It seems awfully convenient that your posited process of personal identity survives exactly those events, blinking ones eyes, epileptic fits, sleep, coma, which are not assumed to disrupt personal identity in everyday thought.
The philosophical habit of skeptically deconstructing basic appearances seems to prepare people badly for the task of scientifically understanding consciousness. When considering the relationship between mind and matter, it's a little peculiar to immediately jump to complicated possibilities ("whatever process creates my conscious feeling of self ... could be dissolved and created anew several times a second") or to the possibility that appearances are radically misleading (consciousness might be constantly "going away or coming into being" without any impact on the apparent continuity of experience or of personal existence). Just because there might be an elephant around the next corner doesn't mean we should attach much significance to the possibility.
I'm not entirely sure how the process of discovery you describe would happen... The situation is of course likely to be different once we have a better understanding of exactly how the brain works, but lacking that understanding, I'm having some trouble envisioning exactly how the destruction of personal identity could be determined to be intractably tied to the observed entity X.
It is unlikely that society would develop the capacity for mind uploading and cryonic resurrection without also coming to understand, very thoroughly, how the brain works. We may think we can imagine these procedures being performed locally in the brain, with the global result being achieved by brute force, without a systemic understanding. But to upload or reanimate you do have to know how to put the pieces back together, and the ability to perform local reassembly of parts correctly, in a physical or computational sense, also implies some ability to perform local reassembly conceptually.
In fact it would be reasonable to argue that without a systemic understanding, attempts at uploading and cryonic restoration would be a game of trial and error, producing biased copies which deviate from their originals in unpredictable ways. Suppose you use high-resolution fMRI time series to develop state-machine simulations of microscopic volumes in the brain of your subject (each such "voxel" consisting of a few hundred neighboring neurons). You will be developing a causal model of the parts of the subject's brain by analysing the time series. It's easy to imagine the analysis assuming that interactions only occur between neighboring voxels, or even next-nearest neighbors, and thereby overlooking long-range interactions due to long axonal fibers. The resulting upload will have lost some of the causal structure of its prototype.
The possibility of elementary errors like this, to say nothing of whatever more subtle mistakes may occur, implies that we can't really trust procedures like this without simultaneously developing that "better understanding of exactly how the brain works".
I can't think of any phenomenon in classical mechanics where I could point to any property of the system that would be disrupted if the system got disassembled and reassembled mid-evolution.
How about the property of being an asymptotically bound system, in the absence of active disassembly by external forces? To me that still seems way too weak to be the ontological basis of physical identity, but that is (more or less) the philosopher Mario Bunge's definition of systemhood. (Btw, Bunge was a physicist before he was a philosopher.)
The philosophical habit of skeptically deconstructing basic appearances seems to prepare people badly for the task of scientifically understanding consciousness. When considering the relationship between mind and matter, it's a little peculiar to immediately jump to complicated possibilities
It wasn't philosophers who came up with general relativity and quantum mechanics when everyday intuition about nature didn't quite add up in some obscure corner cases. Coming up with a simple model that seems to resolve contradictions even if it doesn't quite fit eve...
Within the immortalist community, cryonics is the most pessimistic possible position. Consider the following superoptimistic alternative scenarios:
Cryonics -- perfusion and vitrification at LN2 temperatures under the best conditions possible -- is by far less optimistic than any of these. Of all the possible scenarios where you end up immortal, cryonics is the least optimistic. Cryonics can work even if there is no singularity or reversal tech for thousands of years into the future. It can work under the conditions of the slowest technological growth imaginable. All it assumes is that the organization (or its descendants) can survive long enough, technology doesn't go backwards (on average), and that cryopreservation of a technically sufficient nature can predate reanimation tech.
It doesn't even require the assumption that today's best possible vitrifications are good enough. See, it's entirely plausible that it's 100 years from now when they start being good enough, and 500 years later when they figure out how to reverse them. Perhaps today's population is doomed because of this. We don't know. But the fact that we don't know what exact point is good enough is sufficient to make this a worthwhile endeavor at as early of a point as possible. It doesn't require optimism -- it simply requires deliberate, rational action. The fact is that we are late for the party. In retrospect, we should have started preserving brains hundreds of years ago. Benjamin Franklin should have gone ahead and had himself immersed in alcohol.
There's a difference between having a fear and being immobilized by it. If you have a fear that cryonics won't work -- good for you! That's a perfectly rational fear. But if that fear immobilizes you and discourages you from taking action, you've lost the game. Worse than lost, you never played.
This is something of a response to Charles Platt's recent article on Cryoptimism: Part 1 Part 2