Abstract

If A confirms H and B confirms H, it seems reasonable to infer that A&B confirms H. However, this inference is not valid; it is only a heuristic. I show that the level of confirmation A and B each give to H by itself implies nothing about the level of confirmation that A&B gives to H. Any combination of values is possible for P(H), P(H|A), P(H|B) and P(H|AB) is possible. Still, I show the heuristic leads from true premises to true conclusions whenever A and B are statistically independent or correlated,which includes most situations where we evaluate evidence. There is risk, though, when one does not consider how A and B interact; one can miss anti-correlations that lead the heuristic to fail. The problem is exacerbated when groups of people are motivated to support a favored hypothesis. Each person finds evidence that confirms the hypothesis and contributes that evidence to the group’s discourse (e.g. through a climate change denial website). The temptation to focus solely on the number of individual pieces of evidence can lead people to ignore whether the evidence fits together. In combination with cognitive biases, this can lead to serious errors.