It may also be hard to say we have "higher brain function" than other mammals or other animals... Other animals exhibit social rituals, utilize tools, have song, communicate, and learn! It is almost impossible for us to gauge their smarts!
As a scientist, I think evolution as a game of chance... we just happened to develop physically in a way that promoted the development of higher thought AND the physical means to act upon thoughts (larger brain case, bipedalism, opposing thumbs, etc.) This fed upon itself... we learn, build, learn from that, build, etc.
(yeah, I have done some reading on biological anthropology