Cosmic Confusions: Not Supporting versus Supporting Not

Abstract

Bayesian probabilistic explication of inductive inference conflates neutrality of supporting evidence for some hypothesis H (“not supporting H”) with disfavoring evidence (“supporting not-H”). This expressive inadequacy leads to spurious results that are artifacts of a poor choice of inductive logic. I illustrate how such artifacts have arisen in simple inductive inferences in cosmology. In the inductive disjunctive fallacy, neutral support for many possibilities is spuriously converted into strong support for their disjunction. The Bayesian “doomsday argument” is shown to rely entirely on a similar artifact.