The epistemological aspect of these criteria, viz. how could we know whether or not a particular case was continuous over time in any of these ways, led to a sort of empiricism, viz. if we cannot tell any differences then they must be the same. Against this tendency came a metaphysical backlash, viz. the question is not whether person A is the same as person B on some set of criteria after a particular case, rather what matters in A actually surviving as B is that he wakes up with the proper causal connections.
Since the advent of split-brain patients, and their unusual cognitive deficits, a growing speculation about the mechanism of surviving death in a future technology has given the philosophical debate a twist with a decidedly practical flavor, viz. cryonics, nano-technology, anaerobic replacement, social and political consequences of cloning, etc.
Understandably, the metaphysical question of 'After I go through the procedure, will I wake up or someone else?' became more pressing than the epistemological one of 'After I go through the procedure, will anyone reasonably believe on the evidence that I exist?'
The proposed transmigration methods are survival by replacement, and survival by copying. In addition, there is the view that speculating about these methods at this point in time risks mistaking what we are by what we appear to be.
Our normal metabolic activity leads us to believe that we can survive by replacing parts in our brain with new parts. Searle has raised the possibility that our subjectivity may fade away during the procedure. However, this presupposes that subjectivity is not all or nothing. Is survival an all or nothing affair, or a matter of degree, as Parfit has claimed? The nice feature of in-place replacement is that no blueprint is needed. The copy method requires creation of a blueprint or diagram. To do that is go from fact to fiction, from instantiation to plan, from physical space to logical space. We cannot numerically transmigrate through logical space, even if we can qualitatively transmigrate in that fashion.
To avoid mistaking what we are by what we appear to be requires neuroscience. I believe the wake state of the brain has our subjective character and is what matters in survival. This wake state may be a cortical or cortico-reticular electrical network phenomenon, and may be an attractor on the network. It may be that in the absence of memory, the network can still support the wake state, in which case, the philosophical emphasis on memory in the personal identity debate is beside the point. Parfit has claimed that having someone else's memories will not change your subjective character. In any event, physical understanding of the brain is vital to resolving the philosophical question of what constitutes survival.