"[...] There are things I know I learned from studying philosophy. The most dramatic I learned immediately, in the first semester of freshman year, in a class taught by Sydney Shoemaker. I learned that I don't exist. I am (and you are) a collection of cells that lurches around driven by various forces, and calls itself I. But there's no central, indivisible thing that your identity goes with. You could conceivably lose half your brain and live. Which means your brain could conceivably be split into two halves and each transplanted into different bodies. Imagine waking up after such an operation. You have to imagine being two people.
The real lesson here is that the concepts we use in everyday life are fuzzy, and break down if pushed too hard. Even a concept as dear to us as I. It took me a while to grasp this, but when I did it was fairly sudden, like someone in the nineteenth century grasping evolution and realizing the story of creation they'd been told as a child was all wrong.  Outside of math there's a limit to how far you can push words; in fact, it would not be a bad definition of math to call it the study of terms that have precise meanings. Everyday words are inherently imprecise. They work well enough in everyday life that you don't notice. Words seem to work, just as Newtonian physics seems to. But you can always make them break if you push them far enough.
I would say that this has been, unfortunately for philosophy, the central fact of philosophy. Most philosophical debates are not merely afflicted by but driven by confusions over words. Do we have free will? Depends what you mean by "free." Do abstract ideas exist? Depends what you mean by "exist." Paul Graham