On the elusive formalisation of the risky condition for hypothesis testing

Abstract

In this paper, we examine possible formalisations of the riskiness condition for hypothesis testing. First, we informally introduce derivability and riskiness as testing conditions together with the corresponding arguments for refutation and confirmation. Then, we distinguish two different senses of confirmation and focus our discussion on one of them with the aid of a historical example. In the remaining sections, we offer a brief overview of the main references to the risky condition in the literature and scrutinise different options for formally capturing riskiness; we show why none of them works. We conclude with some remarks about the relation between derivability and riskiness and claim that riskiness essentially involves a contextual, pragmatic component that eludes a complete formal reconstruction.