Part of the problem is, we don’t have a list from the Church wherein the Church says “These are the Church encyclicals that are ex cathedra and these are the ones that aren’t”.
Ex cathedra means “from the chair,” i.e., the chair of Peter. Since encyclicals are issued by the Pope it follows that all encyclicals are
ex cathedra. I’m not sure what this has to do with infallibility.
I am not trying to be cheeky here - I still cannot figure out whether Lumen Gentium is Church doctrine or not.
A document isn’t doctrine, so no, it isn’t “Church doctrine.” The principles it elucidates, to the extent they touch on matters of morality, are doctrine. To the extent they touch on matters of faith, they are dogma. Insofar as
Lumen Gentium nor VII didn’t issue any new dogmas, any dogmatic statements they contained are simply reiterations of earlier dogmas. To my knowledge,
Lumen Gentium didn’t issue any new doctrines, either.
If you mean you don’t know whether its principles are infallible, well, ecumenical councils are extraordinary exercises in the infallible Magisterium of the Church. So to the extent
Lumen Gentium touches on doctrinal and dogmatic points (i.e., matters of faith and morals), yes, those points are infallible.
As to infallibility, I do believe that the Church is infallible, and I was probably overreaching when I said that I would leave the Church if the situation on unbaptized infants were what it was 100 years ago, since that was just a matter of Church practice rather than dogma. But as I’ve asked, does infallibility mean that the Church is right because it is the Church or does it mean the Church is the Church because it is right?
It doesn’t mean either of those things. It means it is right (under the circumstances where it exercises its teaching authority formally) because Christ protects it from error. Christ protects it from error because orthodoxy in matters of faith and morals are normatively necessary for salvation. You cannot be saved if you don’t accept salvation which means you need to know what salvation is, what sin is, who Christ is, etc. Christ promised that he would be with the Church always, and he said this at the same time he expressly charged them with carrying on his ministry of teaching and redemption. So either he meant it or he is a liar. Since God isn’t a liar but truth itself, it must be true.
Infallibility is mostly prophylactic. It means the Church will not teach error, which is a positive thing. It doesn’t guarantee that the Church won’t leave something out, that its teachings will be properly understood by anyone, that it will express them very well, etc. For instance it’s easy for me to give assent to
Gaudium et Spes even though it more or less sounds like gibberish to me precisely because it is the product of an ecumenical council which is an extraordinary exercise of the infallible Magisterium. So the extent it’s doctrinal/dogmatic, it cannot be in error, and to the extent it isn’t, it doesn’t concern my salvation so I don’t really care about it.
If you believe in the infallible Magisterium then your earlier statement to the effect that you would be “completely without integrity” to defer to the judgment of your betters even when you don’t understand or “rationally accept” what they say, simply isn’t true. On the contrary, it would be irrational for you
not to accept their judgment; that’s why they’re your “betters,” after all. They’re protected from error, you aren’t. So whatever you have trouble “rationally accepting” can only because of some deficiency on your part, not theirs. If you really believe in infallibility, the only position without integrity is the one that would drive you to abandon the Church because of your own lack of insight in that instance.