Where does A come from? Well it can come from other logical conclusions, but ultimately one must have a starting place before logic is applied. One must believe in A without having concluded it logically.
I wonder if our senses aren't the start of every logical conclusion we come to. I wonder how much faith goes into our senses. Most humans are born with the same senses, excluding the deaf, the blind, the colorblind, etc. It is what has been given to us to observe and perceive our universe. I could argue that little faith goes into trusting our senses, because we have logical reasons to do so.
One reason is that consistently, people perceive stimuli almost exactly the same way. The world over, people agree that the sky is blue, the grass is green, a ball is round, etc. We have evidence to support our senses being accurate: consistency from person to person. Another reason is that few things are perceived by one sense at a time; in that way, each sense sort of verifies what the others are perceiving. If we are perhaps deaf, other senses may point to the same perception; for example, when a deaf person sees a person wince at a person drawing their nails down a chalkboard, they can deduce from that that an unpleasant sound is being produced.
Sure, you could argue that basically everything could be a figment of our imaginations; we could be imagining everyone in the world and what they perceive; we could be imagining everything we perceive. We could. I almost hesitate to call it faith, because I have logical reason to believe that everything is not just a big cataclysmic explosion of my imagination (though that would be a huge ego boost). I DO have logical reasons to support my faith in my five senses. I just don't feel like pondering what all of those reasons are at the moment. I'm pretty sure my trust in my five senses, and my belief that everything isn't just a product of my imagination, isn't based entirely, if at all, on faith.
Shit, I'm confusing myself. I suppose my point is: just because something can't be proven undividedly doesn't mean one didn't arrive at that conclusion using logic.
I'm also trying to figure out what my logical reasons are for believing in logic. One, it's done right by me so far, by allowing me to predict the most probable outcome of things and generally be correct, according to my five senses. What are my reasons for believing that everything isn't a big product of my imagination? Well, I really doubt my imagination could be this consistent for this long, considering dreams I've had where I could fly and all. Still, I suppose it comes down to this: going back to Nemo's 4=5 post, anything can be logically true depending on your perceptions.
I can't prove nothing is a figment of my imagination, but I can logically deduce that my perceptions are reliable and consistent with others' perceptions. I can't prove that 2 absolutely equals two, but I can logically support that theory. Night's kind of faith still doesn't exist, in my perception, because every conclusion I arrive at is arrived at logically.
I think there's a common misconception (but not necessarily overwhelmingly common) that feelers use less logic than thinkers. Based on my definition of logic, this is pretty much impossible. What I think is true is that feelers more naturally consider the impact of their actions on other people. In contrast, thinkers are more concerned with efficiency and results. Neither definition correlates with logic or lack thereof.