Cushman, Matthew
(2019)
Anthropic Indexical Sampling and Implications for The Doomsday Argument.
[Preprint]
Abstract
Anthropic reasoning refers to a class of arguments that incorporate the information entailed by our own existence to make inferences about the world in which we live. One prominent example is the Doomsday Argument, which makes predictions about the future total population of human observers yet to be born based on the ordinal rank of our birth among humans that have been born so far. A central question in anthropic reasoning is from which distribution should we consider ourselves to be randomly sampled. The Self Sampling Assumption (SSA) states that we should reason as if we're a random sample from the set of actual existent observers, while the self indication assumption (SIA) states that we should reason as if we're a random sample from among the set of all possible observers (Bostrom 2002). Effectively, SIA weighs the probability of our actual world by the number of observers relative to SSA. The distinction is important, as SSA supports the Doomsday Argument, while SIA refutes it. We consider a new thought experiment called {\em Geometric Incubator} and show that SSA implies precognition of coin flips in this hypothetical world. We consider this to be very strong evidence in favor of SIA over SSA and against the Doomsday Argument. We use this observation to develop a more axiomatic mathematical theory of anthropic reasoning. We also introduce an empirical version of the Doomsday Argument.
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