I really hate to bury this in the religion thread, even though it seems relevant, so I'm giving it its own thread:
When I was a young child, I remember when I was first introduced to fractions in mathematics. I was told you could have numbers like one half, one quarter, and so on. You weren't only limited to one, two, three. With my head spinning, my immediate question was, "But, a half of what? You can't just have a half by itself, it has to be a half of something!" I guess I was born a nominalist.