Wittgenstein's Arm

Wittgenstein tried to get to the bottom of the range and nature of human agency—our willpower, our ability freely to choose and will—by asking: ‘what is left over if I subtract the fact that my arm goes up from the fact that I raise my arm?’ Of course, this is a recedingly meta question. ‘What is left over if I subtract the thought of the fact that my arm goes up from the thought of the fact that I raise my arm?’ Or, indeed: ‘what is left over if I subtract the concept of subtraction from the thought-experiment I am conducting about balancing the fact that my arm goes up and the fact that I raise my arm?’