Any given system can either be useful or limitless... it can't be both.
Godel's incompleteness theorem shows us that a system cannot prove its own validity unless that system is incoherent. In an incoherent system, you can prove everything, including the coherency of the system itself. However, an incomplete system cannot prove its coherency. Coherent systems can surmise things about reality. If I place 1 thing in a box, and then 2 additional things in the box... I now have 3 things in the box. In reality this works.
Now if I assign 1 to equal 2, I can now show that adding 1 thing in a box and 2 additional things I now have 2 things in the box. We know that 2 is 1, so I have 1 thing in the box. -- In the end... you can prove everything including that I am the pope (not just the pope of Discordianism).
The pope and I are two.
2 = 1.
The pope and I are one.
I am the pope.
In a system which allows for a contradiction, every statement is true (even false ones). This is why we disallow contradictions within mathematics and logical systems, not for some arcane reasons like being wrong or some elegant proof. Rather, without disallowing contradictions we end up with a worthless system in which everything can be proven true. And, in fact, by Godel's proof we can show that an "elegant proof" of this fact is impossible. In a very real sense, we need to take this on faith.
You need limits to be useful. If science could prove everything it would be worthless, it needs to be limited to only proving true things. Falsifiability is a method of differentiating science from pseudoscience. If you can't prove something wrong then it isn't science. It is an immortal idea, a limitless idea, then it is a useless idea.
So do we accept the coherency on faith? And if so, by what criteria do I condemn the faith of others?
-- Faith, in the religious sense, can prove everything. Religious faith is thusly worthless and fundamentally incoherent. There is a world of difference between accepting something as true in order to produce a useful system and accepting something as true and producing a limitless system. These are not Non-Overlapping MAgesteria. Everything science or any coherent systems can be established as true can be established by faith as well. In this regard the overlapping section (as far as science goes is 100%): every statement of science could be a statement of religion because religion produces a limitless system and science produces a useful one. If God tells me the universe is 14 billion years old... so be it.
How are coherent systems such as science limited? - They are limited by their ability to declare true that which is false. They are limited in proving things which can be proven with their correlation to reality.
What's left? Faith can prove everything science can prove. Science cannot prove everything faith can prove. What are these additional things which faith can prove but science cannot? -- False things.
Those things left over in the realm of faith, which science cannot establish ( and tend to discredit at every junction) are probably left over because they are false. It is far from proven, but it seems that Dan Barker was right when he wrote, "Faith is a cop-out. If the only way you can accept an assertion is by faith, then you are conceding that it cant be taken on its own merits." -- At the very least, one should ask why such notions can be established by those systems which can establish false things and cannot be established by those systems which cannot establish false things.
We limit science and coherent systems by assuming true things cannot be false. This places a massive limit those systems. However, the resulting system, which no longer being limitless cannot prove its own validity, is amazingly useful. This assumption produces a system capable of proving useful things about reality.
Next time you hear that, "With faith, all things are possible." Realize, that being true, this statement establishes that faith is worthless, useless, and does not correlate with reality.
With science, the possible is possible... and nothing else.