Okay, just for the sake of argument, let us assume Pope Pius XI’s encyclical is entirely fallible. Then what is the Church’s dogma on education? Is there any?
Is it necessary that everything that touches life be an infallibly defined?
One might as well ask for the Church’s dogma on how much to spend at the grocery store, or what kind of pets to have.
Or should we ask Pope Benedict to declare the multiplication table or Pythagorean theorem infallible dogma de fide–or maybe simply acceptable theologoumena–before we believe it?
Furthermore, there’s a big difference between a statement being an infallible teaching and being “entirely fallible”. Something a pope or any other bishop says can easily be counsel and advice rather than command or definition, and it’s up to the individual to determine how well the advice applies to his own situation.
And something I was just thinking today:
Papal infallibility is basically a dead issue because there’s no general agreement about which papal statements are infallible!