Final answer:
The brain-splitting case challenges previous accounts of personal identity. Parfit argues for a different account based on psychological continuity.
Step-by-step explanation:
The brain-splitting case, as discussed by Parfit, challenges previous accounts of personal identity and highlights their shortcomings. Parfit argues that this case demonstrates the problems with the notion of personal identity based on physical or psychological continuity.
In the brain-splitting case, imagine two hemispheres of a person's brain being transplanted into two different bodies. Each body now has one hemisphere of the person's brain. According to Parfit, this case shows that personal identity cannot be solely dependent on the physical body or memories, as both bodies can claim to be the person based on different criteria.
Parfit proposes a different account of personal identity called psychological continuity theory. This theory suggests that personal identity is not solely based on physical or psychological continuity, but rather on the continuity of a person's mental states, memories, and personality traits.