Spielman and Lewis on Inductive Immodesty

Extract

An inductive method C_λ 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 C_λ′. Immodesty seems to be a condition of stable trust: if you trusted a modest C_λ, 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 C_λ 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 C_λ. Unfortunately, that one sometimes turns out to be C₀ (the straight rule); and since nobody in his right mind would trust C₀ we are then left with no acceptable C_λ. 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 C_λ is immodest on any evidence.