Actually, that's a modern idea of "faith." The word translated as "faith" from the original Greek is pistis which is a noun form of "believe" pisteuo. But it doesn't translate completely as belief because some think that it implies an action of sorts. It has the idea of trust and confidence. So the idea is that there is reason for that trust. Evidence, experience, what have you. It was later translated to the Latin fidis and ultimately became "faith." But faith as it is used in modern vernacular isn't what the average person in the first century would necessarily attribute to pristis.
Today we say things like "your faith" or "blind faith." But we all have faith when we put trust into someone. A good illustration might be a soldier's trust and confidence in a leader. That trust or faithfulness isn't what we would refer to as "faith in that which cannot be seen or proven" though it could be in the sense that the blanket term could encompass that notion.
Well put!
An example of faith from the older meaning, which I got from a Greek Orthodox priest, is a wailing child: picked up by a stranger, he continues to wail; picked up by a nurse, he continues to wail -- but picked up by his mother, he at once relaxes and begins to smile. What happened? He knew his mother, and had faith, i.e. trusted her.
I've seen that in my dog; when a puppy, he would sometimes get frightened, and no one could calm him -- but all I had to do was speak his name, and he would settle down.
From my skydiving days, here's another illustration: blind faith would be picking up a parachute without asking who packed it or if the job was done well, just trusting that since it was a the drop zone it was fine; the Greek word from the first century, though, is far closer to the jumper who asks, "Who packed this?", and when the packer identifies himself, asks, "Is it done right?" -- and the packer replies, "I'd jump it." That faith isn't blind, because it depends on two things: confidence that the packer knows his stuff, and confidence that the packer would commit himself to his work.
(Just in passing, I gave that response more than once, since I got good at packing chutes and it paid for jumps; once, the chute got tossed at me and the gal grabbed another -- she said "Show me"... and then she jumped at the same moment I did and watched my chute deploy. After that, if anyone asked if I'd packed a chute right, if she was there, she answered for me, "He'll jump it". And others had faith in her word.)