI who stated at the close of Vatican II that "The magisterium of the Church did not wish to pronounce itself under the form of extraordinary dogmatic pronouncements..." suggesting that the Pope did not state and did not intend to use his infallible charism when promulgating the decrees of the Second Vatican Council
Papal infallibility, since Vatican I, has only been used once. It was by Pius XII in Munificentissimus Deus, 1950, to define the Bodily Assumption of Mary into Heaven. Other papal teachings which meet Vatican I's criteria of infallibility preceding Vatican I but post 16th century include:
1)Cum occasione, Pope Innocent X, 1653 (condemning some of the Reformer Jansen's teachings.
2)Auctorem fidei, Pope Pius VI, 1794 (Also condemning Jansenists.
3)Ineffabilis Deus, Pope Pius IX, 1854, defining the immaculate conception