Tacking by conjunction, genuine confirmation and convergence to certainty

Abstract

Tacking by conjunction is a well-known problem for Bayesian confirmation theory. In the first section, disadvantages of existing Bayesian solution proposals to this problem are pointed out and an alternative solution proposal is presented: that of genuine confirmation (GC). In the second section, the notion of GC is briefly recapitulated and three versions of GC are distinguished: full (qualitative) GC, partial (qualitative) GC and quantitative GC. In the third section, the application of partial GC to pure post-facto speculations is explained. In the fourth section it is demonstrated that full GC is a necessary condition for Bayesian convergence to certainty based on the accumulation of conditionally independent pieces of evidence. It is found that whenever a hypothesis is equivalent to a disjunction of more fine-grained hypotheses conveying different probabilities to the evidence, then conditional independence of the evidence fails. This failure occurs typically for unspecific negations of hypotheses. A refined version of the convergence to certainty theorem that overcomes this difficulty is developed in the final section.