@JoeMorgue
Actually, I think you're overcomplicating things. Faith doesn't mean magical internal evidence, it literally means "belief that is not based on proof." Cf:
https://www.dictionary.com/browse/faith
So yeah, when someone says they have faith, they just told you up front that it's without evidence.
That said, and to also continue addressing David's point in the process, even if they do believe in some internal woowoo support for their faith, as long as it's at the level of "I believe X", the problem there is that it's an intensional context. Any time you add "X believes", "X thinks", "it is generally thought", etc, it automatically becomes intensional.
For those who don't know wth I'm talking about, an extensional context is one where extension works. E.g.,
P1: Clark Kent is Superman.
P2: Clark Kent works as a reporter.
therefore
C: Superman works as a reporter.
An intensional context is simply anything that isn't extensional, by relying on what someone thinks, believes, knows, etc, and which is really only about their own mental state rather than a general fact about the world. E.g.
P1: Lois Lane knows who Clark Kent is.
P2: Clark Kent is Superman.
therefore
C: Lois Lane knows who Superman is.
That doesn't work because P2 is not something that Lois knows.
This also doesn't work in the other direction, namely from intensional to extensional. The
masked man fallacy for example is also known as the intensional fallacy, because that's really what it is. It's trying to mix intensional and extensional, to basically break out from the intensional context into the wide extensional world.
And that's the problem with supporting anything with "truths of the heart or faith." Those "truths" are in an intensional context. You cannot argue from there into the extensional context of the outside world. Hell, you can't even mix them with someone else's intensional context.
Which is why such internal "truths of heart or faith" are dead ends. As long as they aren't already shared across context borders, you can't break them out of their intensional prison.