And just like that we prove the soul. Well, not really I'm afraid; you can't prove anything (although Descartes thought this was the only thing you could prove). There are several answers, replies, and rebuttals to this simple little thought experiment, and many people will simply laugh at the fact that philosophers think about these things at all. Yet books are still being written about it by intelligent people from various disciplines, both academic and popular. And I believe these little puzzles suggest at something. I call these sorts of things hints--it's a hint that reality is more than meets the eye.
Picturing a blue box in your head, of course, is just a subset of the larger human ability to think, to be self-aware, meta-conscious. To have the very peculiar ability to think about the very thing that is doing the thinking--our brain, which just doesn't seem right damn it. Even if you don't believe in mind, it's bizarre. Thus the history. For Rene Descartes (pronounced "Day-Cart"), the existence of the mind (not the brain or body) was the only thing we know for sure exits. He famously said "I think: therefore I am." He could doubt that his body and brain existed--perhaps they were illusions, like a dream--but he could never doubt that a thinking being existed (i.e. himself), even if he was plugged into the Matrix this was a self-evident truth that his entire philosophy rested on. The philosopher of science Dan Dennet would say "mind" is nothing more than a word we use that means "brain." Mind is reduced to brain. A thought literally is a group of neurons in the brain, nothing more ("I am having a neuron X34 right now"). The philosopher John Searle gets a little more complex. He says we will always have to describe the mind and its contents in a fundamentally different way than the brain and neurons. Therefore, they sort of have a special ontological status and always will. But he doesn't want to be a "dualist" which to me sounds like he wants to have his cake and eat it too. Most religious philosophers are perfectly fine with saying we have a brain that causes events in the mind, and that they are different things and one doesn't decay and this is all okay because a transcendent God exists so I'm pretty much open to that kind of stuff. :)
I prefer to think of the everything--brain, trees, body, galaxies--as a manifestation of Mind, instead of Mind as a manifestation of matter (which I admit makes a lot of sense, after all mind took millions of years to evolve in the first place...I'm using Mind in a special metaphysical way so fuck off this works). In the tradition of Berkeley, Kant, Emerson, Philosophical Idealism is the belief that Matter is on some metaphysical level an expression of Mind, as a painting. My entire life is a manifestation of my own mind. If you were to look in my brain, you would find a manifestation of the choices of my ancestors, then my parents, then myself, and the Author of Nature in the first place. And this is a beautiful way to live my life.