Before discussing the details of a hemispheric transplant case, it is important to set the context by commenting on split brains in a single skull as in the case of commisurotomy to treat certain epilepsies.
Split brain cases have shaken our preconceptions about the unity of consciousness. The idealized Holo-Left and Holo-Right cases differ from actual split brain cases in two important respects. First, in actual cases the brain stem is not split, but is required to support the wake state. In actual cases, the two halves fall asleep at the same time and wake up at the same time. In addition, the two halves normally work together in an integrated way exactly as before the split except in experimental circumstances designed to take advantage of the separate cognitive processing caused by the commisurotomy. Not only passive cognitive processing is affected by the operation, but volitional states as well. A monkey has been observed in a tug of war with a peanut between the right and left hands, and in one patient, his left hand had a very disagreeable relationship with his wife. The left hand is associated with the right half of the brain which normally does not support speech.
We may be able to glimpse at what it is like to have a split brain by closing the right eye and then alternately closing the left, and reflecting that there are obviously two visual fields experienced. To do this without the corpus callosum, what would it be like? Parfit imagines the case where we can turn on and off our corpus callosum connection at will. He concludes that our identity is not tied to the unity afforded by the corpus callosum, otherwise when we turned off the connection, we would cease to exist as one, and a la Wiggins, split as an amoeba into two. Then, when we turned on the connection and integrated the results of the separate processing we would cease to be two, and become one again. Our numerical identity should not be linked to the temporary splitting and reintegration of some cognitive and volitional functions of our brain.
If we lost our left half, we would survive as our right. Likewise, if we lost our right half, we would survive as our left. These are not separate people. These are just parts of our self. If we lost our occipital lobe, we would survive without sight. If we lost our Broca's area and Wernicke's area, we would survive without speech. Even in dogs which have had their entire cortex removed, they survive with whatever functionality is left. As long as it has a wake cycle, then waking consciousness continues. In the case of split brains, the tendency we have to generalize and infer separate numerically identical consciounesses, instead of disconnected fragments of a single consciousness is partly due to the separate volitional states exhibited by the independent intentions of the two halves. Yet, if we reflect on our current integrated states, I believe we can discern separate left and right volitional acts acting in concert for some integrated task like typing. I wonder how well a split-brain patient could type.
Now, on to the transplant case. We will grant the idealized symmetry between the two halves at the cortical level for two reasons. First, there are cases of individuals with speech centers on both sides, and individuals relearning speech on the right after having lost the left side, so full symmetry is possible through careful conditioning to exploit the brain's plasticity. Second, the cognitive parity points out that assymetries are really incidental to the case. However, granting that we can split the brain stem to effect this idealized operation gives away too much if the numerical identity of the physical brain stem is the unity that matters in survival. In an amoeba splitting, there is a period where the nucleus has not yet replicated. We tend to identify the number of amoeba by counting the nuclei. As Parfit and Nagel have pointed out, in split-brain cases we cannot count the number of minds. There is no mental replication in the splitting cases. In addition, mental replication is exactly the process that the causal theorist is concerned is not survivable. As such, it is the topic of other cases.
I believe that the causal theorist can agree with Parfit about quasi- memories. So, by transplanting parts of another's brain into mine, I may acquire certain experiences, abilities, or knowledge that the other person had. I can augment my brain by grafting. How far can this process go? Can I attach a third hemisphere to my brain stem? With a third set of volitions, possibly integrated by an engineering bridge? Imagine a society where when a man and woman wed, they voluntarily have a hemispheric swap, where she gets one of his halves in exchange for hers. In this way, they would be more intimately connected, knowing more about each other, etc. The Holo-Left and Holo-Right example invites us to entertain these other possiblities as well.
Reasonably assuming that the brain stem is not split down the middle in this case, but is cloned, or that at worst half of it is cloned, and, for the sake of the case, that all the extraordinary science required is available, we see at once that there is a crucial element of physical replication that enables us to count another individual even before the transplant is completed and memories/functions grafted in. This case involves a physical completion of a genetically cloned copy using parts of the original. Half a brain split down the middle simply won't function, and the missing pieces, if replicated, are a second copy.
As for the reports of Holo-Left and Holo-Right, any psychological continuity is due to the physical grafting of quasi-memories and cannot identify the cloned status of the brain stem. As in the above case of the married couple, if the hemisphere is grafted in to a skull that already has the other half, the patient would probably regard itself psychologically with a different result.