http://arxiv.org/abs/2106.07738
Typicality arguments attempt to use the Copernican Principle to draw conclusions about the cosmos and presently unknown conscious beings within it. The most notorious is the Doomsday Argument, which purports to constrain humanity’s future from its current lifespan alone. These arguments rest on a likelihood calculation that penalizes models in proportion to the number of distinguishable observers. I argue that such reasoning leads to solipsism, the belief that one is the only being in the world, and is therefore unacceptable. Using variants of the “Sleeping Beauty” thought experiment as a guide, I present a framework for evaluating observations in a large cosmos: Fine Graining with Auxiliary Indexicals (FGAI). FGAI requires the construction of specific models of physical outcomes and observations. Valid typicality arguments then emerge from the combinatorial properties of third-person physical microhypotheses. Indexical (observer-relative) facts do not directly constrain physical theories. Instead they serve to weight different provisional evaluations of credence. These weights define a probabilistic reference class of locations. As indexical knowledge changes, the weights shift. I show that the self-applied Doomsday Argument fails in FGAI, even though it can work for an external observer. I also discuss how FGAI could handle observations in large universes with Boltzmann brains.
B. Lacki
Wed, 16 Jun 21
45/57
Comments: 34 pages, 12 figures, 2 tables of examples, submitted