I have read about the argument that the Self-Indication Assumption (SIA) cancels the Doomsday Argument (DA), and I think that the argument fails to take into account the fact that it is not more likely that an observer of a particular birth rank will have existed given the general hypothesis that there will have been many observers in her reference class than given the general hypothesis that there will have been few observers in her reference class, as long as there will have been at least as many as would be necessary for anyone with her birth rank to exist at all.
Please ignore the following if it has been stated elsewhere.
The form of the argument that I am criticizing assumes both the Self Sampling Assumption (SSA) and the SIA. The SIA asserts that you would be more likely to ever exist given the general hypothesis that many observers will have existed. I could be wrong, but I think the argument is that each observer that will have existed can naively be thought of as a “slot,” and that the more “slots,” the more likely your “card” is to be dealt. For the argument to work, I think your “card” must include not only your (non rank dependent) physical properties (your position in time-space, physical composition, etc.), but also necessarily your birth rank. What this means is that, in order for the argument to work, we must ignore the fact that the proposition, “someone of birth rank R will have existed” is in fact not more likely to be true given the general hypothesis that there will have been X*Y observers than given the general hypothesis that there will have been only X observers (R, X and Y are positive integers and R is less than both X and Y). (I am ignoring the “no outsider” issue, and assuming that there are no outsiders, in order to focus on the issue of birth rank.)
We can separate birth rank from other properties and apply both the SSA and the SIA, and see that the DA still applies. Suppose there are n possible (non rank dependent) types of observers, and m types of observers that will actually have existed. The probability that your (non rank dependent, n.r.d.) type of observer will have existed is m/n, and the probability that your (n.r.d.) type of observer will have existed, given that the hypothesis “i (n.r.d.) types of observers will have existed” is true is i/n. We are leaving the SIA intact except for the fact that we are separating rank out from it, and the SIA seems to implicitly rely on a the principle of indifference—indifference as to the probability of any particular (n.r.d.) type of observer existing, or existing in any particular quantity. We can apply the SSA to say that, although your (n.r.d.) type of observer is a priori more likely to exist given the hypothesis that there will have been X observers than given the hypothesis that there will have been X*Y observers, the probability that an observer randomly selected from the set of all observers is equal on both hypotheses.
We can say that there are c possible birth ranks and z birth ranks that will have existed. Here we can use a fact about birth ranks that is not taken into account in the naive application of the SIA: The probability that a birth rank will have existed is 1 given that it is less than or equal to z, and zero otherwise. So the SIA doesn’t apply to rank.
Finally, we can apply the SSA to rank and all of the normal implications of the DA apply. First, a (n.r.d.) type of observer was randomly selected from the set of observers that will have existed. Then a birth rank was randomly selected from the birth ranks that will have existed among those with the selected (n.r.d.) type. Since the SIA implicitly relies on the principle of indifference, selecting a (n.r.d.) type of observer first is equally likely to make it more/less likely that we would select some particular rank instead of another. And if there are some rank dependent properties other than birth rank, it is assumed that the number of permutations of those possible rank dependent properties are equally distributed among the ranks that will have existed.
I have read about the argument that the Self-Indication Assumption (SIA) cancels the Doomsday Argument (DA), and I think that the argument fails to take into account the fact that it is not more likely that an observer of a particular birth rank will have existed given the general hypothesis that there will have been many observers in her reference class than given the general hypothesis that there will have been few observers in her reference class, as long as there will have been at least as many as would be necessary for anyone with her birth rank to exist at all.
Please ignore the following if it has been stated elsewhere.
The form of the argument that I am criticizing assumes both the Self Sampling Assumption (SSA) and the SIA. The SIA asserts that you would be more likely to ever exist given the general hypothesis that many observers will have existed. I could be wrong, but I think the argument is that each observer that will have existed can naively be thought of as a “slot,” and that the more “slots,” the more likely your “card” is to be dealt. For the argument to work, I think your “card” must include not only your (non rank dependent) physical properties (your position in time-space, physical composition, etc.), but also necessarily your birth rank. What this means is that, in order for the argument to work, we must ignore the fact that the proposition, “someone of birth rank R will have existed” is in fact not more likely to be true given the general hypothesis that there will have been X*Y observers than given the general hypothesis that there will have been only X observers (R, X and Y are positive integers and R is less than both X and Y). (I am ignoring the “no outsider” issue, and assuming that there are no outsiders, in order to focus on the issue of birth rank.)
We can separate birth rank from other properties and apply both the SSA and the SIA, and see that the DA still applies. Suppose there are n possible (non rank dependent) types of observers, and m types of observers that will actually have existed. The probability that your (non rank dependent, n.r.d.) type of observer will have existed is m/n, and the probability that your (n.r.d.) type of observer will have existed, given that the hypothesis “i (n.r.d.) types of observers will have existed” is true is i/n. We are leaving the SIA intact except for the fact that we are separating rank out from it, and the SIA seems to implicitly rely on a the principle of indifference—indifference as to the probability of any particular (n.r.d.) type of observer existing, or existing in any particular quantity. We can apply the SSA to say that, although your (n.r.d.) type of observer is a priori more likely to exist given the hypothesis that there will have been X observers than given the hypothesis that there will have been X*Y observers, the probability that an observer randomly selected from the set of all observers is equal on both hypotheses.
We can say that there are c possible birth ranks and z birth ranks that will have existed. Here we can use a fact about birth ranks that is not taken into account in the naive application of the SIA: The probability that a birth rank will have existed is 1 given that it is less than or equal to z, and zero otherwise. So the SIA doesn’t apply to rank.
Finally, we can apply the SSA to rank and all of the normal implications of the DA apply. First, a (n.r.d.) type of observer was randomly selected from the set of observers that will have existed. Then a birth rank was randomly selected from the birth ranks that will have existed among those with the selected (n.r.d.) type. Since the SIA implicitly relies on the principle of indifference, selecting a (n.r.d.) type of observer first is equally likely to make it more/less likely that we would select some particular rank instead of another. And if there are some rank dependent properties other than birth rank, it is assumed that the number of permutations of those possible rank dependent properties are equally distributed among the ranks that will have existed.