There are many variations of the cloned consciousness problem, including the hypothetical scenario of translating our pattern of neural activity into computer code or recreating a dead person’s brain down to individual neurons.
One question which arises out of such hypotheticals is the question of whether a clone of your consciousness is actually you. In different words: if a digital or biological clone of you were to be created immediately before your death, would your stream of consciousness continue through the cloned version, which has your memories.
I’m not so sure about the digital clone, but at least with regards to the biological clone scenario the answer would probably be yes since an analogue of this already happens in real life with molecular-level recycling. Looking into the subject, there’s debate on how frequently cells in your body replace, but the general consensus is that most of the cells in your body are replaced every 7 years or so. Neurons don’t get replaced at the cellular level like other cells of the body do, but the individual lipids, proteins and other molecules making up these cells do undergo recycling. Thus even your brain is mostly made up of different atoms than it was 7 years ago.
Despite the fact that you are materially different from the you that existed 7 years ago, it nonetheless seems that both “yous” are part of the same stream of consciousness. Therefore it seems to be not the preservation of substance-identity which allows for continuity of consciousness, but rather the patterns of connectivity and neural transmission within the brain.
If a person is biologically cloned and then dies, therefore, the stream of consciousness should continue when the clone is awakened no? If the only difference between this hypothetical and the actual process of biomolecular replacement is that in the second case the change occurs “bit by bit”, do we have any good rational as to why this difference should matter as far as stream of consciousness is concerned?