Bradley develops some theory of the linear opinion pool, in apparent contradiction to results of Dawid et al.. We investigate the sources of these contradictions, and in particular identify a mathematical error in Bradley that invalidates his main result.

We consider the meaning of the assignment of probabilities to events implied by the kind of model regularly used by Statisticians. Traditional frequentist understandings are reviewed and rejected. It is argued that many statistical models may be justified purely on the basis of the symmetry properties enjoyed by the observables being modelled.