Parfit thinks that the whole philosophical discussion about personal identity has been confused because people are using a technical term, identity, to talk about something other than strict numerical identity.
Parfit’s negative thesis is that the reason why personal identity is so important to people is because we want to survive, not because we want to remain identical to ourselves. We call this a negative thesis because he is making a claim against traditional philosophy. Parfit’s positive thesis is that our interest in personal identity comes from our interest in survival. We call this a positive thesis because it’s the claim that he thinks is correct.
Survival is a lot like identity but not as strict. It involves that there is some connection between an original person and his or her successor.
Parfit on Identity vs. Survival. Both identity and survival are states of continuity. Identity requires a one-to-one correspondence. Both fission and fusion are ruled out by identity because both fission and fusion violate the transitivity of identity. Survival does not require a one-to-one correspondence. Survival allows for both fusion and fission. Identity is an all-or nothing deal. Things are either identical or not identical. Survival can vary in degrees. Also, the two views differ on the “Only X and Y Principle”
Only X and Y Principle: If we want to determine if X is identical to Y, we must only consider the relation between X and Y. Identity must reject this principle in order to reject fission cases. Once we reject the principle, then we can say that X and Y can only be identical if they are the same to one another and there is no other candidate for identity. Survival does not reject the “Only X and Y Principle”. Indeed, it willingly accepts the notion that X and Y may also be the same as Z. This is because survival can happen in many different people.