An excellent paper on why split-brain cases don't show to separate streams of consciousness. http://www.philosophy.ox.ac.uk/__data/assets/pdf_file/0003/2757/split-brain_web.pdf. I talked about split brain patient cases before presenting reasons why it doesn't show two separate streams of consciousness well there is more reasons as well.
Split–brain cases do not show the results we would expect if two fully independent, separate streams of consciousness were being generated by callosotomy; subjects can for instance continue to operate both halves of their bodies in unity and perform sometimes highly complex tasks. The evidence, therefore is more compatible with phenomenal unity without joint access (thus, the side of the brain responsible for speech cannot access the contents of that which is seen by the right side of the brain, even though both are contained within a single stream of subjective consciousness). This conclusion is also more parsimonious; and since the two–separate–streams hypothesis is (unlike dualism) an empirical one (instead of metaphysical), considerations of parsimony apply. Therefore, split–brain cases pose no serious difficulty to phenomenal unity, and thus in turn pose no serious difficulty towards dualism.
See also several other papers from Tim Bayne, including an important one with David Chalmers titled ‘What is the Unity of Consciousness?’ as well as from Torin Alter.
Incidentally, subjects born without a corpus callosum altogether, as well as those with agenesis of the corpus callosum, do not experience even the relatively mild symptoms which callosotomy patients do.
What we have here is one subject with a fragmented brain, not the sudden appearance of two ‘persons’ in one skull as some argue. Peter Ellis’ paper, ‘The Decider System Model: A Defense of the Cartesian Theatre’ is also of important relevance both to those interested in criticism of Dennett’s theories as well as the import of callosotomy experiments to philosophy of mind.