Degree-of-Belief and Degree-of-Support: Why Bayesians Need Both Notions

J. Hawthorne
2005 Mind  
I argue that Bayesians need two distinct notions of probability. We need the usual degree-of-belief notion that is central to the Bayesian account of rational decision. But Bayesians also need a separate notion of probability that represents the degree to which evidence supports hypotheses. Although degree-of-belief is well suited to the theory of rational decision, Bayesians have tried to apply it to the realm of hypothesis confirmation as well. This double duty leads to the problem of old
more » ... ence, a problem that, we will see, is much more extensive than usually recognized. I will argue that degree-of-support is distinct from degree-of-belief, that it is not just a kind of counterfactual degree-of-belief, and that it supplements degree-of-belief in a way that resolves the problems of old evidence and provides a richer account of the logic of scientific inference and belief. 1 The idea that Bayesian epistemology should draw on two distinct probability functions is not new. Carnap (1971) suggested a two-function Bayesian model. He calls the degree-of-belief notion 'rational credence' and calls the degree-of-support notion 'credibility'. He takes initial credence functions to derive from credibility functions, which should themselves be logical probability functions. Brian Skyrms largely adopts this Carnapian idea in the third edition of Choice and Chance (1986, Ch. 1, Ch. 6, Sects. 7 and 8), but does not identify his version of credibility functions with Carnapian logical
doi:10.1093/mind/fzi277 fatcat:jkynpf663nhnjkzjathbr7ozu4