Blurring Out Cosmic Puzzles

TL;DR

This paper proposes using imprecise probabilities within Bayesian reasoning to better handle ignorance and resolve paradoxes like the Doomsday argument and anthropic reasoning.

Contribution

It introduces an imprecise probabilistic framework that effectively addresses epistemic puzzles challenging traditional Bayesian approaches.

Findings

Imprecise probabilities better represent ignorance in Bayesian reasoning.

The framework dissolves paradoxes like the Doomsday argument.

Provides a more adequate Bayesian approach to probabilistic puzzles.

Abstract

The Doomsday argument and anthropic reasoning are two puzzling examples of probabilistic confirmation. In both cases, a lack of knowledge apparently yields surprising conclusions. Since they are formulated within a Bayesian framework, they constitute a challenge to Bayesianism. Several attempts, some successful, have been made to avoid these conclusions, but some versions of these arguments cannot be dissolved within the framework of orthodox Bayesianism. I show that adopting an imprecise framework of probabilistic reasoning allows for a more adequate representation of ignorance in Bayesian reasoning and explains away these puzzles.