There's something closely related to this that I think should be pointed out...
Before the enlightenment, the common understanding was that things COULD be proven through logical argument alone. You can easily see this in methodology the Dialogues of Plato for example, where they would seek to prove things by starting with some "truths" and then logically deducing a long line of if/then's until they arrive at various conclusions. This was considered to have "proven" the conclusion. Both philosophy and religion used this methodology. It was during this pre-enlightenment period that folks like Thomas Aquinas presented their "proofs for god" and so on.
However, during the enlightenment they began to realize that this methodology was flawed. They finally figured out that logical rules allowed for an argument to be both logically valid and false at the same time! Basically, if an argument is illogical in structure it likely has a false conclusion, but if it is logical in structure, the conclusion could be true or false. In other words, there can be many possible stories that fit the facts and are logical but contradictory. This is why you'd have Socrates starting out with a sentence like "we all know birds can fly correct?" and have his audience at a point an hour, after a chain of conclusions, later saying "therefore the soul must be immortal!"
So the solution was to understand that logic is useful for ensuring your argument is on track, and it is great for handling and processing the data you have, but that data must come from somewhere - it must come from actual empirical observation. This was the birth of the scientific method (and all the wonders that came from it which we take for granted). Finally we got the process right and the result was all of the things mysticism had promised - flight, remote communication, future prediction, healing the sick, etc.
So the key here is that logic alone cannot prove things - you have to have empirical physical evidence in order to provide "proof" of anything. Sadly, many religions, mystics, new agers, and pseudoscience doesn't seem to have caught on to this realization and still believes that they can conduct meaningful exploration of the universe without a laboratory, using nothing more than logical argument without the physical evidence to back it up. I'm not trying to be critical here, just laying out the history of the philosophic developments as I understand them.
