Bayesian confirmation by uncertain evidence: epistemological and psychological issues

Inductive reasoning is of remarkable interest as it plays a crucial role in many human activities, including hypotheses evaluation in scientific inquiry, learning processes, prediction of future events, and diagnosis of a phenomenon (e.g., medical diagnosis). Despite the relevance of these cognitive processes in a variety of settings, there still remains much to understand about the basis of human inductive inferences. For example, it is not yet clear whether the same psychological mechanisms underlie both inductive reasoning and deductive reasoning or, on the contrary, whether induction and deduction correspond to distinct mental processes. The study of inductive reasoning has been a traditional topic in epistemology, and is more recently being explored in cognitive psychology as well. In the present contribution, I focus on both the epistemological and the psychological accounts. To begin with, I illustrate the state-of-art of research on inductive reasoning. On one hand, epistemologists have been working to develop normative theories in which the notion of inductive strength (or confirmation) is formalized. I discuss some of the alternative Bayesian measures of confirmation proposed in the literature on inductive logic. On the other hand, psychologists have been empirically investigating inductive reasoning, discovering important phenomena such as systematic effects of similarity, typicality, and diversity. I illustrate some of the most significant models of induction proposed in the psychological literature to account for such phenomena. Both lines of inquiry – epistemological and psychological – have focused on a restricted kind of induction problem: when assessing the inductive strength of arguments, premises are assumed to be true, that is, ascertained with the maximum degree of probability. However, inductive arguments occurring in real settings often depart from this pattern. Indeed, in a variety of situations, one may need to assess the impact of a piece of evidence whose probability may have significantly changed while not attaining certainty. Evidential uncertainty in inductive inferences is at the core of the present research. After exploring a selection of psychological phenomena concerning uncertainty, I address the epistemological problem of how to extend Bayesian confirmation theory to include cases where the evidence is not certain. A straightforward solution is proposed for a major class of confirmation measures called P-incremental. The solution proposed is based on Jeffrey conditionalization, an essential formal principle discussed below in greater detail. On the psychological account, I discuss two experimental studies conducted to test whether and how people’s judgments of inductive strength depend on the degree of evidential uncertainty. In the first study the uncertainty of evidence is explicitly manipulated by means of numerical values, whereas in the second study uncertainty is implicitly manipulated by means of ambiguous pictures. The results show that people’s judgments are highly correlated with those predicted by two normatively sound Bayesian measures of confirmation. This sensitivity to the degree of evidential uncertainty supports the centrality of inductive reasoning in cognition, and opens the path to further investigations on induction in real contexts.