First of all, “ex cathedra” does not mean actually, physically sitting in some particular chair.
There have been two exercises of “papal infallibility”—i.e., actual statements by the Pope which explicitly affirmed that the Pope intended to teach the entire Church infallibly, in 1854 (Immaculate Conception) and 1950 (Assumption), and 1994 (ordination of females).
In all cases, the statements were the result of long study by scholars of the historical record, and inquiries sent to every bishop in the world, specifically on the question: Has this dogma been a part of the Deposit of Faith from the beginning?
Worst case possible regarding the Synod is that Francis emits a statement as vapid, juvenile, and destructive as the ones Kasper, Wuerl, O’Malley, et al., have been putting out.
If he does that, he WILL NOT assert that he is teaching infallibly.
At the risk of sounding superstitious, I will say that IF Francis were stupid and wicked enough to make up his mind to claim to teach infallibly something different from what the Church has always taught about marriage, Communion, etc., that he would die the night before.
Seriously, if he DID do that, he would cause a schism. The real Catholics would reject this new teaching, and elect a new Pope.
It appears to me that this has already happened in all but formally taking action, given the rampant dislike of Francis that we see here on the FR religion forum by Roman Catholics. Vatican II, too.
Akin says --- that is wrong, for it can as well be interpreted that there are many more...
But as usual on these pages, it does appear that some wish to have most everything both ways, as in even ordinary magesterium is also considered infallible in it's teachings, but papal encyclicals (for instance) which teach on faith and morals can be downplayed(?) if any portion of the contents ever prove embarrassing.
Some split the baby even further and talk about alleged distinction between what is held [see The Meaning of Papal Infallibility, Thomas J. Shanahan, S.J.] and what must be believed.
How many preztels are in that box?
I do not agree the following is unadulterated, unvarnished truth itself (but the papacy sure as shooting does -- at least did on March 17, 1993), from;
http://www.vatican.va/holy_father/john_paul_ii/audiences/alpha/data/aud19930317en.html
The Successor of Peter Teaches Infallibly ... The magisterial function of bishops, then, is strictly tied to that of the Roman Pontiff. Therefore, the conciliar text goes on aptly to say:
"This religious submission of mind and will must be shown in a special way to the authentic Magisterium of the Roman Pontiff, even when he is not speaking ex cathedra; that is, it must be shown in such a way that his supreme Magisterium is acknowledged with reverence, the judgments made by him are sincerely adhered to, according to his manifest mind and will. His mind and will in the matter may be known either from the character of the documents, from his frequent repetition of the same doctrine, or from his manner of speaking" (LG 25).
This supreme authority of the papal Magisterium, to which the term apostolic has been traditionally reserved, even in its ordinary exercise derives from the institutional fact that the Roman Pontiff is the Successor of Peter in the mission of teaching, strengthening his brothers, and guaranteeing that the Church's preaching conforms to the "deposit of faith" of the apostles and of Christ's teaching. However, it also stems from the conviction, developed in Christian tradition, that the Bishop of Rome is also the heir to Peter in the charism of special assistance that Jesus promised him when he said: "I have prayed for you" (Lk 22:32). This signifies the Holy Spirit's continual help in the whole exercise of the teaching mission, meant to explain revealed truth and its consequences in human life.
For this reason the Second Vatican Council states that all the Pope's teaching should be listened to and accepted, even when it is not given ex cathedra but is proposed in the ordinary exercise of his Magisterium with the manifest intention of declaring, recalling and confirming the doctrine of faith. It is a consequence of the institutional fact and spiritual inheritance that completes the dimensions of the succession to Peter. ...
The example on this thread of how concept of infallibility is spoken of one way, when there are yet a few other ways to "hold to" or believe in the thing/condition which can be raised at any one time (according to whichever is most convenient it seems), is one of the reasons many outsiders cannot get past the fact that Rome and Romanists do seem to speak out of both sides of the face at once on this issue, and a few others...
As James White(?) put it, "what Rome giveth with one fork of it's tongue, it taketh away with the other"