Abstract

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.