In this paper, I examine the possibility of accounting for the rationality of belief-formation by utilising decision-theoretic considerations. I consider the utilities to be used by such an approach, propose to employ verisimilitude as a measure of cognitive utility, and suggest a natural way of generalising any measure of verisimilitude defined on propositions to partial belief-systems, a generalisation which may enable us to incorporate Popper's insightful notion of verisimilitude within a Bayesian framework. I examine a dilemma generated by the decision-theoretic (...) procedure and consider an adequacy condition (immodesty) designed to ameliorate one of its horns. Finally, I argue in a sceptical vein that no adequate verisimilitude measure can be used decision-theoretically. (shrink)

An inductive method Cλ in the λ-system of Carnap [1] is immodest, on evidence e, iff its estimate, on e, of its own accuracy is higher than its estimate, on e, of the accuracy of any rival method Cλ′. Immodesty seems to be a condition of stable trust: if you trusted a modest Cλ, you should start by trusting its advice to replace it by a rival that it estimates to be more accurate. One might guess that any Cλ would (...) be immodest on any evidence. But in [2] I proved that, under a certain accuracy measure taken from Carnap [1], §§ 20–21, there would be exactly one immodest Cλ. Unfortunately, that one sometimes turns out to be C0 ; and since nobody in his right mind would trust C0 we are then left with no acceptable Cλ. Stephen Spielman [3] has proposed a remedy: an estimate of accuracy, on evidence e, should disregard accuracy under circumstances that are ruled out by e. Spielman proves that if this change is made, any Cλ is immodest on any evidence. (shrink)