Abstract

It can be demonstrated in a very straightforward way that confirmation and evidence as spelled out by us can vary from one case to the next, that is, a hypothesis may be weakly confirmed and yet the evidence for it can be strong, and conversely, the evidence may be weak and the confirmation strong. At first glance, this seems puzzling; the puzzlement disappears once it is understood that confirmation is of single hypotheses, in which there is an initial degree of belief which is adjusted up or down as data accumulate, whereas evidence always has to do with a comparison of one hypothesis against another with respect to the data and is belief-independent. Confusing them is, we suggest, a plausible source of the so-called “base-rate fallacy” identified by Kahneman and Tversky which leads most of us to make mistaken statistical inferences. It is also in the background, or so we argue in some detail, of the important policy controversies concerning human-induced global warming.