It's a neat view: the world-in-itself is an undifferentiated "will" that we individuate through categories such as space, time, and causation which (following Kant) Schopenhauer thought that we bring to our experience of the world. These differentiated parts of the world-as-experienced include different people with conflicting desires and interests (i.e., conflicting bits of will). The metaphysical realization that in the realm beyond appearances there is only an undifferentiated will motivates the fundamental Schopenhauerian ethical attitude of compassion: to take on another's perspective as one's own is appropriate since the world beyond appearances is inter-subjectively undifferentiated. I don't believe in a transcendental world beyond experience that has the properties Schopenhauer claimed for it. I believe in a real world that is (at least partly) mind-independent, but I don't think there are good reasons to hold that it is undifferentiated and will-full in Schopenhauer's sense. So, although...

My pet rock, Rocky exists--he's on the desk in front of me. But this doesn't entail that Rocky thinks. In fact, I'm pretty sure he doesn't. That's why I like him so much. But if Rocky were to think something, then he would surely think. "I am" is something that a thinker could think. So is "I think". So, someone (not Rocky, alas) could think either of these, and on the basis of doing so conclude that she thinks. But of course her thinking wouldn't follow from her existence any more than it does in Rocky's case. Her thinking would follow from her thinking one of those thoughts. So, what does "I am, therefore I think" mean? It's false if means: I exist, and because of this I think. It's true if it means (roughly): I think that I exist, and because of this I think. (Or: I'm a speaker/thinker (as we can see from my currently asserting that I exist), and because of this I think.) On the second interpretation, the statement is "truer" than what Descartes said, if what he said is...