Question: My understanding is that the Catholic Church teaches that when the Pope speaks ex cathedra, he is infallible, because what he says in such instances is divinely protected from error. There are a lot of questions that the Church considers open, e.g. the question of whether infants who die without being baptized are saved. It seems like it would be a great idea for the Pope to *attempt* to assert ex cathedra that they are saved. Either the pronouncement would succeed, in which case we would know with certainty that it is true, or else something would prevent the pronouncement from going through, in which case we would have a hint that it is false.

I assume that I am misunderstanding something about papal infallibility and there is a catch somewhere. **What's the catch?** Naturally, I'm interested in the teaching of the Catholic Church.

Here are a couple of possible answers:

* Technically, the Pope *could* "exploit" infallibility in this way, but it would be immoral.
* If the Pope decided to try this sort of thing, he would be divinely prevented from making the ex cathedra pronouncement regardless of whether the doctrine in question was true or false, so we wouldn't actually learn anything from the exercise.

In either case, I'm left wondering: What exactly differentiates "legitimate" ex cathedra pronouncements, like the pronouncement of the immaculate conception in Ineffabilis Deus, from the sort of "illegitimate" ex cathedra pronouncement that I suggested?

Answer: 
You massively misunderstand the process of promulgating doctrine. It's not a magic process where God causes true statements to be generated out of thin air. Doctrine is developed through prayer, research, consultation, discernment and much more, and involves the whole church, not just the Pope. The belief is that God guides this process to ensure it is correct. Shortcutting the means would be equivalent to cheating God.
Do not put the LORD your God to the test (Deuteronomy 6:16).

We know the Pope is infallible because God gave Peter specifically, and the Apostles generally, the Keys of the Kingdom. What the Apostles can do collectively (like in an Ecumenical Council), Peter can do as an individual. Same keys, but different ways to excerise them.

Furthermore, the Pope and the Bishops generally aren't creating new doctrine, but rather discovering or emphasizing or interpretating the Revelation the Christ already gave us.

Christi pax,

Lucretius