You don't want to check your phone. You feel it buzz. You won't check it. You can feel the pull. You're not going to give in. You're using willpower. The phone wins three minutes later, or it doesn't. Either way, what just happened was a fight between two parts of you.
K's analysis of willpower: it's the fragment, divided. One part wants to check. Another part has decided not to. The "will" is one part forcing the other. The fight is between two equally manufactured pieces of self. The "good" self triumphs over the "bad" self, or vice versa. Either way, the division has been deepened. The self is more fragmented, not less.
This is why willpower is unstable. The fight requires energy. The energy comes from a finite supply. When the supply runs out, the suppressed side wins. People interpret this as moral failure. K interpreted it as structural failure. You can't suppress a fragment with another fragment indefinitely. The suppression IS the fragmentation, dressed up as virtue.
Willpower has a clench. The jaw, the shoulders, the breath. The body holds itself together against itself. When willpower works, there's a small surge of pride. The "good" self won. When it fails, there's shame. The "bad" self won. The surge and the shame are the same currency. Both reward the division.
K's alternative wasn't to give in. It was to see the fragmentation itself. The phone-wanting and the phone-resisting are both small pieces of the same self defending its different positions. See that and the fight loses some of its grip. Not all. Some. The grip was the fragments believing in themselves.