I agree with Robin Hanson that if two instances of me exist, and one is terminated, I didn’t die, I simply got smaller.
I am not to sure about this idea. To the best of my knowledge I am a biological being existing a universe obeying some sort of physics related to quantum mechanics and general relativity. If there are multiple instances of me then it is probably due to reality being some kind of multiverse. Lets keep things simple and assume that it is a Tegmark Level I Multiverse. This implies that there are an infinite number of copies of me.
Next what are these copies likely to be like? One arguement is that they could be Boltzman brains. This requires there to be enough of a statistical fluctuation in the randomness of the universe to arrange all of the atoms into a brain that remembers reading this article and experiences being in the process of typing a reply. Highly unlikely. Much more likely is that a set of atoms or stuff in general in the far distance past were in such a configuration that it evolved into a configuration including me. I expect this to me more likely because the level of organisation required at that time was much less than the level required now. Now if all of these parts of the universe that contain me evolved from parts of the universe that had similar initial conditions then all of them require for example my mother and father to be in them, both to get my DNA right, and also to create the meories that I have of them. Similarly all the other people that I have met need to be in all of those locations so that I would have memories of them. Thus all of those infinite copies of me would live in a world just like my own.
Now, given all this, for me to be terminated means to die. Whatever it is that kills this instance of me probably exists in the environment of each of those infinite copies of me. Thus I would expect that the fate of all of those instances of me to be highly correlated. If this correlation is high enough (say unity) then being terminated means that my measure is reduced all the way to zero, which is a bit more then just getting smaller.
I am not to sure about this idea. To the best of my knowledge I am a biological being existing a universe obeying some sort of physics related to quantum mechanics and general relativity. If there are multiple instances of me then it is probably due to reality being some kind of multiverse. Lets keep things simple and assume that it is a Tegmark Level I Multiverse. This implies that there are an infinite number of copies of me.
Next what are these copies likely to be like? One arguement is that they could be Boltzman brains. This requires there to be enough of a statistical fluctuation in the randomness of the universe to arrange all of the atoms into a brain that remembers reading this article and experiences being in the process of typing a reply. Highly unlikely. Much more likely is that a set of atoms or stuff in general in the far distance past were in such a configuration that it evolved into a configuration including me. I expect this to me more likely because the level of organisation required at that time was much less than the level required now. Now if all of these parts of the universe that contain me evolved from parts of the universe that had similar initial conditions then all of them require for example my mother and father to be in them, both to get my DNA right, and also to create the meories that I have of them. Similarly all the other people that I have met need to be in all of those locations so that I would have memories of them. Thus all of those infinite copies of me would live in a world just like my own.
Now, given all this, for me to be terminated means to die. Whatever it is that kills this instance of me probably exists in the environment of each of those infinite copies of me. Thus I would expect that the fate of all of those instances of me to be highly correlated. If this correlation is high enough (say unity) then being terminated means that my measure is reduced all the way to zero, which is a bit more then just getting smaller.