Personal identity

What is personal identity? In the article “Brain Transplants and Personal Identity: A Dialogue” Derek Parfit and Godfrey Vesey try to solve the problem of personal identity. Vesey presents the split-brain transplant to question what personal identity is and who would survive in this situation. Parfit then gives a few cases like one where his brain would be split in half and another where he is duplicated.
The article begins with describing a situation in which Mr. Brown and Mr. Robinson had a brain extraction, the brain of Mr. brown was put into Mr. Robinson’s head and Mr. brown got Mr. Robinson’s brain. The one with Mr. Robinson’s body and Mr. Brown’s brain is the only one who survives. After he becomes conscious he states that the body he is in is not his and he believes he is Mr. Brown. He then remembers Mr. Brown’s life and has the same characteristics Brown had.
Parfit uses the split-brain transplant example to imagine his brain was split in half and each half is given to two different people. The two people who receive half of the brain would remember the whole of Parfit’s life and they will also display the same traits and characteristics as him. A question that comes from this would be “what happens to him?” Parfit develops three possibilities but they all have objections so he believes there isn’t an answer.
The first possibility he proposes is that he would be both of the people with the half’s of his brain. Parfit argues that this answer