I think that, based on what I recall of Derek Parfit, there is a distinction that could be made between the continuity of consciousness and the connectivity. In the teletransporter problem, the continuity of your mind (or at least the body that constitutes your mind) is interrupted, and therefore your previous personal identity ends and a new one is created. However, the connectivity of your mind (relation R) is maintained, as your memory can still chart the path moment to moment as it went through the transporter.
This raises the question of which is more important, personal identity or relation R. Parfit argued that what really matters are your beliefs, memory, feelings, the things that make up your consciousness and not the body that “holds” it. Since these are maintained through relation R, you may not be “you” after going through the transporter, but everything important about you is still there.
I don’t have the time right at the moment to go through all of that, but a little ways in I saw the concept of mereology mentioned, so I thought I might expand on my view a bit by mentioning that I subscribe to an idea similar to what I’ve seen called “mereological nihilism” in that I think that, when you have a thing made up of other things, like a person or a ship or whatever else, that larger thing doesn’t truly exist as a distinct object with objective significance, merely as an illusion of our perception resulting from the way our brains and language work, and that properties ascribed to it are just emergent behavior of the parts said to make it up when arranged in that way.
As a result, in my view, the kind of personal identity you refer to simply doesn’t exist in the first place, so to speak of it’s continuity or lack thereof becomes meaningless, at which point the thing you call relation R is the only basis left to define a specific person by.
That also makes a specific person a somewhat “fuzzy” concept without clear objective borders around where you stop and end, and how much must be changed about a copy before it ceases to be you is in my view somewhat arbitrary, without a truly objective answer and more based on you eventually finding the changes too distinct to continue to refer to as the same person as what existed before.
What you are describing sounds a lot like a material constitution view of consciousness.
I think that, based on what I recall of Derek Parfit, there is a distinction that could be made between the continuity of consciousness and the connectivity. In the teletransporter problem, the continuity of your mind (or at least the body that constitutes your mind) is interrupted, and therefore your previous personal identity ends and a new one is created. However, the connectivity of your mind (relation R) is maintained, as your memory can still chart the path moment to moment as it went through the transporter.
This raises the question of which is more important, personal identity or relation R. Parfit argued that what really matters are your beliefs, memory, feelings, the things that make up your consciousness and not the body that “holds” it. Since these are maintained through relation R, you may not be “you” after going through the transporter, but everything important about you is still there.
I don’t have the time right at the moment to go through all of that, but a little ways in I saw the concept of mereology mentioned, so I thought I might expand on my view a bit by mentioning that I subscribe to an idea similar to what I’ve seen called “mereological nihilism” in that I think that, when you have a thing made up of other things, like a person or a ship or whatever else, that larger thing doesn’t truly exist as a distinct object with objective significance, merely as an illusion of our perception resulting from the way our brains and language work, and that properties ascribed to it are just emergent behavior of the parts said to make it up when arranged in that way.
As a result, in my view, the kind of personal identity you refer to simply doesn’t exist in the first place, so to speak of it’s continuity or lack thereof becomes meaningless, at which point the thing you call relation R is the only basis left to define a specific person by. That also makes a specific person a somewhat “fuzzy” concept without clear objective borders around where you stop and end, and how much must be changed about a copy before it ceases to be you is in my view somewhat arbitrary, without a truly objective answer and more based on you eventually finding the changes too distinct to continue to refer to as the same person as what existed before.