What about the theorems of logic? They aren't falsifiable, but neither are they fundamentally alogical. What does it mean to say that one has faith in the theorems of logic?
(oi, this is The Goof, btw--I'm in disguise)
(Ok I wrote this, and realized it was one massive tangent that didn't address your question at all. But I'm going to post it anyway. That's just how I am.)
This is an extremely interesting question in my perspective.
A lot of people don't realize how arbitrarily systems of logic can be defined. Technically, you just make up rules when you move P's and Q's around and put => in between them. But what's weird is that only a few seem to be meaningful. What makes them meaningful? That's a slippery question.
But it remains that if you come up with something like 4 = 5, you can prove anything. And I do mean
anything.
E.g: 4 = 5.
Taking 3 from both sides gives 1 = 2.
CC and I are two.
However, 2 = 1. CC and I are one person.
Hence I am CC!
Another: Dinosaurs exist.
I define 1 "nemo" of time to be 80 million years.
4 = 5 => 0 = 1.
The present is 0 nemos away in time. Thus, it is 1 nemo away. Dinosaurs existed 80 million years ago. Hence, dinosaurs exist now.
Just a side note, but it's fun to see what batshit insane stuff you can prove with 4 = 5! It's interesting to think about how much logical consistency is inherent in human cognition -- e.g. syntactic rules of language seem to be largely universal. I wonder if that's indicative of some innate "logical system" that is some kind of prerequisite to the mind, and how much of it would be responsible for what we're capable of precieving, and if the "logical system" was different how it'd effect our perception of the world. Or if the universe just possesses the logic itself.
Also weirder -- truth values are typically thought of as either given a 0 (false) or 1 (true) status. However, you can come up with systems of logic where there's
more than just 0 and 1 truth values -- as in 0, 1, 2, 3, 4, ... , n.
What's fascinating to me is that some of these 0, 1, 2 logic-systems also work. They're used in quantum mechanics quite a bit, the rules of which were established empirically.
There were two articles, "Is logic empirical" by Hilary Putnam and another (same title) by M. Dummett. I suggest you look them up if you have any interest in this.
But the question remains: why does logic work so well? In some ways, I think it is a bit "empirical", and we just choose the systems of logic that don't insult our conception of reality with "4 = 5" scenarios, and the ones that don't are the ones we are used to. Maybe these are hard-wired into our brains and are part of the reason language works etc. I dunno.
Getting way the f*** off track so I'll stop.
Note: stop medicating yourself with nyquil and bourbon.