Money works because we all believe that paper or metal (or numbers in a computer system, to get even more abstract) has some value beyond simply what you could use to to make or burn or eat or whatever. We've been known to lose some faith in it in the past, too, which takes a while to work back up. Community support, community belief, you can call it what you like.
Government works because we're most of us willing to buy into (in the case of my country) various democratic ideals that most of us take on faith. Gov't would work whether or not I personally believe in it, true, but if no one believed it, do you think it'd work (obviously that's not going to happen, but that's not my point).
I'm willing to get onto an airplane because I believe that it will, in a vast majority of the time, remain in the air as long as it's supposed to. If I didn't believe that, you can bet I wouldn't get on a plane except in the direst need. Based on my past experience, planes stay up, and I'm willing to accept that this will continue to hold true in the future.
Science requires the belief that the universe is as it appears to be/can be measured, and not some sort of joke G-d's playing, or some hallucination on our part, or whatever. Have to start somewhere, after all, and that's where science starts.