TLDR: Science is inconsistent, and so is faith. "Gut-level judgements" are all we have, both in science and in faith. Can people please stop ignorantly claiming otherwise ?

The laws of mathematics actually prohibit anything other than a "gut-level" judgement. Let's take one problem (but go ahead and take 5 books about "constructivism" out of the library and you'll get to 50 problems soon). Godel's theorem, because it's the most generic, but there's plenty of them. Assuming you believe in any science that uses natural numbers, rational ones, or real ones (ie. all of them), then there's 2 possibilities :

- you're not convinced that there are no contradictions. In this case, what do you have that faith doesn't ?

- you're convinced that there are no contradictions. In this case you can be sure : you're wrong. Either because you don't realize there are contradictions, or because you've got a wrong theory.

So how exactly is science better than faith ? It's not.

Here's how this argument evolved :

1) Faith does not follow reason ! It kind of does, or rather we can't find good examples of obvious inconsistencies. (the bible was written by people who had studied under Greek philosophers, so it really is quite consistent. It's not perfect, but compared to say, the quran or the vedas, it's bloody hard to find conclusive contradictions. Whereas the quran simply says that it has inconsistencies and you shouldn't care about that, for example, and points out a specific inconsistency in itself. But this was not a real argument at the time)

2) oh-oh the vatican claims they do follow reason. They have some good arguments on that too. But they don't follow reason entirely !

3) oops ... science doesn't actually follow reason either. We don't actually have proofs of consistency, and worse : we don't even construct most arguments. Let's fix that.

4) (~100 years later) we give up. This is not possible. Let's be brutally dishonest and at least look for a proof that we could write a constructivist science and do that. (this is brutally dishonest because it would be a non-constructivist proof that constructivism could work without actually making it work)

5) (~10 years later) okay, that can't be done either. We can't have a science without pulling new concepts out of thin air without any real reason to assume they work other than that we haven't found any mistakes !

6) (~20 years later) This idiot "Godel" comes on stage and claims if you have a proof that a scientific theory is consistent you can rewrite that into a proof that that theory is wrong ! Prepostrous ! Let's pelt him with tomatoes !

7) (1 day later) "Say guys ... I've been looking through that proof of Mr. Godel and I can't seem to find a mistake" ... followed by 1 month of doing nothing but looking for errors in that proof.

8) (1 month later) Success ! Godel made a mistake.

9) (2 days later) Godel writes an article fixing the mistake

10) (~2-20 years later, depending on who you ask) Okay, we give up. Science is not consistent and can never be consistent. "We cannot pull ourselves out of the mud".

Given this history, can we please drop the argument that science is consistent and faith is not ? (Christian faith, because it is the only one that claims and tries to be consistent, not saying you couldn't create others, but no-one did)

Science is inconsistent, and so is faith. Can people stop claiming otherwise ?