Self-indication assumption doomsday argument rebuttal

The argument is sometimes expressed in an alternative way by having the posterior marginal distribution of n based on N without explicitly invoking a non-zero chance of existing.

The name for this attack within the DA community is the "self-indication assumption" (SIA), proposed by one of its opponents, the DA-advocate Nick Bostrom.

His (2000) definition reads: A development of Dieks's original paper by Kopf, Krtous and Page (1994), showed that the SIA precisely cancels out the effect of the doomsday argument, and therefore, one's birth position (n) gives no information about the total number of humans that will exist (N).

The SIA-mathematics considers the chance of being the nth human as being conditioned on the joint probability of two separate events, both of which must be true: This means that the pdf for n, is concentrated at P(n = 0) = 1 - P(b), and that for P(n > 0) the marginal distribution can be calculated from the conditional: J. Richard Gott's DA could be formulated similarly up to this point, where it has P(b | N) = P(b) = 1, producing Gott's inference of n from N. However, Dennis Dieks argues that P(b) < 1, and that P(b | N) rises proportionally in N (which is a SIA).

This can be expressed mathematically: The SIA's effect was expressed by Page et al. as Assumption 2 for the prior probability distribution, P(N): They note that similar assumptions had been dismissed by Leslie on the grounds that: "it seems wrong to treat ourselves as if we were once immaterial souls harbouring hopes of becoming embodied, hopes that would have been greater, the greater the number of bodies to be created."

(1992) One argument given for P(b | N) rising in N that does not create Leslie's "immaterial souls" is the possibility of being born into any of a large number of universes within a multiverse.

Whatever the reasoning, the essential idea of the self-indication assumption is that the prior probability of birth into this universe is rising in N, and is generally considered to be proportional to N. (The following discussion assumes they are proportional so P(b | N) = 2 P(b | 2N), since other functions increasing in N produce similar results.)

Therefore: To clarify the exposition, Gott's vague prior N distribution is 'capped' at some "universal carrying capacity",

limit has no specified upper bounds (to habitable planets in the Galaxy, say) but makes N's posterior distribution more tractable: The

However, other proponents of indefinite survival of human (and posthuman) intelligence have postulated a finite endpoint, as the (extremely high) "Omega".

, was not a part of Dieks's argument, and critics of the SIA have argued that an infinite upper bound on N creates an Improper integral (or summation) in the bayesian inference on N, which is a challenge to the logic of the critique.

(For example Eastmond, and Bostrom, who argues that if the SIA cannot rule out an infinite number of potential humans, it is fatally flawed.)

) omits a significant hurdle to the credibility of the self-indication assumption doomsday argument rebuttal.

Many people, (such as Bostrom) believe the leading candidate for doomsday argument refutation is a self-indication assumption of some kind.

It is popular partly because it is a purely Bayesian argument which accepts some of the DA's premises (such as the Indifference and Copernican principles).

Other observations: Under the self-indication assumption the 'reference class' of which we are part includes a potentially vast number of the unborn (at least into this universe).

In order to overturn the conventional DA calculation so completely the reservoir of souls (potential births) in the reference class must be astoundingly large.

th) birth at around 5%; to shift this probability above 90% the SIA requires a potential number of humans (

However, the SIA differs from the normal DA in having the reference class include all septillion unborn potential-humans at this point in history, when only sixty billion have been born.

This puts the SIA at odds with philosophical approaches requiring strictly falsifiable constructs, such as logical positivism.

The following two examples of estimating the size of a darkened space show how the probability shift can occur: The Bayesian inference shifts from the cloak-room case to the lost-property case, because of the chance that the coat would not be found in the aisle it was found in, and some estimate of the aisle's dimensions.

In Dieks, they may never have been born and the end of the human race is independent of their birth order number.

One of the most prominent objections to SIA concerns Bostrom's "presumptuous philosopher" scenario.

In this example, the non-anthropic evidence has led scientists to place equal credence on two rival cosmological theories

Just as the scientists are preparing to run a cheap experiment that will definitively rule out one of the two theories, they are interrupted by a philosopher who believes SIA.

An open scientific question such as the size of the universe cannot be settled, he writes, "simply by leaning back in your armchair and registering the fact that you exist.

SIA says that the number of observers in our unique position at the center of the universe is the same on either theory, so no anthropic update is needed.