> So the first article is definitely talking about doubt in the sense of "not being sure of the meaning of something"

The first article quotes Ratzinger as saying "Both the believer and the unbeliever share, each in his own way, doubt and belief..."

If by "doubt" Ratzinger means "not being sure of the meaning of something", what is it that the unbeliever is unsure of the meaning of?

Immediately before that quote, it speaks of the unbeliever wondering that "Perhaps it is true". That is doubt about the correctness of one's belief positions, not doubt about what something means. But if that is what Ratzinger means by "doubt" with respect to the unbeliever, he must mean the same thing for the believer, or else his claim that they share "doubt" doesn't make any sense.

> You can have absolute doubt in science without problem

I don't agree. Philosophers have absolute doubt, scientists do not. Take a proposition such as "Human reason is generally reliable". Philosophers will doubt that proposition, and ask how the doubt may be answered; it is not within the scope of physics or chemistry to doubt that proposition, only to assume its truth, to have faith in it–for without that faith, physics and chemistry are impossible. If an individual physicist or chemist approaches that proposition with doubt instead of faith, they are no longer doing physics or chemistry, they are now doing philosophy. To doubt the most fundamental assumptions of science is beyond the scope of the scientific enterprise. Philosophers are allowed to doubt anything and everything, and still be working within the confines of their discipline. The same does not hold for the natural sciences.

> Absolute doubt will not deepen your faith... "doubting the validity or the veracity of something" will not deepen your faith.

I don't think you are understanding Pope Francis correctly. Let us consider doubting the existence of God. Are you saying doubting God's existence could not deepen the faith of a religious believer? A quite traditional Catholic response to doubts about the existence of God, is to go read the tradition of philosophical theology which attempts to prove God's existence. (Everything from St. Thomas' "Five Ways" through to recent works such as Edward Feser's Five Proofs.) So, from a Catholic viewpoint, doubting God's existence could actually lead to becoming educated in the Catholic tradition of arguments for God's existence, and I believe the Pope would consider such an education to be a way to "deepen your faith".

> Abstract theory is basically science.

I think what Pope Francis is actually talking about here, is an overemphasis on the intellectual side of religion (such as philosophical arguments for God's existence) while ignoring other aspects of it (experiential, mystical, social, communal, ethical, liturgical, ritual, sacramental, prayerful, etc) – religion as an abstract theory as opposed to a lived practice. I don't think he is saying people shouldn't study the intellectual side of Catholicism, I think he is warning that a sole focus on that to the exclusion of living it is not going to answer their doubts. While the natural sciences often involve "abstract theory", not all abstract theories belong to the natural sciences – abstract theories are also found in mathematics, in philosophy, in the humanities, and yes also in religion and theology. The particular abstract theories he is talking about here are, I think, the philosophical and theological ones rather than those of the natural sciences.

And I think there is some truth in what he says. Whatever one believes in (whether a religion or a non-religious worldview), a lot of the confidence one has in one's beliefs is not purely due to abstract arguments, it is also due to other factors such as social reinforcement, pragmatic experience (do the beliefs produce positive results when you try to live by them?), etc. Purely focusing on abstract intellectual arguments may not resolve doubts to the same extent as also paying attention to those other factors.

> How is that a test? Again, a bit of semantics here, "test" I refer to as something being done by science--a scientific experiment/test.

Well, not all tests are "scientific"-not all tests form part of the natural sciences. If I want to test whether my wife is happy, I could ask her, observe her facial expressions, listen to her tone of voice, etc. That's a test, but I wouldn't claim it is a "scientific" one. Scientific tests are a subset of all tests, and involve various forms of methodological rigour which tests-in-general often lack. Psychologists have rigorous methodologies with which they attempt to measure human happiness, but I make no claim to be practising the science of psychology when I inquire after my wife's feelings. Similarly, not all "experiments" are "scientific experiments" – when cooking, one sometimes tries varying the recipe, and one might call such a variation an "experiment", but – unless you are doing food science – it lacks the rigour to be properly called "scientific".

You said that a difference between religion and science is that science is testable, religion is not. I don't see how restricting "testability" to "scientific testability" makes sense in the context of that claim. It turns the claim into "Scientific claims can be tested by science, but religious claims can't be tested by science". I wouldn't disagree, but if there are ways of testing things outside of science, religious claims may still be testable. If each discipline's claims can only be tested by its own respective methods – well, that seems a rather obvious statement: you could say the same thing about different natural sciences. The methodologies which palaeontologists use to test theories are rather different from those used by particle physicists.