Full Idea
If the two halves of my brain are transplanted into different bodies just like mine, they cannot both be me, since that would make them the same person. ..But my relation to these two contains everything that matters, so identity is not what matters.
Gist of Idea
If my brain-halves are transplanted into two bodies, I have continuity, and don't need identity
Source
Derek Parfit (The Unimportance of Identity [1995], p.314)
Book Reference
'Personal Identity', ed/tr. Martin,R /Barresi,J [Blackwells 2003], p.314
A Reaction
I challenge his concept of what 'matters'. He has a rather solipsistic view of the problem, and I take Parfit to be a rather unsociable person, since his friends and partner will be keenly interested in the identities of the new beings.