Bottom up thinkers try to start from experience and move from experience to understanding. They don't start with certain general principles they think beforehand are likely to be true; they just hope to find out what reality is like.
I'm a very passionate believer in the unity of knowledge. There is one world of reality - one world of our experience that we're seeking to describe.
If the experience of science teaches anything, it's that the world is very strange and surprising. The many revolutions in science have certainly shown that.